LAPLACE'S EQUATION FROM TWO PERSPECTIVES MICHAEL FOSCO
May, J. Peter
LAPLACE'S EQUATION FROM TWO PERSPECTIVES MICHAEL FOSCO Abstract. We study Laplace's equation from the perspectives of partial differential equations and probabil- ity theory. We formulate the problem using both. Laplace's Equation In Probability 10 Acknowledgments 14 References 14 1. Introduction A natural way
Um, E.S.
2013-01-01
mod- eling of the acoustic wave equation: Geophysics, 39,solution analysis of acoustic wave equation in the Laplace-solutions to the acoustic wave equation in the Laplace-
Laplace Operators on Fractals and Related Functional Equations
Gregory Derfel; Peter Grabner; Fritz Vogl
2012-06-06
We give an overview over the application of functional equations, namely the classical Poincar\\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\\'nski gasket.
Multipole matrix elements of Green function of Laplace equation
Karol Makuch; Przemys?aw Górka
2015-01-02
Multipole matrix elements of Green function of Laplace equation are calculated. The multipole matrix elements of Green function in electrostatics describe potential on a sphere which is produced by a charge distributed on the surface of a different (possibly overlapping) sphere of the same radius. The matrix elements are defined by double convolution of two spherical harmonics with the Green function of Laplace equation. The method we use relies on the fact that in the Fourier space the double convolution has simple form. Therefore we calculate the multipole matrix from its Fourier transform. An important part of our considerations is simplification of the three dimensional Fourier transformation of general multipole matrix by its rotational symmetry to the one-dimensional Hankel transformation.
Shao, Yan-Lin Faltinsen, Odd M.
2014-10-01
We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.
Um, E.S.
2013-01-01
mod- eling of the acoustic wave equation: Geophysics, 39,and C. Shin, 2011, 3D acoustic wave form inversion in thesolution analysis of acoustic wave equation in the Laplace-
Solving nth order fuzzy differential equation by fuzzy Laplace transform
Latif Ahmad; Muhammad Farooq; Saleem Abdullah
2014-03-02
In this paper, we generalize the fuzzy Laplace transformation (FLT) for the nth derivative of a fuzzy-valued function named as nth derivative theorem and under the strongly generalized differentiability concept, we use it in an analytical solution method for the solution of an nth order fuzzy initial value problem (FIVP). This is a simple approach toward the solution of nth order fuzzy initial value problem (FIVP) by the nth generalized (FLT) form, and then we can use it to solve any order of FIVP. The related theorems and properties are proved. The method is illustrated with the help of some examples. We use MATLAB to evaluate the inverse Laplace transform.
Tug-of-war and infinity Laplace equation with vanishing Neumann boundary condition
Antunovi?, Ton?i; Sheffield, Scott; Somersille, Stephanie
2011-01-01
We study a version of the stochastic "tug-of-war" game, played on graphs and smooth domains, with the empty set of terminal states. We prove that, when the running payoff function is shifted by an appropriate constant, the values of the game after n steps converge in the continuous case and the case of finite graphs with loops. Using this we prove the existence of solutions to the infinity Laplace equation with vanishing Neumann boundary condition.
Kim, Yong Jung
Features and numerical Tools Laplace Biharmonic Helmholtz Maxwell Solving Fredholm second kind and numerical Tools Laplace Biharmonic Helmholtz Maxwell Outline Recursively Compressed Inverse Preconditioning. There are, of course, other methods. #12;Features and numerical Tools Laplace Biharmonic Helmholtz Maxwell
Application of the Laplace transformation to the solution of the wave equation
Booton, Richard Crittenden
1948-01-01
be denoted by f(s). Whenever a different letter is used for the transform, the symbol used is defined where it is introduced. Most of the theorems and equations are numbered, the numbe'rs being assigned consecutively. The first part of the number...-transformation" by Gustav Doetsch (l) and "Theory of Four1er Integrals" by E. C. Titchmarsh (l). The latter contains a thorough d1s- cuss1on of the Fourier transformation& with which the Laplace transformation 1s 1ntimately connected. This f1rst part introduces those...
Mark Chanachowicz; Claudia M. Chanu; Raymond G. McLenaghan
2007-11-13
An invariant characterization of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space is given in terms of invariants and covariants of a real binary quartic canonically associated to the characteristic conformal Killing tensor which defines the webs.
Mead, Jodi L.
MATH 333 Laplace Transform Lab 9 May 7, 2008 In this lab we will compute the Laplace transform symbolically and the inverse Laplace transform both symbolically and numerically. Symbolic representation The command syms assigns a variable to be symbolic, laplace(f) finds the Laplace transform of a function f
Grabner, Peter J.
. It turns out that heat and wave transfer in disordered media (such as polymers, fractured and porous rocks: Math. Theor. 45 (2012) 463001 (34pp) doi:10.1088/1751-8113/45/46/463001 TOPICAL REVIEW Laplace, amorphous semiconductors, etc) can be adequately modelled by means of fractals and random walks on them
Localization of Fourier-Laplace Series of Distributions
Anvarjon Ahmedov; Ahmad Fadly Nurullah; Abdumalik Rakhimov
2015-10-25
This work was intended as an attempt to extend the results on localization of Fourier-Laplace series to the spectral expansions of distributions on the unit sphere. It is shown that the spectral expansions of the distribution on the unit sphere can be represented in terms of decompostions of Laplace-Beltrami operator. It was of interest to establish sufficient conditions for localization of the spectral expansions of distribution to clarify the latter some relevant counter examples are indicated.
Laplace-Runge-Lenz vector for arbitrary spin
Nikitin, A. G.
2013-12-15
A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary spin. The presented systems describe neutral particles with non-trivial multipole momenta. Their spectra can be found algebraically like in the case of hydrogen atom. Solutions for the systems with spins 1/2 and 1 are presented explicitly, solutions for spin 3/2 can be expressed via solutions of an ordinary differential equation of first order. A more extended version of this paper including detailed calculations is published as an e-print arXiv:1308.4279.
Technical Note Variational free energy and the Laplace approximation
Daunizeau, Jean
Technical Note Variational free energy and the Laplace approximation Karl Friston,a, Jérémie October 2006 This note derives the variational free energy under the Laplace approximation, with a focus. This is relevant when using the free energy as an approximation to the log-evidence in Bayesian model averaging
Technical Note Variational free energy and the Laplace approximation
Penny, Will
Technical Note Variational free energy and the Laplace approximation Karl Friston,a, Jérémie the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy
A. V. Pavlov-Maxorin
2014-10-19
In article a new class of the odd ore even transforms of Laplace is presented. The class leads to some unforeseeable consequences in direction of the Fourier transforms.The potential of Newton as one of the form of the double Laplace transform is considered too.
Dirk Veestraeten
2015-05-21
The Laplace transforms of the transition probability density and distribution functions for the Ornstein-Uhlenbeck process contain the product of two parabolic cylinder functions, namely D_{v}(x)D_{v}(y) and D_{v}(x)D_{v-1}(y), respectively. The inverse transforms of these products have as yet not been documented. However, the transition density and distribution functions can be obtained by alternatively applying Doob's transform to the Kolmogorov equation and casting the problem in terms of Brownian motion. Linking the resulting transition density and distribution functions to their Laplace transforms then specifies the inverse transforms to the aforementioned products of parabolic cylinder functions. These two results, the recurrence relation of the parabolic cylinder function and the properties of the Laplace transform then enable the calculation of inverse transforms also for countless other combinations in the orders of the parabolic cylinder functions such as D_{v}(x)D_{v-2}(y), D_{v+1}(x)D_{v-1}(y) and D_{v}(x)D_{v-3}(y).
Walton, Andrew G
Aero III/IV Laplace Transforms Handout 1 A. G. Walton The Laplace transform 8Er of a function s _? _r? 8Er ' E?ud|?sE|o #12;Aero III/IV Laplace Transforms Handout 2 A. G. Walton Table of elementary
Exact Vacuum Solutions to the Einstein Equation
Ying-Qiu Gu
2007-06-17
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution.
Laplace Transforms An integral transform is an operator
Ikenaga, Bruce
9281998 Laplace Transforms An integral transform is an operator F (s) = Z b a K(s; t)f(t) dt: The input to the transform is the function f(t); the output is the function F (s). (By convention, small letters denote the inputs to a transform, and the corresponding capital letters denote the corresponding
A 3D Volumetric Laplace-Beltrami Operator based Cortical Thickness Estimation Method
Wang, Yalin
A 3D Volumetric Laplace-Beltrami Operator based Cortical Thickness Estimation Method Gang Wanga the cortical tetrahedral mesh, we adopt the heat kernel [1] based on volumetric Laplace-Beltrami operator can construct the discrete volumetric Laplace-Beltrami operator under the Dirichlet boundary condition
Control System Design Using Finite Laplace Transform Theory
Das, Subhendu
2011-01-01
The Laplace transform theory violates a very fundamental requirement of all engineering systems. We show that this theory assumes that all signals must exist over infinite time interval. Since in engineering this infinite time assumption is not meaningful and feasible, this paper presents a design for linear control systems using the well known theory of Finite Laplace transform (FLT). The major contributions of this paper can be listed as: (a) A design principle for linear control systems using FLT, (b) A numerical inversion method for the FLT with examples, (c) A proof that the FLT does not satisfy the convolution theorem as normally required in engineering design and analysis, and (d) An observation that the FLT is conceptually similar to the analog equivalent of the Finite Impulse Response (FIR) digital filter.
Building accurate initial models using gain functions for waveform inversion in the Laplace domain
Wansoo Ha; Changsoo Shin
2014-08-20
We suggest an initial model building technique using time gain functions in the Laplace domain. Applying the gain expressed as a power of time is equivalent to taking the partial derivative of the Laplace-domain wavefield with respect to a damping constant. We construct an objective function, which minimizes the logarithmic differences between the gained field data and the partial derivative of the modeled data with respect to the damping constant. We calculate the modeled wavefield, the partial derivative wavefield, and the gradient direction in the Laplace domain using the analytic Green's function starting from a constant velocity model. This is an efficient method to generate an accurate initial model for a following Laplace-domain inversion. Numerical examples using two marine field datasets confirm that a starting model updated once from a scratch using the gradient direction calculated with the proposed method can be successfully used for a subsequent Laplace-domain inversion.
Elementary Differential Equations with Boundary Value Problems
William F. Trench
2014-02-24
Dec 1, 2013 ... For more information, please contact jcostanz@trinity.edu. ..... (Laplace's Equation), the functions defining the boundary conditions on a given side of the rectangular .... change in heat of the object as its temperature changes from T0 to T is a(T ...... Let y be the angle measured from the rest position (vertically ...
Broader source: Directives, Delegations, and Requirements [Office of Management (MA)]
2006-04-06
REPLACED BY DOE-STD-1063 | SUPERSEDING DOE-STD-1063-2000 (MARCH 2000) The purpose of the DOE Facility Representative Program is to ensure that competent DOE staff personnel are assigned to oversee the day-to-day contractor operations at DOE’s hazardous nuclear and non-nuclear facilities.
Quantum systems related to root systems and radial parts of Laplace operators
M. A. Olshanetsky; A. M. Perelomov
2002-03-18
The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.
Anzor Khelashvili; Teimuraz Nadareishvili
2015-02-13
Singular behavior of the Laplace operator in spherical coordinates is investigated. It is shown that in course of transition to the reduced radial wave function in the Schrodinger equation there appears additional term consisting the Dirac delta function, which was unnoted during the full history of physics and mathematics. The possibility of avoiding this contribution from the reduced radial equation is discussed. It is demonstrated that for this aim the necessary and sufficient condition is requirement the fast enough falling of the wave function at the origin. The result does not depend on character of potential:is it regular or singular. The various manifestations and consequences of this observation are considered as well. The cornerstone in our approach is the natural requirement that the solution of the radial equation at the same time must obey to the full equation.
Khelashvili, Anzor
2015-01-01
Singular behavior of the Laplace operator in spherical coordinates is investigated. It is shown that in course of transition to the reduced radial wave function in the Schrodinger equation there appears additional term consisting the Dirac delta function, which was unnoted during the full history of physics and mathematics. The possibility of avoiding this contribution from the reduced radial equation is discussed. It is demonstrated that for this aim the necessary and sufficient condition is requirement the fast enough falling of the wave function at the origin. The result does not depend on character of potential:is it regular or singular. The various manifestations and consequences of this observation are considered as well. The cornerstone in our approach is the natural requirement that the solution of the radial equation at the same time must obey to the full equation.
Vertex Singularities Associated with Conical Points for the 3D Laplace Equation
Yosibash, Zohar
in electromagnetic fields and magnetic recording, as well as in heat transfer problems, which may be described will be compared to demonstrate their conver- gence rate and accuracy. In section III, we formulate the weak
Solution of the space-time reactor kinetics equations using the method of Laplace transforms
Rottler, Jerry Stephen
1982-01-01
Reactors CHAPTER V. CONCLUSIONS REFERENCES APPENDIX A. EVALUATED DATA FOR THE THERMAL AND FAST SUBCRITICAL AND SUPERCRITICAL REACTORS AT SELECTED TIMES VITA 1V V1 V11 12 26 47 61 73 77 82 88 LIST OF TABLES PAGE I DATA FOR THE THERMAL... AND FAST REACTOR TEST PROBLEMS. II VALUES FOR THE CROSS SECTIONS AND k ~~ IN THE CRITICAL, SUBCRITICAL, AND SUP ERCRITICAL THERMAL REACTOR. II I VALUES FOR THE CROSS SECTIONS AND k IN THE CRITICAL, SUBCRITICAL, AND SUPERCRITICAL FAST REACTOR . IV...
A Bme Solution Of The Stochastic Three-Dimensional Laplace Equation...
using measurements in a set of vertical drill holes. These measurements showed that hot fluids rising from the deep enter the reservoir in a restricted area of the field and flow...
A Bme Solution Of The Stochastic Three-Dimensional Laplace Equation
AFDC Printable Version Share this resource Send a link to EERE: Alternative Fuels Data Center Home Page to someone by E-mail Share EERE: Alternative Fuels Data Center Home Page on Facebook Tweet about EERE: Alternative Fuels Data Center Home Page on Twitter Bookmark EERE: Alternative Fuels Data Center Home Page on Google Bookmark EERE: Alternative Fuels Data Center Home Page on QA:QA J-E-1 SECTION J APPENDIX E LIST OFAMERICA'SHeavyAgencyTendo NewYanbu, SaudideveloperftftKU Renewables
Rabindra Nath Das
2007-01-16
The linear non homogeneous singular integral equation (LNSIE)derived from the nonlinear non homogeneous integral eauation (NNIE)of Chandrsasekhar's H- functions is considered here to develop a new form of H - functions.The Plemelj's formulae are applied to that equation to determine a new linear non homogeneous integral equation(LNIE)for H- functions in complex plane . The analytic properties of this new linear integral equation are assessed and compared with known linear integral equations satisfied by H- functions. The Cauchy integral formulae in complex plane are used to obtain this form of H- functions not dependent on H- function in the integral . This new form of H-function is represented as a simple integral in terms of known functions both for conservative and non conservative cases. This is identical with the form of H- functions derived by this author by application of Wiener HOpf technique. The equivalence of application of the theory of linear singular integral equation in Riemann Hilbert Problem and of the technique of Wiener- Hopf in linear integral in representing the H- functions is therefore eatablished .This new form may be used for solving the problems of radiative transfer in anisotropic and non coherent scattering by the method of Laplace Transform and Wiener -Hopf technique.
A Brief Comment on Post inversion formula for the Laplace transform
Jose Javier Garcia MOreta
2007-03-06
In this paper we comment the Post inversion formula for Laplace transform, and its possible application to the branch of Analytic Number theory (Arithmetical functions, RH and PNT), involving a condition in the form of iterated limit to calculate the Riemann Hypothesis.
ENGI 2422 Laplace Transforms Page 5-01 5.01 Transforms
George, Glyn
ENGI 2422 Laplace Transforms Page 5-01 5.01 Transforms In some situations, a difficult problem can be transformed into an easier problem, whose solution can be transformed back into the solution of the original problem. For example, an integrating factor can sometimes be found to transform a non-exact first order
Chapter 3 Representing Geography 32 Representing
Wright, Dawn Jeannine
Chapter 3 Representing Geography 32 Representing Geography OVERVIEW This chapter introduces;Chapter 3 Representing Geography 33 KEY WORDS AND CONCEPTS Digital, binary, representation, Tobler`s First Law of Geography, attributes, the fundamental problem (the world is infinitely complex), discrete
Temme, N.M.
1987-11-01
The analytical approach of Temme (1983 and 1985), based on uniform asymptotic expansions, is extended to an additional class of incomplete Laplace integrals. The terminology is introduced; the construction of the formal series is explained; representations for the remainders are derived; the asymptotic nature of the expansions is explored; and error bounds are determined. Numerical results are presented for the case of the incomplete beta function. 14 references.
Jeanjean, Louis
"Infinite energy solutions" Fractal Laplace operator Nonlocal problem & well-posedness Renormalized #12;"Infinite energy solutions" Fractal Laplace operator Nonlocal problem & well-posedness Renormalized sol's definition Hints & Proof Plan of the talk 1 "Infinite energy solutions" for elliptic PDEs 2
Preisendorfer, Rudolph W
1957-01-01
dealt vdth a pair of irradiance functions representing twoHjC^.n^)^ which i s the irradiance a t time t on a unit areaCalifornia UNIFIED IRRADIANCE EQUATIONS R. W. Preisendorfer
Rhoads, James
Representative Staffing & Management Reviews & Control Gates The NASA Program/Project Life Cycle Concept C Concept/Design Evaluation Criteria ° Feasibility Assessment ° Life Cycle Cost Estimates ° Trade Requirements Establish Optimum System Design Analyze Mission Requirements Establish Optimum Architecture
The relativistic Pauli equation
David Delphenich
2012-07-24
After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charged spinning particle in an external electromagnetic field then implies a second order equation in the matrix-valued wave functions that is of Klein-Gordon type and represents the relativistic analogue of the Pauli equation. We conclude by presenting the Lagrangian form for the relativistic Pauli equation.
Monge equation of arbitrary degree in 1 + 1 space
A. N. Leznov; R. Torres-cordoba
2013-01-31
Solution of Monge equation of arbitrary degree (non linear differential equation n-orden) is connected with solution of functional equation for 4 functions with 4 different arguments. Some number solutions of this equation is represented in explicit form.
The equations Linear plate equation
Grunau, Hans-Christoph
The equations Linear plate equation Paneitz equation Willmore equation, one dimensional Some fourth order differential equations related to differential geometry Hans-Christoph Grunau OttovonGuerickeUniversit¨at Magdeburg Nice, January 26, 2006 Hans-Christoph Grunau Differential equations of fourth order #12;The
QG Equations QG Vorticity Equation
Hennon, Christopher C.
QG Equations QG Vorticity Equation The vorticity equation can be written in isobaric and vector Vorticity Equation: 1) Frictional effects are negligible 2) Tilting terms are negligible on the synoptic these assumptions are applied, the vorticity equation becomes: ( ) ( )Hgg g VffV t vv ·-+·-= (1) Furthermore, f
Differential-Equation Based Absorbing Boundary Conditions
Schneider, John B.
Chapter 6 Differential-Equation Based Absorbing Boundary Conditions 6.1 Introduction A simple in the analysis of a wide range of FDTD-related topics. 6.2 The Advection Equation The wave equation that governs.2) The second form represents the equation in terms of an operator operating on Ez where the operator
Representative Albert R. Public Policy
Sibille, Etienne
District. During the last 12 years, he served on the powerful House Energy and Commerce Committee, most of the Subcommittee on Energy and Air Quality. While on Energy and Commerce, Representative Wynn also served OF CONCENTRATION Energy Representative Wynn helped craft the Energy Independence and Security Act of 2007. He added
Schroedinger equation and classical physics
Milos V. Lokajicek
2012-05-30
Any time-dependent solution of Schr\\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to existence of quantization). There is not any reason to the physical interpretation according to Copenhagen alternative as Bell's inequalities are valid in the classical physics only (and not in any alternative based on Schr\\"{o}dinger equation). The advantage of Schr\\"{o}dinger equation consists then in that it enables to represent directly the time evolution of a statistical distribution of classical initial states (which is usual in collision experiments). The Schr\\"{o}dinger equation (without assumptions added by Bohr) may then represent the common physical theory for microscopic as well as macroscopic physical systems. However, together with the last possibility the solutions of Schr\\"{o}dinger equation may be helpful also in analyzing the influence of other statistically distributed properties (e.g., spin orientations or space structures) of individual matter objects forming a corresponding physical system, which goes in principle beyond the classical physics. In any case, the contemporary quantum theory represents the phenomenological approximative description of some matter characteristics only, without providing any insight into quantum mechanism emergence. In such a case it is necessary to take into account more detailed properties at least of some involved objects.
Wave represents displacement Wave represents pressure Source -Sound Waves
Colorado at Boulder, University of
is wavelength Number of crests passing a point in 1 second is frequency Wave represents pressure Target - Radio. The Sound Waves simulation becomes the source of an analogical mapping to Radio Waves. Concepts Radio Waves 1 - Sound Waves references water waves 2 - Water is analogy for Sound Waves 3 - Radio
Representing Periodic Functions by Fourier
Vickers, James
Representing Periodic Functions by Fourier Series 23.2 Introduction In this Section we show how, then the Fourier series expansion takes the form: f(t) = a0 2 + n=1 (an cos nt + bn sin nt) Our main purpose here Fourier coefficients of a function of period 2 calculate Fourier coefficients of a function of general
Atilhan, Mert
2004-09-30
and thermophysical properties of natural gas for practical engineering applications. This thesis presents a new cubic EOS for pure argon. In this work, a theoretically based EOS represents the PVT behavior of pure fluids. The new equation has its basis...
Influence of Kaluza Scalar on the Raychaudhuri Equation
R. Parthasarathy
2013-11-01
It is shown that the influence of Kaluza scalar is to induce expansion in the Raychaudhuri equation for two representative solutions of the Kaluza theory.
R. K. Saxena; A. M. Mathai; H. J. Haubold
2011-09-29
The object of this paper is to present a computable solution of a fractional partial differential equation associated with a Riemann-Liouville derivative of fractional order as the time-derivative and Riesz-Feller fractional derivative as the space derivative. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computable form in terms of the H-function. It provides an elegant extension of the results given earlier by Debnath, Chen et al., Haubold et al., Mainardi et al., Saxena et al., and Pagnini et al. The results obtained are presented in the form of four theorems. Some results associated with fractional Schroeodinger equation and fractional diffusion-wave equation are also derived as special cases of the findings.
Inverse Problems in Engng, 2002, Vol. 10, No. 5, pp. 467483 INVERSION OF NOISE-FREE LAPLACE
Valkó, Peter
inversion algorithm; Multi-precision calculation; Test problems INTRODUCTION The basic idea of integral in many applications of science and engineering whenever ordinary and partial differential equations or integral equations are solved. The increasing number of available numerical methods and computer codes has
The generating functions of Lame equation in Weierstrass's form
Yoon Seok Choun
2014-11-07
Lame equation arises from deriving Laplace equation in ellipsoidal coordinates; in other words, it's called ellipsoidal harmonic equation. Lame function is applicable to diverse areas such as boundary value problems in ellipsoidal geometry, chaotic Hamiltonian systems, the theory of Bose-Einstein condensates, etc. By applying generating function into modern physics (quantum mechanics, thermodynamics, black hole, supersymmetry, special functions, etc), we are able to obtain the recursion relation, a normalization constant for the wave function and expectation values of any physical quantities. For the case of hydrogen-like atoms, generating function of associated Laguerre polynomial has been used in order to derive expectation values of position and momentum. By applying integral forms of Lame polynomial in the Weierstrass's form in which makes B_n term terminated [29], I consider generating function of it including all higher terms of A_n's. This paper is 8th out of 10 in series "Special functions and three term recurrence formula (3TRF)". See section 4 for all the papers in the series. Previous paper in series deals with the power series expansion and the integral formalism of Lame equation in the Weierstrass's form and its asymptotic behavior [29]. The next paper in the series describes analytic solution for grand confluent hypergeometric function [31].
Phung, Kim-dang.- Le Laboratoire de MathÃ©matiques
I: Heat equation II: SchrÃ¶dinger equation III: Wave equation IV: Radiative transfer equation;I: Heat equation II: SchrÃ¶dinger equation III: Wave equation IV: Radiative transfer equation QUCP: Heat equation II: SchrÃ¶dinger equation III: Wave equation IV: Radiative transfer equation QUCP
Francesco Costanzo; James G. Brasseur
2013-02-05
The quantification of the stiffness of tubular biological structures is often obtained, both in vivo and in vitro, as the slope of total transmural hoop stress plotted against hoop strain. Total hoop stress is typically estimated using the "Laplace law." We show that this procedure is fundamentally flawed for two reasons: Firstly, the Laplace law predicts total stress incorrectly for biological vessels. Furthermore, because muscle and other biological tissue are closely volume-preserving, quantifications of elastic modulus require the removal of the contribution to total stress from incompressibility. We show that this hydrostatic contribution to total stress has a strong material-dependent nonlinear response to deformation that is difficult to predict or measure. To address this difficulty, we propose a new practical method to estimate a mechanically viable modulus of elasticity that can be applied both in vivo and in vitro using the same measurements as current methods, with care taken to record the reference state. To be insensitive to incompressibility, our method is based on shear stress rather than hoop stress, and provides a true measure of the elastic response without application of the Laplace law. We demonstrate the accuracy of our method using a mathematical model of tube inflation with multiple constitutive models. We also re-analyze an in vivo study from the gastro-intestinal literature that applied the standard approach and concluded that a drug-induced change in elastic modulus depended on the protocol used to distend the esophageal lumen. Our new method removes this protocol-dependent inconsistency in the previous result.
Does the Poynting vector always represent electromagnetic power flow?
Changbiao Wang
2015-07-07
Poynting vector as electromagnetic power flow has prevailed over one hundred years in the community. However in this paper, it is shown from Maxwell equations that the Poynting vector may not represent the electromagnetic power flow for a plane wave in a non-dispersive, lossless, non-conducting, anisotropic uniform medium; this important conclusion revises the conventional understanding of Poynting vector. It is also shown that this conclusion is clearly supported by Fermat's principle and special theory of relativity.
Does the Poynting vector always represent electromagnetic power flow?
Wang, Changbiao
2015-01-01
Poynting vector as electromagnetic power flow has prevailed over one hundred years in the community. However in this paper, it is shown from Maxwell equations that the Poynting vector may not represent the electromagnetic power flow for a plane wave in a non-dispersive, lossless, non-conducting, anisotropic uniform medium; this important conclusion revises the conventional understanding of Poynting vector. It is also shown that this conclusion is clearly supported by Fermat's principle and special theory of relativity.
The Fractional Kinetic Equation and Thermonuclear Functions
H. J. Haubold; A. M. Mathai
2000-01-16
The paper discusses the solution of a simple kinetic equation of the type used for the computation of the change of the chemical composition in stars like the Sun. Starting from the standard form of the kinetic equation it is generalized to a fractional kinetic equation and its solutions in terms of H-functions are obtained. The role of thermonuclear functions, which are also represented in terms of G- and H-functions, in such a fractional kinetic equation is emphasized. Results contained in this paper are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.
May 7, 2007 Syllabus in Differential Equations
Turc, Catalin
-dimensional elliptic eigenvalue problems: orthogonality and completeness of eigenfunctions · Laplace, heat and wave. 5. Green's functions and fundamental solutions: · Green' identities; · Generalized functions · Fourier method: series and integral expansions of Green's functions · Symmetries and the Method of images
Three approaches for representing Lindblad dynamics by a matrix-vector notation
Morag Am-Shallem; Amikam Levy; Ido Schaefer; Ronnie Kosloff
2015-12-10
Markovian dynamics of open quantum systems are described by the L-GKS equation, known also as the Lindblad equation. The equation is expressed by means of left and right matrix multiplications. This formulation hampers numerical implementations. Representing the dynamics by a matrix-vector notation overcomes this problem. We review three approaches to obtain such a representation. The methods are demonstrated for a driven two-level system subject to spontaneous emission.
Representative Atmospheric Plume Development for Elevated Releases
Eslinger, Paul W.; Lowrey, Justin D.; McIntyre, Justin I.; Miley, Harry S.; Prichard, Andrew W.
2014-03-03
An atmospheric explosion of a low-yield nuclear device will produce a large number of radioactive isotopes, some of which can be measured with airborne detection systems. However, properly equipped aircraft may not arrive in the region where an explosion occurred for a number of hours after the event. Atmospheric conditions will have caused the radioactive plume to move and diffuse before the aircraft arrives. The science behind predicting atmospheric plume movement has advanced enough that the location of the maximum concentrations in the plume can be determined reasonably accurately in real time, or near real time. Given the assumption that an aircraft can follow a plume, this study addresses the amount of atmospheric dilution expected to occur in a representative plume as a function of time past the release event. The approach models atmospheric transport of hypothetical releases from a single location for every day in a year using the publically available HYSPLIT code. The effective dilution factors for the point of maximum concentration in an elevated plume based on a release of a non-decaying, non-depositing tracer can vary by orders of magnitude depending on the day of the release, even for the same number of hours after the release event. However, the median of the dilution factors based on releases for 365 consecutive days at one site follows a power law relationship in time, as shown in Figure S-1. The relationship is good enough to provide a general rule of thumb for estimating typical future dilution factors in a plume starting at the same point. However, the coefficients of the power law function may vary for different release point locations. Radioactive decay causes the effective dilution factors to decrease more quickly with the time past the release event than the dilution factors based on a non-decaying tracer. An analytical expression for the dilution factors of isotopes with different half-lives can be developed given the power law expression for the non-decaying tracer. If the power-law equation for the median dilution factor, Df, based on a non-decaying tracer has the general form Df=a?×t?^(-b) for time t after the release event, then the equation has the form Df=e^(-?t)×a×t^(-b) for a radioactive isotope, where ? is the decay constant for the isotope.
Non-linear equations for electron waves in Maxwellian low-collision ion-electron plasmas
Soshnikov, V N
2008-01-01
The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic equations, and the use of 2D Laplace transform method are applied to an evaluation of collision damping decrements of plane electron longitudinal and transverse waves. Damping decrement tends to infinity when the wave frequency tends to electron Langmuir frequency from above values. We considered recurrent relations for amplitudes of the overtones which form in their sum the all solution of the plasma wave non-linear equations including collision damping and quadratic (non-linear) terms. Collisionless damping at frequencies more the Langmuir one is possible only in non-Maxwellian plasmas.
Relativistic quaternionic wave equation
Schwartz, C
2006-01-01
Schrodinger ?time dependent? equation, ? 1 and ? 2 , then?TCP?. The current conservation equation ?3.2? is still truefor this extended wave equation ?8.1?, however, Eq. ?6.7?
Transport Equations Thomas Hillen
Hillen, Thomas
Transport Equations Thomas Hillen supported by NSERC University of Alberta, Edmonton Transport V , V compact and symmetric. Transport Equations p.2/33 #12;Directed Movement The equation pt(t, x of v. Transport Equations p.3/33 #12;With Directional Changes µ: turning rate. T(v, v ): probability
Einstein's Equation in Pictures
Matthew Frank
2002-03-28
This paper gives a self-contained, elementary, and largely pictorial statement of Einstein's equation.
Differential Equations: Page 1 Differential equations
Hogg, Andrew
) is a nth order differential equation. The aim is calculate the unknown function y(x). A linear differential First order differential equations 1.1 Direct integration If dy dx = g(x) subject to y(b) = y0 then y and is to be downloaded or copied for your private study only. #12;Differential Equations: Page 2 1.3 Integrating factor
A Modified Equation for Neural Conductance and Resonance
M. Robert Showalter
1999-05-06
A modified equation, the S-K equation, fits data that the current neural conduction equation, the K-R equation, does not. The S-K equation is a modified Heaviside equation, based on a new interpretation of cross terms. Elements of neural anatomy and function are reviewed to put the S-K equation into context. The fit between S-K and resonance-like neural data is then shown. Appendix 1: Derivation of crossterms that represent combinations of physical laws for a line conductor of finite length. Appendix 2: Evaluation of crossterms that represent combinations of physical laws according to consistency arguments. Appendix 3: Some background on resonance. Appendix 4: Web access to some brain modeling, correspondence with NATURE, and discussion of the work in George Johnson's New York Times forums.
Decoupling vector wave equation, Proca and Maxwell equations in Petrov type N space-times
Koray Düzta?; ?brahim Semiz
2015-08-23
In this work we use Newman-Penrose (NP) two-spinor formalism to derive decoupled equations for vector fields in Petrov type N space-times. In the NP formalism, a four vector can be represented by one complex and two real scalars. Then, a decoupled second order differential equation for one of the real scalars can be derived from the vector wave equation if the space-time is of type N. The solution for this scalar can --in principle-- be used to derive decoupled equations for the other scalars. These results can be directly applies to Proca equation for massive vector fields. We also evaluate Maxwell equations in terms of NP complex scalars of electromagnetism. We derive a decoupled second order differential equation for $\\phi_0$, valid in type N space-times. Substituting any solution for $\\phi_0$ in Maxwell equations, leads to two first order differential equations for $\\phi_1$. We show that these first order equations identically satisfy integrability conditions. Thus, any solution for $\\phi_0$ guarantees the existence of a solution for $\\phi_1$, via either of the first order differential equations.
An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations
R. K. Saxena; A. M. Mathai; H. J. Haubold
2010-01-13
An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.
M. J. Holst The Poisson-Boltzmann Equation
Holst, Michael J.
discontinuous coefficients representing material interfaces, rapid nonlinearities, and three spatial dimensions. Similar equations occur in various applications, including nuclear physics, semiconductor physics complex biomolecule lying in a solvent. We next study the theoretical properties of the linearized
Graph-based approach for the approximate solution of the chemical master equation
Basile, Raffaele
2015-07-01
The chemical master equation (CME) represents the accepted stochastic description of chemical reaction kinetics in mesoscopic systems. As its exact solution – which gives the corresponding probability density function – ...
Finite Temperature Schrödinger Equation
Xiang-Yao Wu; Bai-Jun Zhang; Xiao-Jing Liu; Nuo Ba; Yi-Heng Wu; Qing-Cai Wang; Yan Wang
2011-06-11
We know Schr\\"{o}dinger equation describes the dynamics of quantum systems, which don't include temperature. In this paper, we propose finite temperature Schr\\"{o}dinger equation, which can describe the quantum systems in an arbitrary temperature. When the temperature T=0, it become Shr\\"{o}dinger equation.
Facility Representative Program, Criteria & Review Approach Documents
Office of Energy Efficiency and Renewable Energy (EERE)
This page provides Criteria Review and Approach Documents (CRADS) to assist Facility Representatives. Please submit your CRADS for posting by sending them to the HQ FR Program Manager. Please include the subject, date, and a contact person.
REPRESENTATIVE COURSE SEQUENCE SOFTWARE ENGINEERING (SE)
Huang, Haiying
REPRESENTATIVE COURSE SEQUENCE SOFTWARE ENGINEERING (SE) Freshman Year First Semester Second Semester Second Semester CSE 3310 Fundamentals of Software CSE 3302 Programming Languages Engineering CSE 3320 Operating Systems CSE 3315 Theoretical Concepts in CSE CSE 4310 Software Engineering
A Capital Market Test of Representativeness
Safdar, Mohammad
2012-07-16
While some prior studies document that investors overreact to information in sales growth as consistent with representativeness bias, other studies find no evidence of investor overreaction to either sales or earnings growth. Other recent studies...
Representing Information Collections for Visual Cognition
Koh, Eunyee
2009-05-15
The importance of digital information collections is growing. Collections are typically represented with text-only, in a linear list format, which turns out to be a weak representation for cognition. We learned this from empirical research...
Relativistic Quaternionic Wave Equation II
Schwartz, Charles
2007-01-01
Relativistic quaternionic wave equation. II J. Math. Phys.Relativistic quaternionic wave equation. II Charles Schwartzcomponent quaternionic wave equation recently introduced. A
Morin, Pedro
Trabajo Pr´actico 8 Ecuaciones en Derivadas Parciales (1) Hallar la soluci´on1 de la ecuaci´on de´on de la ecuaci´on de Laplace dentro del rect´angulo 0 x L, 0 y H con las condiciones de borde: ux(0 m´etodo s´olo funciona bajo la condici´on de la parte (a). (c) Considerar la ecuaci´on del calor
INTEGRAL EQUATION PRECONDITIONING FOR THE SOLUTION OF POISSON'S EQUATION ON
Ferguson, Thomas S.
INTEGRAL EQUATION PRECONDITIONING FOR THE SOLUTION OF POISSON'S EQUATION ON GEOMETRICALLY COMPLEX with the implementation and investigation of integral equation based solvers as preconditioners for finite difference discretizations of Poisson equations in geometrically complex domains. The target discretizations are those
Separable Differential Equations
PRETEX (Halifax NS) #1 1054 1999 Mar 05 10:59:16
2010-01-20
Feb 16, 2007 ... preceding differential equation and several mem- bers of the given family of curves. Describe the family of orthogonal trajectories. 34. Consider ...
Integrating the Jacobian equation
Airton von Sohsten de Medeiros; Ráderson Rodrigues da Silva
2014-09-16
We show essentially that the differential equation $\\frac{\\partial (P,Q)}{\\partial (x,y)} =c \\in {\\mathbb C}$, for $P,\\,Q \\in {\\mathbb C}[x,y]$, may be "integrated", in the sense that it is equivalent to an algebraic system of equations involving the homogeneous components of $P$ and $Q$. Furthermore, the first equations in this system give explicitly the homogeneous components of $Q$ in terms of those of $P$. The remaining equations involve only the homogeneous components of $P$.
Fractional Heisenberg Equation
Vasily E. Tarasov
2008-04-03
Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h)[H, ], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule. In this paper, we consider a fractional derivative on a set of quantum observables as a fractional power of the commutator (i/h)[H, ]. As a result, we obtain a fractional generalization of the Heisenberg equation. The fractional Heisenberg equation is exactly solved for the Hamiltonians of free particle and harmonic oscillator. The suggested Heisenberg equation generalize a notion of quantum Hamiltonian systems to describe quantum dissipative processes.
On the generalized continuity equation
Arbab I. Arbab; Hisham. M. Widatallah
2010-02-27
A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by Schrodinger-like equation and not by the diffusion equation.
Gravitational instability via the Schrodinger equation
C. J. Short; P. Coles
2006-11-22
We explore a novel approach to the study of large-scale structure formation in which self-gravitating cold dark matter (CDM) is represented by a complex scalar field whose dynamics are governed by coupled Schrodinger and Poisson equations. We show that, in the quasi-linear regime, the Schrodinger equation can be reduced to the free-particle Schrodinger equation. We advocate using the free-particle Schrodinger equation as the basis of a new approximation method - the free-particle approximation - that is similar in spirit to the successful adhesion model. In this paper we test the free-particle approximation by appealing to a planar collapse scenario and find that our results are in excellent agreement with those of the Zeldovich approximation, provided care is taken when choosing a value for the effective Planck constant in the theory. We also discuss how extensions of the free-particle approximation are likely to require the inclusion of a time-dependent potential in the Schrodinger equation. Since the Schrodinger equation with a time-dependent potential is typically impossible to solve exactly, we investigate whether standard quantum-mechanical approximation techniques can be used, in a cosmological setting, to obtain useful solutions of the Schrodinger equation. In this paper we focus on one particular approximation method: time-dependent perturbation theory (TDPT). We elucidate the properties of perturbative solutions of the Schrodinger equation by considering a simple example: the gravitational evolution of a plane-symmetric density fluctuation. We use TDPT to calculate an approximate solution of the relevant Schrodinger equation and show that this perturbative solution can be used to successfully follow gravitational collapse beyond the linear regime, but there are several pitfalls to be avoided.
Sergei Kuksin; Alberto Maiocchi
2015-01-17
In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behaviour of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three-- and four--wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. In the case of the NLS equation we use next some heuristic approximation from the arsenal of wave turbulence to show that under the iterated limit "the volume goes to infinity", taken after the limit "the amplitude of oscillations goes to zero", the energy spectrum of solutions for the effective equation is described by a Zakharov-type kinetic equation. Evoking the Zakharov ansatz we show that stationary in time and homogeneous in space solutions for the latter equation have a power law form. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanology.
An iconic approach to representing climate change
Feigon, Brooke
1 An iconic approach to representing climate change Saffron Jessica O'Neill A thesis submitted-experts to be meaningfully engaged with the issue of climate change. This thesis investigates the value of engaging non-experts with climate change at the individual level. Research demonstrates that individuals perceive climate change
Generalized Harmonic Equations in 3+1 Form
J. David Brown
2011-11-29
The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature, lapse function and shift vector, plus fields that represent the time derivatives of the lapse and shift. This allows for a direct comparison between the generalized harmonic and the Arnowitt-Deser-Misner formulations. The 3+1 generalized harmonic equations are also written in terms of conformal variables and compared to the Baumgarte-Shapiro-Shibata-Nakamura equations with moving puncture gauge conditions.
Natale, Michael J.
Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more importantly, they experience numerical convergence difficulties...
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION
Maier, Robert S.
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION: I. POLYNOMIAL TRANSFORMATIONS ROBERT S. MAIER #3; Abstract. The reductions of the Heun equation to the hypergeometric equation parameter and normalized accessory parameter of the Heun equation are each restricted to take values
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION
Maier, Robert S.
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION: I. POLYNOMIAL TRANSFORMATIONS ROBERT S. MAIER Abstract. The reductions of the Heun equation to the hypergeometric equation by rational accessory parameter of the Heun equation are each restricted to take values in a discrete set. The possible
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION
TRANSFORMING THE HEUN EQUATION TO THE HYPERGEOMETRIC EQUATION: I. POLYNOMIAL TRANSFORMATIONS ROBERT S. MAIER #3; Abstract. The reductions of the Heun equation to the hypergeometric equation and normalized accessory parameter of the Heun equation are each restricted to take values in a discrete set
Data structures and apparatuses for representing knowledge
Hohimer, Ryan E; Thomson, Judi R; Harvey, William J; Paulson, Patrick R; Whiting, Mark A; Tratz, Stephen C; Chappell, Alan R; Butner, Robert S
2014-02-18
Data structures and apparatuses to represent knowledge are disclosed. The processes can comprise labeling elements in a knowledge signature according to concepts in an ontology and populating the elements with confidence values. The data structures can comprise knowledge signatures stored on computer-readable media. The knowledge signatures comprise a matrix structure having elements labeled according to concepts in an ontology, wherein the value of the element represents a confidence that the concept is present in an information space. The apparatus can comprise a knowledge representation unit having at least one ontology stored on a computer-readable medium, at least one data-receiving device, and a processor configured to generate knowledge signatures by comparing datasets obtained by the data-receiving devices to the ontologies.
PWR representative behavior during a LOCA
Allison, C.M.
1981-01-01
To date, there has been substantial analytical and experimental effort to define the margins between design basis loss-of-coolant accident (LOCA) behavior and regulatory limits on maximum fuel rod cladding temperature and deformation. As a result, there is extensive documentation on the modeling of fuel rod behavior in test reactors and design basis LOCA's. However, modeling of that behavior using representative, non-conservative, operating histories is not nearly as well documented in the public literature. Therefore, the objective of this paper is (a) to present calculations of LOCA induced behavior for Pressurized Water Reactor (PWR) core representative fuel rods, and (b) to discuss the variability in those calculations given the variability in fuel rod condition at the initiation of the LOCA. This analysis was limited to the study of changes in fuel rod behavior due to different power operating histories. The other two important parameters which affect that behavior, initial fuel rod design and LOCA coolant conditions were held invarient for all of the representative rods analyzed.
Yucca Mountain Climate Technical Support Representative
Sharpe, Saxon E
2007-10-23
The primary objective of Project Activity ORD-FY04-012, “Yucca Mountain Climate Technical Support Representative,” was to provide the Office of Civilian Radioactive Waste Management (OCRWM) with expertise on past, present, and future climate scenarios and to support the technical elements of the Yucca Mountain Project (YMP) climate program. The Climate Technical Support Representative was to explain, defend, and interpret the YMP climate program to the various audiences during Site Recommendation and License Application. This technical support representative was to support DOE management in the preparation and review of documents, and to participate in comment response for the Final Environmental Impact Statement, the Site Recommendation Hearings, the NRC Sufficiency Comments, and other forums as designated by DOE management. Because the activity was terminated 12 months early and experience a 27% reduction in budget, it was not possible to complete all components of the tasks as originally envisioned. Activities not completed include the qualification of climate datasets and the production of a qualified technical report. The following final report is an unqualified summary of the activities that were completed given the reduced time and funding.
First order differential equations
Samy Tindel
2015-09-29
Logistic growth. Hypothesis: Growth rate depends on population. Related equation: dy dt. = h(y)y. Specifications for h: h(y) ? r > 0 for small values of y y ?
Relativistic Guiding Center Equations
White, R. B.; Gobbin, M.
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Nazari-Golshan, A.; Nourazar, S. S.; Department of Mechanical Engineering, Amirkabir University of Technology, Tehran
2013-10-15
The time fractional modified Korteweg-de Vries (TFMKdV) equation is solved to study the nonlinear propagation of small but finite amplitude dust ion-acoustic (DIA) solitary waves in un-magnetized dusty plasma with trapped electrons. The plasma is composed of a cold ion fluid, stationary dust grains, and hot electrons obeying a trapped electron distribution. The TFMKdV equation is derived by using the semi-inverse and Agrawal's methods and then solved by the Laplace Adomian decomposition method. Our results show that the amplitude of the DIA solitary waves increases with the increase of time fractional order ?, the wave velocity v{sub 0}, and the population of the background free electrons ?. However, it is vice-versa for the deviation from isothermality parameter b, which is in agreement with the result obtained previously.
Aggregation Equation with Degenerate Diffusion
Yao, Yao
2012-01-01
for Patlak-Keller-Segel Equation with Degenerate Dif-for the aggregation equation with degenerate di?usion,3 An Aggregation Equation with Di?usion in the Periodic
Solving Symbolic Equations with PRESS
Sterling, L.; Bundy, Alan; Byrd, L.; O'Keefe, R.; Silver, B.
1982-01-01
We outline a program, PRESS (PRolog Equation Solving System) for solving symbolic, transcendental, non-differential equations. The methods used for solving equations are described, together with the service facilities. The ...
Differential Equations of Mathematical Physics
Max Lein
2015-08-16
These lecture notes for the course APM 351 at the University of Toronto are aimed at mathematicians and physicists alike. It is not meant as an introductory course to PDEs, but rather gives an overview of how to view and solve differential equations that are common in physics. Among others, I cover Hamilton's equations, variations of the Schr\\"odinger equation, the heat equation, the wave equation and Maxwells equations.
Gauged Knizhnik-Zamolodchikov equation
I. I Kogan; A. Lewis; O. A. Soloviev
1996-11-25
Correlation functions of gauged WZNW models are shown to satisfy a differential equation, which is a gauge generalization of the Knizhnik-Zamolodchikov equation.
Diophantine Equations and Congruent Number Equation Solutions
Mamuka Meskhishvili
2015-04-16
By using pairs of nontrivial rational solutions of congruent number equation $$ C_N:\\;\\;y^2=x^3-N^2x, $$ constructed are pairs of rational right (Pythagorean) triangles with one common side and the other sides equal to the sum and difference of the squares of the same rational numbers. The parametrizations are found for following Diophantine systems: \\begin{align*} (p^2\\pm q^2)^2-a^2 & =\\square_{1,2}\\,, \\\\[0.2cm] c^2-(p^2\\pm q^2)^2 & =\\square_{1,2}\\,, \\\\[0.2cm] a^2+(p^2\\pm q^2)^2 & =\\square_{1,2}\\,, \\\\[0.2cm] (p^2\\pm q^2)^2-a^2 & =(r^2\\pm s^2)^2. \\end{align*}
Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.
2014-08-29
We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.
1Q CY2000 (PDF), Facility Representative Program Performance...
1Q CY2000 (PDF), Facility Representative Program Performance Indicators Quarterly Report 1Q CY2000 (PDF), Facility Representative Program Performance Indicators Quarterly Report...
Representativeness-based Sampling Network Design for the State...
Office of Scientific and Technical Information (OSTI)
Representativeness-based Sampling Network Design for the State of Alaska Citation Details In-Document Search Title: Representativeness-based Sampling Network Design for the State...
Representativeness based Sampling Network Design for the State...
Office of Scientific and Technical Information (OSTI)
Representativeness based Sampling Network Design for the State of Alaska Title: Representativeness-based Sampling Network Design for the State of Alaska Authors: Forrest M. Hoffman...
Representativeness-Based Sampling Network Design for the State...
Office of Scientific and Technical Information (OSTI)
Journal Article: Representativeness-Based Sampling Network Design for the State of Alaska Citation Details In-Document Search Title: Representativeness-Based Sampling Network...
Secretary Chu: China's Clean Energy Successes Represent a New...
Office of Environmental Management (EM)
Chu: China's Clean Energy Successes Represent a New "Sputnik Moment" for America Secretary Chu: China's Clean Energy Successes Represent a New "Sputnik Moment" for America November...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
Reference Buildings by Climate Zone and Representative City: 4B Albuquerque, New Mexico Reference Buildings by Climate Zone and Representative City: 4B Albuquerque, New...
DOE Honors WIPP Representative for Cutting Travel Costs, Greenhouse...
DOE Honors WIPP Representative for Cutting Travel Costs, Greenhouse Gas Emissions DOE Honors WIPP Representative for Cutting Travel Costs, Greenhouse Gas Emissions June 29, 2012 -...
A Least-Squares Transport Equation Compatible with Voids
Hansen, Jon [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Peterson, Jacob [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Morel, Jim [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Ragusa, Jean [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2014-12-01
Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transport equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S_{n} formulation represents an excellent alternative to existing second-order S_{n} transport formulations
Flavored quantum Boltzmann equations
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545 (United States); Center for Theoretical Physics, University of California, and Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, California, 94720 (United States); Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin, 53706 (United States) and Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California, 91125 (United States); Theory Group, TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3 (Canada)
2010-05-15
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
Deviation differential equations. Jacobi fields
G. Sardanashvily
2013-04-02
Given a differential equation on a smooth fibre bundle Y, we consider its canonical vertical extension to that, called the deviation equation, on the vertical tangent bundle VY of Y. Its solutions are Jacobi fields treated in a very general setting. In particular, the deviation of Euler--Lagrange equations of a Lagrangian L on a fibre bundle Y are the Euler-Lagrange equations of the canonical vertical extension of L onto VY. Similarly, covariant Hamilton equations of a Hamiltonian form H are the Hamilton equations of the vertical extension VH of H onto VY.
Dirac Equation at Finite Temperature
Xiang-Yao Wu; Bo-Jun Zhang; Xiao-Jing Liu; Nuo Ba; Yi-Heng Wu; Si-Qi Zhang; Jing Wang; Chun-Hong Li
2012-12-01
In this paper, we propose finite temperature Dirac equation, which can describe the quantum systems in an arbitrary temperature for a relativistic particle of spin-1/2. When the temperature T=0, it become Dirac equation. With the equation, we can study the relativistic quantum systems in an arbitrary temperature.
Assignment II Saha & Boltzmann equations
Spoon, Henrik
Assignment II Saha & Boltzmann equations January 21, 2002 This assignment is meant to give you some practical experience in using the Saha and Boltzmann equations that govern the level populations in atoms;s =kT the partition function of ionization stage r. The Saha equation: N r+1 N r = 2U r+1 U r P e #18
The role of the kinematical constraint and non-linear effects in the CCFM equation
Michal Deak
2015-05-19
We report on recent study [1] of the role of the kinematical constraint in the CCFM equation and its non-linear extension. We compare numerical results obtained by solving the CCFM equation and argue that kinematical constraint represents an important correction.
Knowledge Media Institute Representing Scholarly Claims in Internet Digital
Knowledge Media Institute Representing Scholarly Claims in Internet Digital Libraries: A Knowledge in Computer Science (Eds.) Serge Abiteboul and Anne-Marie Vercoustre. Representing Scholarly Claims with tracking and interpreting scholarly documents in distributed research communities. We argue that current
Tailored Marketing for Under-represented Population Segments...
Tailored Marketing for Under-represented Population Segments (201) Tailored Marketing for Under-represented Population Segments (201) August 13, 2015 3:00PM to 4:3...
What does motor efference copy represent? evidence from speech production
Niziolek, CA; Nagarajan, SS; Houde, JF
2013-01-01
What does motor efference copy represent? Evidence fromAbbreviated title: What does motor efference copy represent?SJ, Wang X (2003) Sensory-Motor Interaction in the Primate
FACILITY REPRESENTATIVE PROGRAM STATUS, 6/21/1999
Broader source: Energy.gov [DOE]
Since September, 1993, the Office of Field Management has served as the Department’s corporate advocate for the Facility Representative Program. The Facility Representative (FR) is a critical...
1999 FACILITY REPRESENTATIVE CONFERENCE June 21 – 25, 1999
Broader source: Energy.gov [DOE]
The Department of Energy will host the Facility Representative Annual Meeting on June 21-25, 1999 at the Alexis Park Hotel in Las Vegas, Nevada. The meeting will give Facility Representatives and...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
Climate Zone and Representative City: 2B Phoenix, Arizona Reference Buildings by Climate Zone and Representative City: 2B Phoenix, Arizona In addition to the ZIP file for each...
Structural Equation Modeling For Travel Behavior Research
Golob, Thomas F.
2011-01-01
STREAMS (Structural Equation Modeling Made Simple) is aGerbing, 1988. Structural equation modeling in practice: aP.M. , 1989. EQS Structural Equations Program Manual. BMDP
SOURCE TERMS IN THE TRANSIENT SEEPAGE EQUATION
Narasimhan, T.N.
2013-01-01
IN THE TRANSIENT SEEPAGE EQUATION T.N. Narasimhan FebruaryIN THE TRANSIENT SEEPAGE EQUATION T. N. Narasimhan Earthan integral transient seepage equation that includes source
A Master Equation Approach to the `3 + 1' Dirac Equation
Keith A. Earle
2011-02-06
A derivation of the Dirac equation in `3+1' dimensions is presented based on a master equation approach originally developed for the `1+1' problem by McKeon and Ord. The method of derivation presented here suggests a mechanism by which the work of Knuth and Bahrenyi on causal sets may be extended to a derivation of the Dirac equation in the context of an inference problem.
Solutions for the Klein-Gordon and Dirac equations on the lattice based on Chebyshev polynomials
Nelson Faustino
2015-05-22
The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of Klein-Gordon and Dirac equations for which Chebyshev polynomials of the first kind may be used to represent a set of solutions. The development of a well-adapted discrete Clifford calculus framework based on spinor fields allows us to represent, using solely projection based arguments, the solutions for the discretized Dirac equations from the knowledge of the solutions of the discretized Klein-Gordon equation. Implications of those findings on the interpretation of the lattice fermion doubling problem is briefly discussed.
On the generalized Jacobi equation
Volker Perlick
2007-10-14
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to the coordinates, but not with respect to the velocities. The resulting equation has been studied by several authors in some detail for timelike geodesics in a Lorentzian manifold. Here we begin by briefly considering the generalized Jacobi equation on affine manifolds, without a metric; then we specify to lightlike geodesics in a Lorentzian manifold. We illustrate the latter case by considering particular lightlike geodesics (a) in Schwarzschild spacetime and (b) in a plane-wave spacetime.
Illite Dissolution Rates and Equation (100 to 280 dec C)
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Carroll, Susan
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a “neutral” and a “basic” mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
Thermodynamically constrained correction to ab initio equations of state
French, Martin; Mattsson, Thomas R.
2014-07-07
We show how equations of state generated by density functional theory methods can be augmented to match experimental data without distorting the correct behavior in the high- and low-density limits. The technique is thermodynamically consistent and relies on knowledge of the density and bulk modulus at a reference state and an estimation of the critical density of the liquid phase. We apply the method to four materials representing different classes of solids: carbon, molybdenum, lithium, and lithium fluoride. It is demonstrated that the corrected equations of state for both the liquid and solid phases show a significantly reduced dependence of the exchange-correlation functional used.
Illite Dissolution Rates and Equation (100 to 280 dec C)
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Carroll, Susan
2014-10-17
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a “neutral” and a “basic” mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
S. C. Tiwari
2007-06-09
A generalized harmonic map equation is presented based on the proposed action functional in the Weyl space (PLA, 135, 315, 1989).
Schroeder's Equation in Several Variables
1910-10-20
2000 Mathematics Subject Classification: Primary: 32H50. Secondary: 30D05, 39B32, 47B33. Keywords: Schroeder's functional equation, iteration, composition
Heun equation, Teukolsky equation, and type-D metrics
D. Batic; H. Schmid
2007-01-15
Starting with the whole class of type-D vacuum backgrounds with cosmological constant we show that the separated Teukolsky equation for zero rest-mass fields with spin $s=\\pm 2$ (gravitational waves), $s=\\pm 1$ (electromagnetic waves) and $s=\\pm 1/2$ (neutrinos) is an Heun equation in disguise.
Appointment of Contracting Officers and Contracting Officer Representatives
Broader source: Directives, Delegations, and Requirements [Office of Management (MA)]
2004-04-21
The Order established procedures governing the selection, appointment and termination of Department of Energy contracting officers and contracting officer representatives. Supersedes DOE O 541.1A.
Name Representing Alam, Mansoor WSA Information Technology Committee
Royer, Dana
Name Representing Alam, Mansoor WSA Information Technology Committee Baird, Dave Chair and Chief Information Officer Beveridge, Dave Faculty, Division III Cope, Miriam Academic Computing Manager, Division
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
akfairbanksnew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 8 Fairbanks, Alaska Reference Buildings by Climate Zone...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
atxhoustonnew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 2A Houston, Texas Reference Buildings by Climate Zone...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
mdbaltimorenew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 4A Baltimore, Maryland Reference Buildings by Climate...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
agaatlantanew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 3A Atlanta, Georgia Reference Buildings by Climate Zone...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
usaflmiaminew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 1A Miami, Florida Reference Buildings by Climate Zone...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
samthelenanew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 6B Helena, Montana Reference Buildings by Climate Zone...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
acobouldernew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 5B Boulder, Colorado Reference Buildings by Climate...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
awaseattlenew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 4C Seattle, Washington Reference Buildings by Climate...
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
nvlasvegasnew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 3B Las Vegas, Nevada Reference Buildings by Climate...
Polytechnic Institute of New York University Researchers Represented...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Polytechnic Institute of New York University Researchers Represented in the E-print Network ResearcherResearch Institution Web page Aronov, Boris - Department of Computer Science...
Saturation and linear transport equation
Krzysztof Kutak
2009-04-29
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term.
Media with no Fresnel equation
Peinke, Joachim
Media with no Fresnel equation Alberto Favaro & Ismo V. Lindell Outline Part 1: Local linear media Part 2: Jump conditions Part 3: media with no G(q) Conclusions Electromagnetic media with no Fresnel with no Fresnel equation Alberto Favaro & Ismo V. Lindell Outline Part 1: Local linear media Part 2: Jump
Representative well models for eight geothermal-resource areas
Carson, C.C.; Lin, Y.T.; Livesay, B.J.
1983-02-01
Representative well models have been constructed for eight major geothermal-resource areas. The models define representative times and costs associated with the individual operations that can be expected during drilling and completion of geothermal wells. The models were made for and have been used to evaluate the impacts of potential new technologies. The nature, construction, and validation of the models are presented.
1-D Dirac Equation, Klein Paradox and Graphene
S. P. Bowen
2008-07-23
Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions across a step potential. Consequences of this exact solution are studied for the step potential and a square barrier. Characteristics of massless Dirac states and the momentum linear band energies for Graphene are shown to have quite different current and momentum properties.
Coherent states, vacuum structure and infinite component relativistic wave equations
Cirilo-Lombardo, Diego Julio
2015-01-01
It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the transformations and symmetries involved in equations of such type correspond to a particular representation of the Lorentz group. In this paper we give the general solution to this problem emphasizing the interplay between the group structure, the corresponding algebra and the physical spectrum. This analysis is completed with a strong discussion and proving that: i) the physical states are represented by coherent states; ii) the solutions in previous references [1] are not general, ii) the symmetries of the considered physical system in [1] (equations and geometry) do not correspond to the Lorentz group but to the fourth covering: the Metaplectic group Mp(n).
Reformulating the Schrodinger equation as a Shabat-Zakharov system
Boonserm, Petarpa
2009-01-01
We reformulate the second-order Schrodinger equation as a set of two coupled first order differential equations, a so-called "Shabat-Zakharov system", (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasise the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrodinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ODE.
Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation
Cao, Hao
2015-01-01
Any non-spherical distribution of density inside planets and stars gives rise to a non-spherical external gravity and change of shape. If part or all of the observed zonal flows at the cloud deck of giant planets represent deep interior dynamics, then the density perturbations associated with the deep zonal flows could generate gravitational signals detectable by the planned Juno mission and the Cassini Proximal Orbits. It is currently debated whether the thermal wind equation (TWE) can be used to calculate the gravity field associated with deep zonal flows. Here we present a critical comparison between the Euler equation and the thermal wind equation. Our analysis shows that the applicability of the TWE in calculating the gravity moments depends crucially on retaining the non-sphericity of the background density and gravity. Only when the background non-sphericity of the planet is taken into account, the TWE makes accurate enough prediction (with a few tens of percent errors) for the high-degree gravity mome...
A Grassmann integral equation K. Scharnhorst a)
Scharnhorst, Klaus
A Grassmann integral equation K. Scharnhorst a) HumboldtÂUniversita Ë? t zu Berlin, Institut fu Ë? r Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann #Berezin# integrations and which is to be obeyed
A Grassmann integral equation K. Scharnhorsta)
Scharnhorst, Klaus
A Grassmann integral equation K. Scharnhorsta) Humboldt-UniversitaÂ¨t zu Berlin, Institut fu Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann Berezin integrations and which is to be obeyed
Energy stories, equations and transition
Ernst, Damien
Energy stories, equations and transition Une histoire d'énergie: équations et transition% - Transition #12;ERoEI · ERoEI for « Energy Sustainable Energy April 28th, 2015 Raphael Fonteneau, University of Liège, Belgium @R_Fonteneau #12;Energy
van de Walle, Axel
Equation (30) should read F (T2) T2 = F (T1) T1 + Z 1/T2 1/T1 E d (1/T) Equation (E1) should be the same as Equation (38). Accordingly, the inlined equation just below Equation (E11) should be: ¡ kAB/ kAAkBB - 1 ¢ ¿ 1. To facilitate comparisons, Equation (E14) gives the effective cluster interac- tion using
Entropic corrections to Einstein equations
Hendi, S. H. [Physics Department, College of Sciences, Yasouj University, Yasouj 75914 (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Sheykhi, A. [Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Department of Physics, Shahid Bahonar University, P.O. Box 76175-132, Kerman (Iran, Islamic Republic of)
2011-04-15
Considering the general quantum corrections to the area law of black hole entropy and adopting the viewpoint that gravity interprets as an entropic force, we derive the modified forms of Modified Newtonian dynamics (MOND) theory of gravitation and Einstein field equations. As two special cases we study the logarithmic and power-law corrections to entropy and find the explicit form of the obtained modified equations.
Changes to the Facility Representative Program, 10/26/1999
Broader source: Energy.gov [DOE]
Effective October 1, 1999, the Deputy Secretary tasked this office to manage the Facility Representative Program. We look forward to working with you in continuing and improving this very important...
Department of Defense Representatives Visit Hanford to Benchmark Safety
Broader source: Energy.gov [DOE]
RICHLAND, Wash., December 16, 2005, Representatives of the Department of Defense's (DoD's) Voluntary Protection Program Center of Excellence (VPP CX) working to reduce injuries at selected (DoD)...
A representative individual from Arrovian aggregation of parametric individual utilities
A representative individual from Arrovian aggregation of parametric individual utilities social choice theory Assumptions Assumption on decisive coalitions Assumptions on individual utility functions Assumptions on the social welfare function Results The socially acceptable utility function
Reference Buildings by Climate Zone and Representative City:...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
hicago-oharenew2004v1-47-2.zip More Documents & Publications Reference Buildings by Climate Zone and Representative City: 5A Chicago, Illinois Reference Buildings by Climate...
REPRESENTING AEROSOLS IN GLOBAL MODELS: FROM MICROMETERS TO MEGAMETERS
Schwartz, Stephen E.
mainly from gas-to- particle conversion of low-volatility gaseous species, mainly sulfuric acid to represent aerosol processes and forcing "on-line" in climate models in order to capture the feedbacks
Appointment of Contracting Officers and Contracting Officer Representatives
Broader source: Directives, Delegations, and Requirements [Office of Management (MA)]
1996-04-30
To establish procedures governing the selection, appointment, and termination of contracting officers and for the appointment of contracting officer representatives. Cancels DOE Order 4200.4A. Canceled by DOE O 541.1A.
Representing and Reasoning about Changing Spatial Extensions of Geographic Features
Bennett, Brandon
. Campelo and Brandon Bennett School of Computing, University of Leeds, Leeds, LS2 9JT, UK, sccec,b.bennett@leeds For a comprehensive review of issues and challenges for representing geographic processes see [10]. #12;Foundational
How accurate is Limber's equation?
P. Simon
2007-08-24
The so-called Limber equation is widely used in the literature to relate the projected angular clustering of galaxies to the spatial clustering of galaxies in an approximate way. This paper gives estimates of where the regime of applicability of Limber's equation stops. Limber's equation is accurate for small galaxy separations but breaks down beyond a certain separation that depends mainly on the ratio sigma/R and to some degree on the power-law index, gamma, of spatial clustering xi; sigma is the one-sigma width of the galaxy distribution in comoving distance, and R the mean comoving distance. As rule-of-thumb, a 10% relative error is reached at 260 sigma/R arcmin for gamma~1.6, if the spatial clustering is a power-law. More realistic xi are discussed in the paper. Limber's equation becomes increasingly inaccurate for larger angular separations. Ignoring this effect and blindly applying Limber's equation can possibly bias results for the inferred spatial correlation. It is suggested to use in cases of doubt, or maybe even in general, the exact equation that can easily be integrated numerically in the form given in the paper.
4.3 Boundary integral equations
2010-10-18
62. CHAPTER 4. OBSTACLE SCATTERING. 4.3 Boundary integral equations. We introduce the equivalent sources for the Helmholtz equation and establish ...
A connection between the shallow-water equations and the Euler-Poincaré equations
Roberto Camassa; Long Lee
2014-04-18
The Euler-Poincar\\'e differential (EPDiff) equations and the shallow water (SW) equations share similar wave characteristics. Using the Hamiltonian structure of the SW equations with flat bottom topography, we establish a connection between the EPDiff equations and the SW equations in one and multi-dimensions. Additionally, we show that the EPDiff equations can be recast in a curl formulation.
E. V. Shiryaeva; M. Yu. Zhukov
2014-10-17
The paper presents the solutions for the zonal electrophoresis equations are obtained by analytical and numerical methods. The method proposed by the authors is used. This method allows to reduce the Cauchy problem for two hyperbolic quasilinear PDE's to the Cauchy problem for ODE's. In some respect, this method is analogous to the method of characteristics for two hyperbolic equations. The method is effectively applicable in all cases when the explicit expression for the Riemann-Green function of some linear second order PDE, resulting from the use of the hodograph method for the original equations, is known. One of the method advantages is the possibility of constructing a multi-valued solutions. Compared with the previous authors paper, in which, in particular, the shallow water equations are studied, here we investigate the case when the Riemann-Green function can be represent as the sum of the terms each of them is a product of two multipliers depended on different variables. The numerical results for zonal electrophoresis equations are presented. For computing the different initial data (periodic, wave packet, the Gaussian distribution) are used.
Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory
Yi-Fang Chang
2010-08-17
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.
Continuous time random walk models for fractional space-time diffusion equations
Sabir Umarov
2014-09-14
In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change process is a L\\'evy's stable subordinator with the stability index $\\beta \\in (0,1).$ In the parer the convergence of constructed CTRWs to time-changed processes associated with the corresponding fractional diffusion equations are proved using a new analytic method.
Equation-Based Power Model Integration in ESESC
Sinha, Meeta
2013-01-01
3.1 Power Equation . . . . . . . . . . . . . . . . . .3.1.1for the power model equation . . . . . . . . . . . .cache energy equations . . . . . . . . . . . . vi Abstract
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Maddalena, Damian; Hoffman, Forrest; Kumar, Jitendra; Hargrove, William
Sampling networks rarely conform to spatial and temporal ideals, often comprised of network sampling points which are unevenly distributed and located in less than ideal locations due to access constraints, budget limitations, or political conflict. Quantifying the global, regional, and temporal representativeness of these networks by quantifying the coverage of network infrastructure highlights the capabilities and limitations of the data collected, facilitates upscaling and downscaling for modeling purposes, and improves the planning efforts for future infrastructure investment under current conditions and future modeled scenarios. The work presented here utilizes multivariate spatiotemporal clustering analysis and representativeness analysis for quantitative landscape characterization and assessment of the Fluxnet, RAINFOR, and ForestGEO networks. Results include ecoregions that highlight patterns of bioclimatic, topographic, and edaphic variables and quantitative representativeness maps of individual and combined networks.
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Maddalena, Damian; Hoffman, Forrest; Kumar, Jitendra; Hargrove, William
2014-08-01
Sampling networks rarely conform to spatial and temporal ideals, often comprised of network sampling points which are unevenly distributed and located in less than ideal locations due to access constraints, budget limitations, or political conflict. Quantifying the global, regional, and temporal representativeness of these networks by quantifying the coverage of network infrastructure highlights the capabilities and limitations of the data collected, facilitates upscaling and downscaling for modeling purposes, and improves the planning efforts for future infrastructure investment under current conditions and future modeled scenarios. The work presented here utilizes multivariate spatiotemporal clustering analysis and representativeness analysis for quantitative landscape characterization and assessment of the Fluxnet, RAINFOR, and ForestGEO networks. Results include ecoregions that highlight patterns of bioclimatic, topographic, and edaphic variables and quantitative representativeness maps of individual and combined networks.
Chapter 2' First order Differential Equations I 2,] Linear Equations ...
1' _ _ , Draw a direction ?eld for the given differential equation. I- a - - - - "/4 ..... in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 g ..... A body falling in a relatively dense ?uid, oil for example, is acted on by three forces.
Nguyen, Dang Van; Li, Jing-Rebecca; Grebenkov, Denis; Le Bihan, Denis
2014-04-15
The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.
Acoustics Beyond the Wave Equation Paul Pereira
Pulfrey, David L.
Acoustics Beyond the Wave Equation Paul Pereira November 20, 2003 #12;2 1 Navier-Stokes Equation). The traditional study of acoustics concerns itself with the linearized equations of fluid mechanics, however. The fundamental equations of Nonlinear Acoustics are those of fluid dynamics, a mathematical description of which
Conservation of Mass The Continuity Equation
Hennon, Christopher C.
Conservation of Mass The Continuity Equation The equations of motion describe the "conservation. Holton derives the continuity equation in two ways: Eulerian and Lagrangian. We will consider to the sum of all the net mass flows coming from all 3 directions (equations 4,5, and 6): ( ) ( ) ( ) tzyx z
Commutative Relations for the Nonlinear Dirac Equation
Ying-Qiu Gu
2008-02-14
By constructing the commutative operators chain, we derive conditions for solving the eigenfunctions of Dirac equation and Schr\\"odinger type equation via separation of variables. Detailed calculation shows that, only a few cases can be completely reduced into ordinary differential equation system. So the effective perturbation or approximation methods for the resolution of the spinor equation are necessary, especially for the nonlinear cases.
Torque Equation (See section 4.9)
McCalley, James D.
1 Torque Equation (See section 4.9) Our goal is to combine the state-space voltage equations with the state-space torque equations. To achieve this, we need to do the following three things to the torque equation: 1. Address the difference in power bases. 2. Address the difference in speed (time) bases. 3
221A Miscellaneous Notes Continuity Equation
Murayama, Hitoshi
221A Miscellaneous Notes Continuity Equation 1 The Continuity Equation As I received questions equation. It appears in Sakurai, pp. 101102, but he does not go into the general discussions about what is meant by the one of the most famous equations in physics (Sakurai (2.4.15)), t + · = 0, (1) called
UNITED STATES HOUSE OF REPRESENTATIVES COMMITTEE on SCIENCE AND TECHNOLOGY
UNITED STATES HOUSE OF REPRESENTATIVES COMMITTEE on SCIENCE AND TECHNOLOGY SUBCOMMITTEE ON ENERGY AND ENVIRONMENT 2318 Rayburn House Office Building The Next Generation of Fusion Energy Research October 29, 2009 fusion energy has been a scientific quest since the 1950s. Inertial and magnetic confinement fusion
REPRESENTING GEO-SCIENTIFIC DOMAIN CONCEPTS Boyan Brodaric
Bennett, Brandon
1 REPRESENTING GEO-SCIENTIFIC DOMAIN CONCEPTS Boyan Brodaric Penn State Geography and Geological Survey of Canada brodaric@NRCan.gc.ca 1. Introduction The geo-sciences, including geology, ecology, soil accumulate and change, and (3) are characterized by degrees of uncertainty and granularity. This suggests
The Computational Complexity of Nash Equilibria in Concisely Represented Games #
Vadhan, Salil
The Computational Complexity of Nash Equilibria in Concisely Represented Games # Grant R#erent representations of games a#ect the complexity of problems associated with games, such as finding a Nash. For these two models, we study the complexity of four questions: determining if a given strategy is a Nash
The Computational Complexity of Nash Equilibria in Concisely Represented Games
Vadhan, Salil
The Computational Complexity of Nash Equilibria in Concisely Represented Games Grant R. Schoenebeck representations of games affect the complexity of problems associated with games, such as finding a Nash. For these two models, we study the complexity of four questions: determining if a given strategy is a Nash
Capturing Post-Silicon Variations using a Representative Critical Path
Sapatnekar, Sachin
1 Capturing Post-Silicon Variations using a Representative Critical Path Qunzeng Liu and Sachin S on measurements on a replica of the nominal critical path, whose variations are intended to reflect those of the entire circuit after manufacturing. For realistic circuits, where the number of critical paths can
Representing Thermal Vibrations and Uncertainty in Molecular Surfaces
Varshney, Amitabh
in a molecule is fuzzy because of its uncertainty in protein structure determination and thermal energy because of its thermal energy. Therefore, the smooth molecular surface will also vibrate. Also in proteinRepresenting Thermal Vibrations and Uncertainty in Molecular Surfaces Chang Ha Lee and Amitabh
AN ALTERNATIVE NOTATION FOR REPRESENTING DENSE LINEAR ALGEBRA ALGORITHMS
van de Geijn, Robert A.
AN ALTERNATIVE NOTATION FOR REPRESENTING DENSE LINEAR ALGEBRA ALGORITHMS PAOLO BIENTINESI AND ROBERT A. VAN DE GEIJN Abstract. We present a notation that allows a dense linear algebra algorithm subvectors and submatrices allowing the details of the algorithm to be the focus while hiding the intricate
Appointment of Contracting Officers and Contracting Officer's Representatives
Broader source: Directives, Delegations, and Requirements [Office of Management (MA)]
2000-10-27
To establish procedures governing the selection, appointment, and termination of contracting officers and for the appointment of contracting officer's representatives. To ensure that only trained and qualified procurement and financial assistance professionals, within the scope of this Order, serve as contracting officers. Cancels DOE O 541.1. Canceled by DOE O 541.1B.
Representing Temporal Knowledge for Case-Based Prediction
Aamodt, Agnar
well drilling. 1 Introduction Most current CBR systems represent episodes as distinct snap. Our focus is on prediction problems for avoiding faulty situations. Based on a well-established theory-intensive CBR system Creek. The paper presents the theoretical foundation of the method, the representation
US House of Representatives Appropriation Committee Report May 18, 2005
US House of Representatives Appropriation Committee Report May 18, 2005 Fusion Energy Sciences The Committee recommendation for fusion energy sciences is $295,155,000, an increase of $5,605,000 over that two-thirds of the proposed increase for the International Thermonuclear Experimental Reactor (ITER
State DOT Representative Report Questions National Concrete Consortium
, Texas April 2, 2009 Theme: Ride Quality for Bridges Please provide your state DOT's perspective regarding the following theme questions. Each NCC state DOT representative will be asked to present requirements set forth in the Caltrans Standard Specification 51-1.17 and which are tested for conformance
Toward Representative Internet Measurements Aditya Akella, Srinivasan Seshan
Akella, Aditya
and understand the structure and behavior of the Internet have a long history in the network research communityToward Representative Internet Measurements Aditya Akella, Srinivasan Seshan Dept. of Computer, and failure modes still is far from complete. Characterizing the operation of the current Internet
Wave Energy Resources Representative Sites Around the Hawaiian Islands
Wave Energy Resources for Representative Sites Around the Hawaiian Islands Prepared by: Luis A Foreword This report provides wave energy resource information required to select coastal segments for specific wave-energy-conversion (WEC) technology and to initiate engineering design incorporating
Fourier's Law from Closure Equations
Jean Bricmont; Antti Kupiainen
2006-09-01
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.
Evolution equation for quantum entanglement
Loss, Daniel
LETTERS Evolution equation for quantum entanglement THOMAS KONRAD1 , FERNANDO DE MELO2,3 , MARKUS of the time evolution of this resource under realistic conditions--that is, when corrupted by environment describes the time evolution of entanglement on passage of either component through an arbitrary noisy
Blink, J.A.
1983-09-01
In 1977, Dave Young published an equation-of-state (EOS) for lithium. This EOS was used by Lew Glenn in his AFTON calculations of the HYLIFE inertial-fusion-reactor hydrodynamics. In this paper, I summarize Young's development of the EOS and demonstrate a computer program (MATHSY) that plots isotherms, isentropes and constant energy lines on a P-V diagram.
Lyapunov Exponents for Burgers' Equation
Alexei Kourbatov
2015-02-23
We establish the existence, uniqueness, and stability of the stationary solution of the one-dimensional viscous Burgers equation with the Dirichlet boundary conditions on a finite interval. We obtain explicit formulas for solutions and analytically determine the Lyapunov exponents characterizing the asymptotic behavior of arbitrary solutions approaching the stationary one.
Use of Regression Equations 1 Running head: Equations from summary data
Crawford, John R.
Use of Regression Equations 1 Running head: Equations from summary data Neuropsychology, in press the final version published in the APA journal. It is not the copy of record Using regression equations.crawford@abdn.ac.uk #12;Use of Regression Equations 2 Abstract Regression equations have many useful roles
Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation
Hironobu Kihara
2011-02-10
We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.
Estimation of saturation and coherence effects in the KGBJS equation - a non-linear CCFM equation
Michal Deak
2012-10-01
We solve the modified non-linear extension of the CCFM equation - KGBJS equation - numerically for certain initial conditions and compare the resulting gluon Green functions with those obtained from solving the original CCFM equation and the BFKL and BK equations for the same initial conditions. We improve the low transversal momentum behaviour of the KGBJS equation by a small modification.
Korteweg-de Vries equation with a forcing term Solitary waves of the Kawahara equation
Fominov, Yakov
Korteweg-de Vries equation with a forcing term Solitary waves of the Kawahara equation Conclusion;Korteweg-de Vries equation with a forcing term Solitary waves of the Kawahara equation Conclusion Overview 1 Korteweg-de Vries equation with a forcing term Model Stationary solutions Stability 2 Solitary
Factorization of Dirac Equation and Graphene Quantum Dot
Youness Zahidi; Ahmed Jellal; Hocine Bahlouli; Mohammed El Bouziani
2014-05-14
We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to enrich our study. Using various potential configurations, we found that in the presence of a mass term an electrostatically confined quantum dot can accommodate true bound states, which is in agreement with previous work. The differential cross section associated with one specific potential configuration has been computed and discussed as function of the various potential parameters.
Equation of State Project Overview
Crockett, Scott
2015-09-11
A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.
Iterative solutions of simultaneous equations
Laycock, Guyron Brantley
1962-01-01
ITERATIVE SOLUTIONS OP SIKJLTANEOUS EQUATIONS G~cn Hrantlep I aycock Approved. as to style snd, content by& (Chairman of Committee) E. c. (Head. of Department August 1/62 ACKNOWLEDGEMENT The author wishes to thank Dr. Hi A. Luther for his time sn4.... . . . ~ ~ . . ~ III. JACOBI AND 6AUSS-SEIDEL METHODS I V ~ C ONCLUS I GN ~ ~ ~ a ~ ~ ~ t ~ ~ ~ ~ a ~ 1 ~ ~ ~ ~ ~ ~ 9 ~ . ~ 18 V BIBLIOGRAPHY ~ ~ ~ o ~ ~ t ~ ~ ~ ~ 1 ~ ~ ~ VI ~ APPENDIX ~ ~ o ~ ~ e ~ o ~ ~ o o ~ ~ ~ . 22 Px'ogl am Lisliiixlgs...
Mahouton Norbert Hounkonnou; André Ronveaux
2013-06-20
This paper addresses a general method of polynomial transformation of hypergeometric equations. Examples of some classical special equations of mathematical physics are generated. Heun's equation and exceptional Jacobi polynomials are also treated.
A HIGH ORDER NYSTROM METHOD FOR BOUNDARY INTEGRAL EQUATIONS ON AXISYMMETRIC SURFACES
Martinsson, Gunnar
. Whenever f can be represented with a moderate number of Fourier modes, the trans- formation of (1.1) to (1. Key words. boundary integral equations, high order discretization, body of revolution AMS subject of uncoupled small linear systems (one for each Fourier mode). Since the system matrices are dense, the gain
A hybrid formulation of map migration and wave-equation-based migration
Snieder, Roel
CWP-549 March 2006 A hybrid formulation of map migration and wave-equation-based migration using through a one-to- one mapping from the data to the image, known as map migration. Using building blocks in a map-migration-based procedure to image seismic data. Fo- cussing on sparsely representing the imaging
Numerical Analysis of a one dimensional Diffusion Equation for a single chamber Microbial Fuel Cell generation within our society. Microbial fuel cells (MFCs) represent a new form of renewable energy using a Linked Simulation Optimization (LSO) technique E521: Advanced Numerical Methods Eric A. Zielke
THE SELF-FINANCING EQUATION IN HIGH FREQUENCY RENE CARMONA AND KEVIN WEBSTER
Carmona, Rene
THE SELF-FINANCING EQUATION IN HIGH FREQUENCY MARKETS REN´E CARMONA AND KEVIN WEBSTER Abstract. High Frequency Trading (HFT) represents an ever growing pro- portion of all financial transactions]) on the divide between high and low frequency traders, M. O'Hara and co-authors identified a number of market
Electron temperature anisotropy instabilities represented by superposition of streams
Inglebert, A.; Ghizzo, A.; Reveille, T.; Bertrand, P. [IJL UMR 7198, Universite de Lorraine, BP 70239 F-54506 Vandoeuvre les Nancy (France); Califano, F. [Department of Physics, University of Pisa, Pisa (Italy)
2012-12-15
The generation of magnetic field, together with the electrostatic activity met in the saturation regime of the Weibel instability (WI), is investigated by means of an analytical multi-stream model in a Hamiltonian framework. Taking advantage from the invariance of the generalized canonical momentum, the model allows to reduce the full kinetic 1D2V Vlasov equation into several 1D1V equations while keeping its kinetic character. The multi-stream model provides a more complete and accurate picture of the Weibel instability, because it is possible to separate the specific contribution of each stream during the development of the Weibel instability. An interesting result for the multi-stream mode is a lower cost in the perpendicular treatment of the p{sub y} momentum component since no differential operator associated with some approximate numerical scheme has to be carried out on this variable. Indeed, a small number of streams or particle classes are sufficient to correctly describe the magnetic field generation and the mixed electrostatic- electromagnetic nature of the instability.
Defining And Characterizing Sample Representativeness For DWPF Melter Feed Samples
Shine, E. P.; Poirier, M. R.
2013-10-29
Representative sampling is important throughout the Defense Waste Processing Facility (DWPF) process, and the demonstrated success of the DWPF process to achieve glass product quality over the past two decades is a direct result of the quality of information obtained from the process. The objective of this report was to present sampling methods that the Savannah River Site (SRS) used to qualify waste being dispositioned at the DWPF. The goal was to emphasize the methodology, not a list of outcomes from those studies. This methodology includes proven methods for taking representative samples, the use of controlled analytical methods, and data interpretation and reporting that considers the uncertainty of all error sources. Numerous sampling studies were conducted during the development of the DWPF process and still continue to be performed in order to evaluate options for process improvement. Study designs were based on use of statistical tools applicable to the determination of uncertainties associated with the data needs. Successful designs are apt to be repeated, so this report chose only to include prototypic case studies that typify the characteristics of frequently used designs. Case studies have been presented for studying in-tank homogeneity, evaluating the suitability of sampler systems, determining factors that affect mixing and sampling, comparing the final waste glass product chemical composition and durability to that of the glass pour stream sample and other samples from process vessels, and assessing the uniformity of the chemical composition in the waste glass product. Many of these studies efficiently addressed more than one of these areas of concern associated with demonstrating sample representativeness and provide examples of statistical tools in use for DWPF. The time when many of these designs were implemented was in an age when the sampling ideas of Pierre Gy were not as widespread as they are today. Nonetheless, the engineers and statisticians used carefully thought out designs that systematically and economically provided plans for data collection from the DWPF process. Key shared features of the sampling designs used at DWPF and the Gy sampling methodology were the specification of a standard for sample representativeness, an investigation that produced data from the process to study the sampling function, and a decision framework used to assess whether the specification was met based on the data. Without going into detail with regard to the seven errors identified by Pierre Gy, as excellent summaries are readily available such as Pitard [1989] and Smith [2001], SRS engineers understood, for example, that samplers can be biased (Gy?s extraction error), and developed plans to mitigate those biases. Experiments that compared installed samplers with more representative samples obtained directly from the tank may not have resulted in systematically partitioning sampling errors into the now well-known error categories of Gy, but did provide overall information on the suitability of sampling systems. Most of the designs in this report are related to the DWPF vessels, not the large SRS Tank Farm tanks. Samples from the DWPF Slurry Mix Evaporator (SME), which contains the feed to the DWPF melter, are characterized using standardized analytical methods with known uncertainty. The analytical error is combined with the established error from sampling and processing in DWPF to determine the melter feed composition. This composition is used with the known uncertainty of the models in the Product Composition Control System (PCCS) to ensure that the wasteform that is produced is comfortably within the acceptable processing and product performance region. Having the advantage of many years of processing that meets the waste glass product acceptance criteria, the DWPF process has provided a considerable amount of data about itself in addition to the data from many special studies. Demonstrating representative sampling directly from the large Tank Farm tanks is a difficult, if not unsolvable enterprise due to li
Optimization and Nonlinear Equations Gordon K. Smyth
Smyth, Gordon K.
Optimization and Nonlinear Equations Gordon K. Smyth Bioinformatics Division, Walter and Eliza Hall, University of Melbourne, Victoria, Australia 12 November 2014 Abstract Optimization means finding. Many optimization al- gorithms are derived from algorithms that solve the nonlinear equations defined
18.03 Differential Equations, Spring 2006
Miller, Haynes
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary ...
Ordinary Differential Equation: Chapter 2.5
2014-09-11
Suppose the maximum population allowed is 500. Simple choice of h(y) = 20(1 ? y/500) leads dy dt. = 20(1 ? y/500)y. This type equation called Logistic equation.
Padé interpolation for elliptic Painlevé equation
Masatoshi Noumi; Satoshi Tsujimoto; Yasuhiko Yamada
2012-08-08
An interpolation problem related to the elliptic Painlev\\'e equation is formulated and solved. A simple form of the elliptic Painlev\\'e equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also given.
Facility Representative of the Year Award | Department of Energy
Broader source: Energy.gov (indexed) [DOE]
AFDC Printable Version Share this resource Send a link to EERE: Alternative Fuels Data Center Home Page to someone by E-mail Share EERE: Alternative Fuels Data Center Home Page on Facebook Tweet about EERE: Alternative Fuels Data Center Home Page on Twitter Bookmark EERE: Alternative Fuels Data Center Homesum_a_epg0_fpd_mmcf_m.xls" ,"Available from WebQuantity of Natural GasAdjustmentsShirleyEnergy A plug-inPPLforLDRD Report to Congress MoreHyd rog enOffice of NuclearRepresentative
Deriving Mathisson - Papapetrou equations from relativistic pseudomechanics
R. R. Lompay
2005-03-12
It is shown that the equations of motion of a test point particle with spin in a given gravitational field, so called Mathisson - Papapetrou equations, can be derived from Euler - Lagrange equations of the relativistic pseudomechanics -- relativistic mechanics, which side by side uses the conventional (commuting) and Grassmannian (anticommuting) variables. In this approach the known difficulties of the Mathisson - Papapetrou equations, namely, the problem of the choice of supplementary conditions and the problem of higher derivatives are not appear.
A Periodic Solution to Impulsive Logistic Equation
Gyong-Chol Kim; Hyong-Chol O; Sang-Mun Kim; Chol Kim
2014-03-28
In this paper is provided a new representation of periodic solution to the impulsive Logistic equation considered in [7].
Boundary conditions for the subdiffusion equation
Shkilev, V. P.
2013-04-15
The boundary conditions for the subdiffusion equations are formulated using the continuous-time random walk model, as well as several versions of the random walk model on an irregular lattice. It is shown that the boundary conditions for the same equation in different models have different forms, and this difference considerably affects the solutions of this equation.
Equation determines pressure drop in coiled tubing
Yang, Y.S.
1995-12-04
A single equation can determine the pressure drop in wells with laminar, transitional, and turbulent incompressible fluid flow in coiled tubing or other steel tubulars. The single equation is useful, especially in computer-aided design and operations. The equation is derived and illustrated by an example.
The Schrodinger equation and negative energies
S. Bruce
2008-06-30
We present a nonrelativistic wave equation for the electron in (3+1)-dimensions which includes negative-energy eigenstates. We solve this equation for three well-known instances, reobtaining the corresponding Pauli equation (but including negative-energy eigenstates) in each case.
On non commutative sinh-Gordon Equation
U. Saleem; M. Siddiq; M. Hassan
2006-05-10
We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon equation with extra constraints, which can be expressed as global conserved currents.
Nonlinear extension of the CCFM equation
Krzysztof Kutak
2012-06-06
In order to study such effects like parton saturation in final states at the LHC one of the approaches is to combine physics of the BK and the CCFM evolution equations. We report on recently obtained resummed form of the BK equation and nonlinear extension of the CCFM equation.
Quantum-mechanical Landau-Lifshitz equation
D. Yearchuck; Y. Yerchak
2008-01-09
Quantum-mechanical analogue of Landau-Lifshitz equation has been derived. It has been established that Landau-Lifshitz equation is fundamental physical equation underlying the dynamics of spectroscopic transitions and transitional phenomena. New phenomenon is predicted: electrical spin wave resonance (ESWR) being to be electrical analogue of magnetic spin wave resonance.
Model solution State variable model: differential equation
Limburg, Karin E.
2/26/2014 1 Model solution State variable model: differential equation Models a rate of change equation General solution: the antiderivative Particular solution: require initial and boundary conditions up the general solution to a differential equation in a book Solve for initial and boundary
On a Modified Klein Gordon Equation
B. S. Lakshmi
2009-08-09
We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example,we get solutions that mimic the Harmonic oscillator energy levels, surprisingly. An equation similar to the beam equation is obtained in the process.
Wave equations with energy dependent potentials
J. Formanek; R. J. Lombard; J. Mares
2003-09-22
We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which conditions such equations can be handled as evolution equation of quantum theory with an energy dependent potential. Once these conditions are met, such theory can be transformed into ordinary quantum theory.
Universal Equation for Efimov States
Eric Braaten; H. -W. Hammer; M. Kusunoki
2003-03-13
Efimov states are a sequence of shallow 3-body bound states that arise when the 2-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a 3-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of 4He atoms. We also extend Efimov's theory to include the effects of deep 2-body bound states, which give widths to the Efimov states.
Universal equation for Efimov states
Braaten, Eric; Hammer, H.-W.; Kusunoki, M.
2003-02-01
Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of {sup 4}He atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.
The Square Root Depth Wave Equations
Colin C. Cotter; Darryl D. Holm; James R. Percival
2009-12-11
We introduce a set of coupled equations for multilayer water waves that removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the presence of shear. The new well-posed equations are Hamiltonian and in the absence of imposed background shear they retain the same travelling wave solutions as MGN. We call the new model the Square Root Depth equations, from the modified form of their kinetic energy of vertical motion. Our numerical results show how the Square Root Depth equations model the effects of multilayer wave propagation and interaction, with and without shear.
Equator-S observations of He+ energization by EMIC waves in the
Carlson, Charles W.
Equator-S observations of He+ energization by EMIC waves in the dawnside equatorial magnetosphere C Equator-S observations of He+ energization by electromagnetic ion cyclotron (EMIC) waves in the dawn side. Introduction [2] Observations suggesting He+ energization by electromag- netic ion cyclotron (EMIC) waves
The properties of the first equation of the Vlasov chain of equations
E. E. Perepelkin; B. I. Sadovnikov; N. G. Inozemtseva
2015-02-06
A mathematically rigorous derivation of the first Vlasov equation as a well-known Schr\\"odinger equation for the probabilistic description of a system and families of the classic diffusion equations and heat conduction for the deterministic description of physical systems was inferred. A physical meaning of the phase of the wave function which is a scalar potential of the probabilistic flow velocity is demonstrated. Occurrence of the velocity potential vortex component leads to the Pauli equation for one of the spinar components. A scheme of the construction of the Schr\\"odinger equation solving from the Vlasov equation solving and vice-versa is shown. A process of introduction of the potential to the Schr\\"odinger equation and its interpretation are given. The analysis of the potential properties gives us the Maxwell equation, the equation of the kinematic point movement, and the movement of the medium within electromagnetic fields equation.
Maxwell equations and the redundant gauge degree of freedom
Chun Wa Wong
2009-07-17
On transformation to the Fourier space $({\\bf k}, \\omega)$, the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the direction of the wave vector {\\bf k}. The concepts of wave motion, causality, scalar and vector potentials and their gauge transformations in vacuum and in materials can also be discussed from an elementary perspective. In particular, the excessive freedom of choice associated with the gauge dependence of the scalar and the longitudinal vector potentials stands out with clarity in Fourier spaces. Since these potentials are introduced to represent the instantaneous longitudinal electric field, the actual cancellation in the latter of causal contributions arising from these potentials separately in most velocity gauges becomes an important issue. This cancellation is explicitly demonstrated both in the Fourier space, and for pedagogical reasons again in space-time. The physical origin of the gauge degree of freedom in the masslessness of the photon, the quantum of electromagnetic wave, is elucidated with the help of special relativity and quantum mechanics.
The Korarchaeota: Archaeal orphans representing an ancestral lineage of life
Elkins, James G.; Kunin, Victor; Anderson, Iain; Barry, Kerrie; Goltsman, Eugene; Lapidus, Alla; Hedlund, Brian; Hugenholtz, Phil; Kyrpides, Nikos; Graham, David; Keller, Martin; Wanner, Gerhard; Richardson, Paul; Stetter, Karl O.
2007-05-01
Based on conserved cellular properties, all life on Earth can be grouped into different phyla which belong to the primary domains Bacteria, Archaea, and Eukarya. However, tracing back their evolutionary relationships has been impeded by horizontal gene transfer and gene loss. Within the Archaea, the kingdoms Crenarchaeota and Euryarchaeota exhibit a profound divergence. In order to elucidate the evolution of these two major kingdoms, representatives of more deeply diverged lineages would be required. Based on their environmental small subunit ribosomal (ss RNA) sequences, the Korarchaeota had been originally suggested to have an ancestral relationship to all known Archaea although this assessment has been refuted. Here we describe the cultivation and initial characterization of the first member of the Korarchaeota, highly unusual, ultrathin filamentous cells about 0.16 {micro}m in diameter. A complete genome sequence obtained from enrichment cultures revealed an unprecedented combination of signature genes which were thought to be characteristic of either the Crenarchaeota, Euryarchaeota, or Eukarya. Cell division appears to be mediated through a FtsZ-dependent mechanism which is highly conserved throughout the Bacteria and Euryarchaeota. An rpb8 subunit of the DNA-dependent RNA polymerase was identified which is absent from other Archaea and has been described as a eukaryotic signature gene. In addition, the representative organism possesses a ribosome structure typical for members of the Crenarchaeota. Based on its gene complement, this lineage likely diverged near the separation of the two major kingdoms of Archaea. Further investigations of these unique organisms may shed additional light onto the evolution of extant life.
Time-periodic solutions of the Benjamin-Ono equation
Ambrose, D.M.
2009-01-01
application to Benjamin Ono equation. Chinese Physics, 14(solutions of Hamiltonian equations. In Dynamics and Pro-quelques generalisations de l’equation de Korteweg-deVries.
Statistically designed study of the variables and parameters of carbon dioxide equations of state
Donohue, M.D.; Naiman, D.Q.; Jin, Gang; Loehe, J.R.
1991-05-01
Carbon dioxide is used widely in enhanced oil recovery (EOR) processes to maximize the production of crude oil from aging and nearly depleted oil wells. Carbon dioxide also is encountered in many processes related to oil recovery. Accurate representations of the properties of carbon dioxide, and its mixtures with hydrocarbons, play a critical role in a number of enhanced oil recovery operations. One of the first tasks of this project was to select an equation of state to calculate the properties of carbon dioxide and its mixtures. The equations simplicity, accuracy, and reliability in representing phase behavior and thermodynamic properties of mixtures containing carbon dioxide with hydrocarbons at conditions relevant to enhanced oil recovery were taken into account. We also have determined the thermodynamic properties that are important to enhanced oil recovery and the ranges of temperature, pressure and composition that are important. We chose twelve equations of state for preliminary studies to be evaluated against these criteria. All of these equations were tested for pure carbon dioxide and eleven were tested for pure alkanes and their mixtures with carbon dioxide. Two equations, the ALS equation and the ESD equation, were selected for detailed statistical analysis. 54 refs., 41 figs., 36 tabs.
1 Ma 15200 Lesson 18 Section 1.7 I Representing an Inequality ...
charlotb
2010-10-04
1. Ma 15200 Lesson 18 Section 1.7. I. Representing an Inequality. There are 3 ways to represent an inequality. (1) Using the inequality symbol (sometime.
1 Ma 15200 Lesson 18 Section 1.7 I Representing an Inequality ...
charlotb
2011-02-22
1. Ma 15200 Lesson 18 Section 1.7. I. Representing an Inequality. There are 3 ways to represent an inequality. (1) Using the inequality symbol (sometime.
Simulating a Nationally Representative Housing Sample Using EnergyPlus
Hopkins, Asa S.; Lekov, Alex; Lutz, James; Rosenquist, Gregory; Gu, Lixing
2011-03-04
This report presents a new simulation tool under development at Lawrence Berkeley National Laboratory (LBNL). This tool uses EnergyPlus to simulate each single-family home in the Residential Energy Consumption Survey (RECS), and generates a calibrated, nationally representative set of simulated homes whose energy use is statistically indistinguishable from the energy use of the single-family homes in the RECS sample. This research builds upon earlier work by Ritchard et al. for the Gas Research Institute and Huang et al. for LBNL. A representative national sample allows us to evaluate the variance in energy use between individual homes, regions, or other subsamples; using this tool, we can also evaluate how that variance affects the impacts of potential policies. The RECS contains information regarding the construction and location of each sampled home, as well as its appliances and other energy-using equipment. We combined this data with the home simulation prototypes developed by Huang et al. to simulate homes that match the RECS sample wherever possible. Where data was not available, we used distributions, calibrated using the RECS energy use data. Each home was assigned a best-fit location for the purposes of weather and some construction characteristics. RECS provides some detail on the type and age of heating, ventilation, and air-conditioning (HVAC) equipment in each home; we developed EnergyPlus models capable of reproducing the variety of technologies and efficiencies represented in the national sample. This includes electric, gas, and oil furnaces, central and window air conditioners, central heat pumps, and baseboard heaters. We also developed a model of duct system performance, based on in-home measurements, and integrated this with fan performance to capture the energy use of single- and variable-speed furnace fans, as well as the interaction of duct and fan performance with the efficiency of heating and cooling equipment. Comparison with RECS revealed that EnergyPlus did not capture the heating-side behavior of heat pumps particularly accurately, and that our simple oil furnace and boiler models needed significant recalibration to fit with RECS. Simulating the full RECS sample on a single computer would take many hours, so we used the 'cloud computing' services provided by Amazon.com to simulate dozens of homes at once. This enabled us to simulate the full RECS sample, including multiple versions of each home to evaluate the impact of marginal changes, in less than 3 hours. Once the tool was calibrated, we were able to address several policy questions. We made a simple measurement of the heat replacement effect and showed that the net effect of heat replacement on primary energy use is likely to be less than 5%, relative to appliance-only measures of energy savings. Fuel switching could be significant, however. We also evaluated the national and regional impacts of a variety of 'overnight' changes in building characteristics or occupant behavior, including lighting, home insulation and sealing, HVAC system efficiency, and thermostat settings. For example, our model shows that the combination of increased home insulation and better sealed building shells could reduce residential natural gas use by 34.5% and electricity use by 6.5%, and a 1 degree rise in summer thermostat settings could save 2.1% of home electricity use. These results vary by region, and we present results for each U.S. Census division. We conclude by offering proposals for future work to improve the tool. Some proposed future work includes: comparing the simulated energy use data with the monthly RECS bill data; better capturing the variation in behavior between households, especially as it relates to occupancy and schedules; improving the characterization of recent construction and its regional variation; and extending the general framework of this simulation tool to capture multifamily housing units, such as apartment buildings.
Modified Bernoulli Equation for Use with Combined Electro-Osmotic and Pressure-Driven Microflows
Adams, Thomas M
2012-01-01
In this paper we present electro-osmotic (EO) flow within a more traditional fluid mechanics framework. Specifically, the modified Bernoulli equation (viz. the energy equation, the mechanical energy equation, the pipe flow equation, etc.) is shown to be applicable to EO flows if an electrical potential energy term is also included. The form of the loss term in the modified Bernoulli equation is unaffected by the presence of an electric field; i.e., the loss term still represents the effect of wall shear stress, which can be represented via a friction factor. We show that that the friction factor for pure EO flow (no applied pressure gradient) varies inversely with the Reynolds number based on the Debeye length of the electric double layer. Expressions for friction factor for combined laminar pressure-driven and EO flow are also given. These are shown to be functions of Reynolds number and geometry, as well as the relative strength of the applied electric field to the applied pressure gradient.
Greening the U.S. House of Representatives
Diamond, Rick; Diamond, Rick; Payne, Christopher
2008-03-01
The Greening the Capitol initiative was launched in March, 2007 with the threefold goals of making the U.S. House of Representatives: 1) carbon neutral within 18 months, 2) reducing energy use by 50percent in ten years, and 3) becoming a model of sustainable operations. We report on the recommendations to meet these goals, looking at the targets of opportunity at the Capitol Power Plant, the existing buildings, and the overall operations of the complex. Our findings have shown that these goals are achievable, and that through an integrated approach the savings in carbon and energy can be met. Specific examples include the lighting retrofits in the House offices, parking areas, and the Capitol dome; the retrofits to the HVAC systems and controls, including duct sealing, improving the efficiency of the energy and water use in the food service areas; and improved operations of the steam and chilled water distribution system. A key aspect has been better tracking and feedback to the building operators of the actual energy consumption. We report on the technical opportunities presented by these historic and symbolic buildings in becoming models of sustainability.
Darboux transformation for the NLS equation
Aktosun, Tuncay; Mee, Cornelis van der
2010-03-08
We analyze a certain class of integral equations associated with Marchenko equations and Gel'fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unperturbed quantities and the finite-rank perturbation. We show that this result provides a fundamental approach to derive Darboux transformations for various systems of ordinary differential operators. We illustrate our theory by providing the explicit Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a simple discrete eigenvalue is added to the spectrum, and thus we also provide a one-parameter family of Darboux transformations for the nonlinear Schroedinger equation.
Riemann-Liouville Fractional Einstein Field Equations
Joakim Munkhammar
2010-03-18
In this paper we establish a fractional generalization of Einstein field equations based on the Riemann-Liouville fractional generalization of the ordinary differential operator $\\partial_\\mu$. We show some elementary properties and prove that the field equations correspond to the regular Einstein field equations for the fractional order $\\alpha = 1$. In addition to this we show that the field theory is inherently non-local in this approach. We also derive the linear field equations and show that they are a generalized version of the time fractional diffusion-wave equation. We show that in the Newtonian limit a fractional version of Poisson's equation for gravity arises. Finally we conclude open problems such as the relation of the non-locality of this theory to quantum field theories and the possible relation to fractional mechanics.
Notes On The Klein-Gordon Equation
Fredrick Michael
2010-04-09
In this article, we derive the scalar parametrized Klein-Gordon equation from the formal information theory framework. The least biased probability distribution is obtained, and the scalar equation is recast in terms of a Fokker-Planck equation in terms of the imaginary time, or a Schroedinger equation for the proper time. This method yields the Green's function parametrized by an evolution parameter. The derivation can then allow the use of potentials as constraints along with the Hamiltonian or moments of the evolution. The information theoretic, analogously the maximum entropy method, also allows one to examine the possibility of utilizing generalized and non-extensive statistics in the derivation. This approach yields non-linear evolution in the parametrized Klein-Gordon partial differential equations. Furthermore, we examine the Klein-Gordon equation in curved space-time, and we compare our results to the results of Schwinger and Dewitt obtained from path integral approaches.
Some generalizations of the Raychaudhuri equation
Abreu, Gabriel
2010-01-01
The Raychaudhuri equation has seen extensive use in general relativity, most notably in the development of various singularity theorems. In this rather technical article we shall generalize the Raychaudhuri equation in several ways. First an improved version of the standard timelike Raychaudhuri equation is developed, where several key terms are lumped together as a divergence. This already has a number of interesting applications, both within the ADM formalism and elsewhere. Second, a spacelike version of the Raychaudhuri equation is briefly discussed. Third, a version of the Raychaudhuri equation is developed that does not depend on the use of normalized congruences. This leads to useful formulae for the "diagonal" part of the Ricci tensor. Fourth, a "two vector" version of the Raychaudhuri equation is developed that uses two congruences to effectively extract "off diagonal" information concerning the Ricci tensor.
Eigen Equation of the Nonlinear Spinor
Ying-Qiu Gu; Ta-tsien Li
2007-04-04
How to effectively solve the eigen solutions of the nonlinear spinor field equation coupling with some other interaction fields is important to understand the behavior of the elementary particles. In this paper, we derive a simplified form of the eigen equation of the nonlinear spinor, and then propose a scheme to solve their numerical solutions. This simplified equation has elegant and neat structure, which is more convenient for both theoretical analysis and numerical computation.
Nuclear Scissors with Pairing and Continuity Equation
E. B. Balbutsev; L. A. Malov; P. Schuck; M. Urban
2008-10-29
The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low lying modes (including scissors) are studied with the help of the Wigner Function Moments (WFM) method generalized to take into account pair correlations. Equations of motion for collective variables are derived on the basis of the Time Dependent Hartree-Fock-Bogoliubov (TDHFB) equations in the harmonic oscillator model with quadrupole-quadrupole (QQ) residual interaction and a Gaussian pairing force. Special care is taken of the continuity equation.
A MULTIDIMENSIONAL NONLINEAR SIXTH-ORDER QUANTUM DIFFUSION EQUATION
heat equation tn = n. The second one is the fourth-order DerridaLebowitzSpeerSpohn (DLSS) equation
A New Integral Equation for the Spheroidal equations in case of m equal 1
Guihua Tian; Shuquan Zhong
2012-01-05
The spheroidal wave functions are investigated in the case m=1. The integral equation is obtained for them. For the two kinds of eigenvalues in the differential and corresponding integral equations, the relation between them are given explicitly. Though there are already some integral equations for the spheroidal equations, the relation between their two kinds of eigenvalues is not known till now. This is the great advantage of our integral equation, which will provide useful information through the study of the integral equation. Also an example is given for the special case, which shows another way to study the eigenvalue problem.
Stochastic Master Equations in Thermal Environment
S Attal; C Pellegrini
2010-04-20
We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. At zero temperature it is well-known that one obtains stochastic differential equations of jump-diffusion type. At strictly positive temperature, we show that only pure diffusion type equations are relevant.
An acoustic wave equation based on viscoelasticity
Andrzej Hanyga
2014-01-30
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are completely monotonic. The acoustic equation differs significantly from the equations proposed by Szabo (1994) and in several other papers. Integral representations of dispersion and attenuation are derived. General properties and asymptotic behavior of attenuation and dispersion in the low and high frequency range are studied. The results are compatible with experiments. The relation between the asymptotic properties of attenuation and wavefront singularities is examined. The theory is applied to some classes of viscoelastic models and to the quasi-linear attenuation reported in seismology.
Electromagnetic Media with no Dispersion Equation
Ismo V. Lindell; Alberto Favaro
2013-03-25
It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e., that the dispersion equation is satisfied identically for any wave vector. In the present paper, a more systematic study to define classes of media with no dispersion equation is attempted. The analysis makes use of coordinate-free four-dimensional formalism in terms of multivectors, multiforms and dyadics.
Localized Induction Equation for Stretched Vortex Filament
Kimiaki Konno; Hiroshi Kakuhata
2006-03-02
We study numerically the motion of the stretched vortex filaments by using the localized induction equation with the stretch and that without the stretch.
A counterexample against the Vlasov equation
C. Y. Chen
2009-04-19
A simple counterexample against the Vlasov equation is put forward, in which a magnetized plasma is perturbed by an electromagnetic standing wave.
Linear Equation in Finite Dimensional Algebra
Aleks Kleyn
2012-04-30
In the paper I considered methods for solving equations of the form axb+cxd=e in the algebra which is finite dimensional over the field.
Quadratic Equation over Associative D-Algebra
Aleks Kleyn
2015-05-30
In this paper, I treat quadratic equation over associative $D$-algebra. In quaternion algebra $H$, the equation $x^2=a$ has either $2$ roots, or infinitely many roots. Since $a\\in R$, $aequation has infinitely many roots. Otherwise, the equation has roots $x_1$, $x_2$, $x_2=-x_1$. I considered different forms of the Viete's theorem and a possibility to apply the method of completing the square. Assumed the hypothesis that, in noncommutative algebra, the equation $$(x-b)(x-a)+(x-a)(x-c)=0$$ $b\
Nonequilibrium Spin Magnetization Quantum Transport Equations
Buot, F A; Otadoy, R E S; Villarin, D L
2011-01-01
The classical Bloch equations of spin magnetization transport is extended to fully time-dependent and highly-nonlinear nonequilibrium quantum distribution function (QDF) transport equations. The leading terms consist of the Boltzmann kinetic equation with spin-orbit coupling in a magnetic field together with spin-dependent scattering terms which do not have any classical analogue, but should incorporate the spatio-temporal-dependent phase-space dynamics of Elliot-Yafet and D'yakonov-Perel scatterings. The resulting magnetization QDF transport equation serves as a foundation for computational spintronic and nanomagnetic device applications, in performing simulation of ultrafast-switching-speed/low-power performance and reliability analyses.
Super compact equation for water waves
Dyachenko, A I; Zakharov, V E
2015-01-01
We derive very simple compact equation for gravity water waves which includes nonlinear wave term (`a la NLSE) and advection term (may results in wave breaking).
Scalable Equation of State Capability
Epperly, T W; Fritsch, F N; Norquist, P D; Sanford, L A
2007-12-03
The purpose of this techbase project was to investigate the use of parallel array data types to reduce the memory footprint of the Livermore Equation Of State (LEOS) library. Addressing the memory scalability of LEOS is necessary to run large scientific simulations on IBM BG/L and future architectures with low memory per processing core. We considered using normal MPI, one-sided MPI, and Global Arrays to manage the distributed array and ended up choosing Global Arrays because it was the only communication library that provided the level of asynchronous access required. To reduce the runtime overhead using a parallel array data structure, a least recently used (LRU) caching algorithm was used to provide a local cache of commonly used parts of the parallel array. The approach was initially implemented in a isolated copy of LEOS and was later integrated into the main trunk of the LEOS Subversion repository. The approach was tested using a simple test. Testing indicated that the approach was feasible, and the simple LRU caching had a 86% hit rate.
Comment on ``Thermodynamically Admissible 13 Moment Equations from the Boltzmann Equation''
, they do not include classical hydrodynam- ics in the limit of small Knudsen numbers. The hydro- dynamic to the equations of hydrodynamics in the limit of small Knudsen numbers. Presently, the R13 equations have
Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation
Sergei V. Zakharov
2015-01-12
The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.
CONTROL VALVE TESTING PROCEDURES AND EQUATIONS
Rahmeyer, William J.
APPENDIX A CONTROL VALVE TESTING PROCEDURES AND EQUATIONS FOR LIQUID FLOWS #12;APPENDIX A CONTROL VALVE TESTING PROCEDURES AND EQUATIONS FOR LIQUID FLOWS 2 Cv Q P Sg net gpm net = / Cv = Q P / Sg 75 is used to relate the pressure loss of a valve to the discharge of the valve at a given valve opening
Optimization and Nonlinear Equations Gordon K. Smyth
Smyth, Gordon K.
Optimization and Nonlinear Equations Gordon K. Smyth May 1997 Optimization means to find that value of x which max imizes or minimizes a given function f(x). The idea of optimization goes to the heart with respect to the components of x. Except in linear cases, optimization and equation solving invariably
The Papapetrou equations and supplementary conditions
O. B. Karpov
2004-06-02
On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin in a circular orbit is considered. An expression for the spin-orbit force in a post-Newtonian approximation is investigated.
A Piece of Magic The Dirac Equation
Satija, Indu
Â·ss destruction nor generators of inexhaustible energy entered his ken. Of all the equations of physics, perhaps-five-year-old recent convert from electrical engineering to theoretical physics, produced a remarkable equation theoretical imperatives (some of which we now know to be wrong). Dirac sought to embody these principles
Switched differential algebraic equations Stephan Trenn
Trenn, Stephan
Switched differential algebraic equations Stephan Trenn Abstract In this chapter an electrical circuit with switches is modeled as a switched differential algebraic equation (switched DAE), i.e. each is the input. The resulting time-variance follows from the action of the switches present in the circuit
NOTE / NOTE Allometric equations for young northern
Battles, John
. Vadeboncoeur, Mary A. Arthur, Russell D. Briggs, and Carrie R. Levine Abstract: Estimates of aboveground-specific equations for estimating aboveground biomass Farrah R. Fatemi, Ruth D. Yanai, Steven P. Hamburg, Matthew A relationships. Despite the widespread use of this approach, there is little information about whether equations
Derivation of a Stochastic Neutron Transport Equation
Edward J. Allen
2010-04-14
Stochastic difference equations and a stochastic partial differential equation (SPDE) are simultaneously derived for the time-dependent neutron angular density in a general three-dimensional medium where the neutron angular density is a function of position, direction, energy, and time. Special cases of the equations are given such as transport in one-dimensional plane geometry with isotropic scattering and transport in a homogeneous medium. The stochastic equations are derived from basic principles, i.e., from the changes that occur in a small time interval. Stochastic difference equations of the neutron angular density are constructed, taking into account the inherent randomness in scatters, absorptions, and source neutrons. As the time interval decreases, the stochastic difference equations lead to a system of Ito stochastic differential equations (SDEs). As the energy, direction, and position intervals decrease, an SPDE is derived for the neutron angular density. Comparisons between numerical solutions of the stochastic difference equations and independently formulated Monte Carlo calculations support the accuracy of the derivations.
Hopf algebras and Dyson-Schwinger equations
Stefan Weinzierl
2015-06-30
In these lectures I discuss Hopf algebras and Dyson-Schwinger equations. The lectures start with an introduction to Hopf algebras, followed by a review where Hopf algebras occur in particles physics. The final part of these lectures is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
Proca Equation for Attosecond Electron Pulses
Magdalena Pelc; Janina Marciak-Kozlowska; Miroslaw Kozlowski
2008-03-03
In this paper the heat transport of attosecond electron pulses is investigated. It is shown that attosecond electrons can propagate as thermal waves or diffused as particle conglommerates, Proca equation as type equation for the thermal transport of the attosecond electron pulsem is formulated
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
Atkinson, Kendall
of numerical methods for calculating fixed points of nonlinear integral operators. The emphasis is on general differential equations, and the methods used are very different than those used for Fredholm integral operatorsJOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS Volume 4, Number 1, Winter 1992 A SURVEY
DELAY DIFFERENTIAL EQUATIONS IN SINGLE SPECIES DYNAMICS
Ruan, Shigui
dynamics. Let x(t) denote the population size at time t; let b and d denote the birth rate and death rate Equations 10. Periodicity 11. State Dependent Delays 12. Diffusive Models with Delay References O. Arino et rate of the population. The solution of equation (1.1) with an initial population x(0) = x0 is given
Comment on ``Discrete Boltzmann Equation for Microfluidics''
Luo, Li-Shi
Comment on ``Discrete Boltzmann Equation for Microfluidics'' In a recent Letter [1], Li and Kwok use a lattice Boltzmann equation (LBE) for microfluidics. Their main claim is that an LBE model for microfluidics can be constructed based on the ``Bhatnagar-Gross-Kooky [sic]'' model by including ``the
Diffractive Nonlinear Geometrical Optics for Variational Wave Equations and the Einstein Equations
Giuseppe Ali; John K. Hunter
2005-11-02
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly nonlinear geometrical optics for the Einstein equations with nonlinear geometrical optics theories for variational wave equations.
The generalized Schrödinger–Langevin equation
Bargueño, Pedro; Miret-Artés, Salvador
2014-07-15
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinger–Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: •We generalize the Kostin equation for arbitrary system–bath coupling. •This generalization is developed both in the Schrödinger and Bohmian formalisms. •We write the generalized Kostin equation for two measurement problems. •We reformulate the generalized uncertainty principle in terms of this equation.
Klein-Gordon Equation in Hydrodynamical Form
Cheuk-Yin Wong
2010-12-22
We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for particle and antiparticle wave function components with positive probability densities. We find that the equation of motion for the probability densities is in the form of relativistic hydrodynamics where various forces have their classical counterparts, with the additional element of the quantum stress tensor that depends on the derivatives of the amplitude of the wave function. We derive the equation of motion for the Wigner function and we find that its approximate classical weak-field limit coincides with the equation of motion for the distribution function in the collisionless kinetic theory.
Gamba, Irene M.; Haack, Jeffrey R.
2014-08-01
We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.
Examination of Hydrate Formation Methods: Trying to Create Representative Samples
Kneafsey, T.J.; Rees, E.V.L.; Nakagawa, S.; Kwon, T.-H.
2011-04-01
Forming representative gas hydrate-bearing laboratory samples is important so that the properties of these materials may be measured, while controlling the composition and other variables. Natural samples are rare, and have often experienced pressure and temperature changes that may affect the property to be measured [Waite et al., 2008]. Forming methane hydrate samples in the laboratory has been done a number of ways, each having advantages and disadvantages. The ice-to-hydrate method [Stern et al., 1996], contacts melting ice with methane at the appropriate pressure to form hydrate. The hydrate can then be crushed and mixed with mineral grains under controlled conditions, and then compacted to create laboratory samples of methane hydrate in a mineral medium. The hydrate in these samples will be part of the load-bearing frame of the medium. In the excess gas method [Handa and Stupin, 1992], water is distributed throughout a mineral medium (e.g. packed moist sand, drained sand, moistened silica gel, other porous media) and the mixture is brought to hydrate-stable conditions (chilled and pressurized with gas), allowing hydrate to form. This method typically produces grain-cementing hydrate from pendular water in sand [Waite et al., 2004]. In the dissolved gas method [Tohidi et al., 2002], water with sufficient dissolved guest molecules is brought to hydrate-stable conditions where hydrate forms. In the laboratory, this is can be done by pre-dissolving the gas of interest in water and then introducing it to the sample under the appropriate conditions. With this method, it is easier to form hydrate from more soluble gases such as carbon dioxide. It is thought that this method more closely simulates the way most natural gas hydrate has formed. Laboratory implementation, however, is difficult, and sample formation is prohibitively time consuming [Minagawa et al., 2005; Spangenberg and Kulenkampff, 2005]. In another version of this technique, a specified quantity of gas is placed in a sample, then the sample is flooded with water and cooled [Priest et al., 2009]. We have performed a number of tests in which hydrate was formed and the uniformity of the hydrate formation was examined. These tests have primarily used a variety of modifications of the excess gas method to make the hydrate, although we have also used a version of the excess water technique. Early on, we found difficulties in creating uniform samples with a particular sand/ initial water saturation combination (F-110 Sand, {approx} 35% initial water saturation). In many of our tests we selected this combination intentionally to determine whether we could use a method to make the samples uniform. The following methods were examined: Excess gas, Freeze/thaw/form, Freeze/pressurize/thaw, Excess gas followed by water saturation, Excess water, Sand and kaolinite, Use of a nucleation enhancer (SnoMax), and Use of salt in the water. Below, each method, the underlying hypothesis, and our results are briefly presented, followed by a brief conclusion. Many of the hypotheses investigated are not our own, but were presented to us. Much of the data presented is from x-ray CT scanning our samples. The x-ray CT scanner provides a three-dimensional density map of our samples. From this map and the physics that is occurring in our samples, we are able to gain an understanding of the spatial nature of the processes that occur, and attribute them to the locations where they occur.
Solution of the Schrödinger equation making use of time-dependent constants of motion
G. F. Torres del Castillo
2015-03-18
It is shown that if a complete set of mutually commuting operators is formed by constants of motion, then, up to a factor that only depends on the time, each common eigenfunction of such operators is a solution of the Schr\\"odinger equation. In particular, the operators representing the initial values of the Cartesian coordinates of a particle are constants of motion that commute with each other and from their common eigenfunction one readily obtains the Green function.
Probabilistic Analysis of a Monod-type equation by use of a single chamber Microbial Fuel Cell
for our society. Microbial fuel cells (MFCs) represent a new form of renewable energy by convertingProbabilistic Analysis of a Monod-type equation by use of a single chamber Microbial Fuel Cell Eric A. Zielke December 9, 2005 #12;Abstract Renewable energy forms have become an increasing need
New wave equation for ultrarelativistic particles
Ginés R. Pérez Teruel
2014-12-15
Starting from first principles and general assumptions based on the energy-momentum relation of the Special Theory of Relativity we present a novel wave equation for ultrarelativistic matter. This wave equation arises when particles satisfy the condition, $p>>m$, i.e, when the energy-momentum relation can be approximated by, $E\\simeq p+\\frac{m^{2}}{2p}$. Interestingly enough, such as the Dirac equation, it is found that this wave equation includes spin in a natural way. Furthermore, the free solutions of this wave equation contain plane waves that are completely equivalent to those of the theory of neutrino oscillations. Therefore, the theory reproduces some standard results of the Dirac theory in the limit $p>>m$, but offers the possibility of an explicit Lorentz Invariance Violation of order, $\\mathcal{O}((mc)^{4}/p^{2})$. As a result, the theory could be useful to test small departures from Dirac equation and Lorentz Invariance at very high energies. On the other hand, the wave equation can also describe particles of spin 1 by a simple substitution of the spin operators, $\\boldsymbol{\\sigma}\\rightarrow\\boldsymbol{\\alpha}$. In addition, it naturally admits a Lagrangian formulation and a Hamiltonian formalism. We also discuss the associated conservation laws that arise through the symmetry transformations of the Lagrangian.
Uniqueness theorems for equations of Keldysh Type
Thomas H. Otway
2010-05-25
A fundamental result that characterizes elliptic-hyperbolic equations of Tricomi type, the uniqueness of classical solutions to the open Dirichlet problem, is extended to a large class of elliptic-hyperbolic equations of Keldysh type. The result implies the non-existence of classical solutions to the closed Dirichlet problem for this class of equations. A uniqueness theorem is also proven for a mixed Dirichlet-Neumann problem. A generalized uniqueness theorem for the adjoint operator leads to the existence of distribution solutions to the closed Dirichlet problem in a special case.
Integral equations of scattering in one dimension
Vania E. Barlette; Marcelo M. Leite; Sadhan K. Adhikari
2001-03-05
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem and unitarity relation. We illustrate the present approach with a Dirac delta potential.
Supersymmetric Ito equation: Bosonization and exact solutions
Ren Bo; Yu Jun [Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000 (China); Lin Ji [Institute of Nonlinear Physics, ZheJiang Normal University, Jinhua, 321004 (China)
2013-04-15
Based on the bosonization approach, the N=1 supersymmetric Ito (sIto) system is changed to a system of coupled bosonic equations. The approach can effectively avoid difficulties caused by intractable fermionic fields which are anticommuting. By solving the coupled bosonic equations, the traveling wave solutions of the sIto system are obtained with the mapping and deformation method. Some novel types of exact solutions for the supersymmetric system are constructed with the solutions and symmetries of the usual Ito equation. In the meanwhile, the similarity reduction solutions of the model are also studied with the Lie point symmetry theory.
Wave Propagation Theory 2.1 The Wave Equation
2 Wave Propagation Theory 2.1 The Wave Equation The wave equation in an ideal fluid can be derived from hydrodynamics and the adia- batic relation between pressure and density. The equation for conservation of mass, Euler's equation (Newton's 2nd Law), and the adiabatic equation of state are respec
Integral representation of solutions to Fuchsian system and Heun's equation
Kouichi Takemura
2007-07-09
We obtain integral representations of solutions to special cases of the Fuchsian system of differential equations and Heun's differential equation. In particular, we calculate the monodromy of solutions to the Fuchsian equation that corresponds to Picard's solution of the sixth Painlev\\'e equation, and to Heun's equation.
California at Santa Barbara, University of
National Center for Geographic Information and Analysis Measuring and Representing Accessibility in the Information Age A Specialist Meeting of Project Varenius' Geographies of the Information Society 19 ........................................................................................................11 Visualizing and Representing Information Space Within Geographic Information Science (GIS) Michael
Gregory H. Friedman: Before the U.S. House of Representatives...
Government Reform Gregory H. Friedman: Before the U.S. House of Representatives Committee on Government Reform March 20, 2003 Before the U.S. House of Representatives Committee on...
Lu, Zhiming
Representing aquifer architecture in macrodispersivity models with an analytical solution] The multi-dimensional transition probability model represents hydrofacies architecture in modeling aquifer heterogeneity. The structure of the aquifer architecture is mathematically characterized by a canonical
U.S. Energy Secretary Steven Chu, U.S. Representatives Larson...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
Steven Chu, U.S. Representatives Larson and Courtney to Visit Research Center in East Hartford U.S. Energy Secretary Steven Chu, U.S. Representatives Larson and Courtney...
Integral equations, fractional calculus and shift operator
D. Babusci; G. Dattoli; D. Sacchetti
2010-07-29
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the exponential shift operator.
Adaptive FE Methods for Conservation Equations
Hartmann, Ralf
Adaptive FE Methods for Conservation Equations Ralf Hartmann Abstract. We present an approach, University of Heidelberg. #12; 2 R. Hartmann by parts on each cell K results in X K2Th h (F (u); rv)K + (F (u
Generalized finite element method for Helmholtz equation
Hidajat, Realino Lulie
2009-05-15
This dissertation presents the Generalized Finite Element Method (GFEM) for the scalar Helmholtz equation, which describes the time harmonic acoustic wave propagation problem. We introduce several handbook functions for ...
MA262: Linear Algebra And Differential Equations
2015-02-23
Feb 23, 2015 ... carrying capacity, which models the maximal allowable population in an environment. A sketch. 9 ... mixig problems and electric circuits. 3.1 1st order ..... derivative, plug into the original equation and solve V . – A Bernoulli DE ...
Inverse Problems for Fractional Diffusion Equations
Zuo, Lihua
2013-06-21
; t > 0; (1.13) combined with the initial condition u(x; 0) = f(x); ?1 : u^t = ?s2u^; t > 0; u^(s; 0) = f^(s): Solving the above equation, we obtain u...
Electric-Magnetic Duality and WDVV Equations
B. de Wit; A. Marshakov
2001-06-11
We consider the associativity (or WDVV) equations in the form they appear in Seiberg-Witten theory and prove that they are covariant under generic electric-magnetic duality transformations. We discuss the consequences of this covariance from various perspectives.
ADAPTIVE DISCRETIZATION OF AN INTEGRODIFFERENTIAL EQUATION
Larsson, Stig
ADAPTIVE DISCRETIZATION OF AN INTEGROÂDIFFERENTIAL EQUATION MODELING QUASIÂSTATIC FRACTIONAL ORDER VISCOELASTICITY Klas Adolfsson # Mikael Enelund ## Stig Larsson ### # Department of Applied Mechanics, Chalmers Mechanics, Chalmers University of Technology, SE--412 96 GË?oteborg, Sweden, mikael
A Lagrangian for the quantionic field equation
Samir Lipovaca
2010-03-02
The purpose of this paper is to present a Lagrangian from which we can derive the quantionic field equation written in the Dirac gauge using the principle of stationary action.
Equator Appliance: ENERGY STAR Referral (EZ 3720)
Broader source: Energy.gov [DOE]
DOE referred Equator Appliance clothes washer EZ 3720 to EPA, brand manager of the ENERGY STAR program, for appropriate action after DOE testing revealed that the model does not meet ENERGY STAR requirements.
On the solutions to the string equation
A. Schwarz
1991-09-10
The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential operators.This fact permits us to describe the set of solutions to the string equation in terms of moduli spa- ces of algebraic curves,however the direct description is much simpler. Some results are obtained for the superanalog to the string equation where $P$ and $Q$ are considered as superdifferential operators. It is proved that this equation is invariant with respect to Manin-Radul, Mulase-Rabin and Kac-van de Leur KP-hierarchies.
MATH 411 SPRING 2001 Ordinary Differential Equations
Alekseenko, Alexander
MATH 411 SPRING 2001 Ordinary Differential Equations Schedule # 749025 TR 01:00-02:15 316 Boucke Instructor: Alexander Alekseenko, 328 McAllister, 865-1984, alekseen@math.psu.edu The course
Charging Capacitors According to Maxwell's Equations: Impossible
Daniele Funaro
2014-11-02
The charge of an ideal parallel capacitor leads to the resolution of the wave equation for the electric field with prescribed initial conditions and boundary constraints. Independently of the capacitor's shape and the applied voltage, none of the corresponding solutions is compatible with the full set of Maxwell's equations. The paradoxical situation persists even by weakening boundary conditions, resulting in the impossibility to describe a trivial phenomenon such as the capacitor's charging process, by means of the standard Maxwellian theory.
Integration Rules for Loop Scattering Equations
Baadsgaard, Christian; Bourjaily, Jacob L; Damgaard, Poul H; Feng, Bo
2015-01-01
We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\\phi^3$-theory. This formalism greatly facilitates the evaluation of amplitudes in the CHY representation at one-loop order, without the need to explicitly sum over the solutions to the loop-level scattering equations.
Finite Element Analysis of the Schroedinger Equation
Avtar S. Sehra
2007-04-17
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical techniques. We then give an introduction to finite element analysis using the diffusion equation as an example. Three numerical time evolution methods are considered: the (tried and tested) Crank-Nicolson method, the continuous space-time method, and the discontinuous space-time method.
Lagrangian submanifolds and Hamilton-Jacobi equation
M. Barbero-Liñán; M. de León; D. Martín de Diego
2012-09-04
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of the Hamilton-Jacobi equation. This interpretation allows us to study some interesting applications of Hamilton-Jacobi equation in holonomic, nonholonomic and time-dependent dynamics from a geometrical point of view.
Conformally Invariant Spinorial Equations in Six Dimensions
Carlos Batista
2015-06-04
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, some useful identities involving the curvature of the spinorial connection are attained and a digression about harmonic forms and more general massless fields is made.
Symmetric Instantons and Discrete Hitchin Equations
Ward, R S
2015-01-01
Self-dual Yang-Mills instantons on $R^4$ correspond to algebraic ADHM data. This paper describes how to specialize such ADHM data so that the instantons have a $T^2$ symmetry, and this in turn motivates an integrable discrete version of the 2-dimensional Hitchin equations. It is analogous to the way in which the ADHM data for $S^1$-symmetric instantons, or hyperbolic BPS monopoles, may be viewed as a discretization of the Nahm equations.
Painleve VI, Rigid Tops and Reflection Equation
A. Levin; M. Olshanetsky; A. Zotov
2006-06-01
We show that the Painlev{\\'e} VI equation has an equivalent form of the non-autonomous Zhukovsky-Volterra gyrostat. This system is a generalization of the Euler top in $C^3$ and include the additional constant gyrostat momentum. The quantization of its autonomous version is achieved by the reflection equation. The corresponding quadratic algebra generalizes the Sklyanin algebra. As by product we define integrable XYZ spin chain on a finite lattice with new boundary conditions.
A Reduced Basis Element Approach for the Reynolds Lubrication Equation
A Reduced Basis Element Approach for the Reynolds Lubrication Equation Lösen der Reynolds Reynolds Lubrication Equation 8 2.1 Introduction of the application, background setting . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Reynolds Lubrication Equation
Pierantozzi, T.; Vazquez, L.
2005-11-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.
Local Gravity Field Modeling by 2DFFT from Gravity Gradients
Stuttgart, Universität
The solution of the Laplace equation ((x, y, z) = 0 for z > 0), (x, y, z) = n=0 m=0 (anm cos nx cos my + bnm cos nx sin my+ cnm sin nx cos my + dnm sin nx sin my)e- n2+m2z Here, (x, y, z) satisfies. If we represent disturbing potential T as, T = n=0 m=0 (anm cos nx cos my + bnm cos nx sin my+ cnm sin
What every designated representative should know about Title IV and Title V enforcement provisions
Bischoff, C.A. [Gallagher and Kennedy, Phoenix, AZ (United States); Dayal, P. [Tucson Electric Power Co., Tucson, AZ (United States)
1995-12-31
Title IV of the Clean Air Act not only created a regulatory program unlike any other under the Clean Air Act, but also established a unique position--the designated representative--as an integral part of the program. The designated representative is required to meet certain basic obligations under Title IV, and a panoply of enforcement mechanisms are available to EPA in the event of noncompliance with these obligations. Also, because a designated representative may take on responsibilities under the permit provisions of Title V of the Clean Air Act, the designated representative can also be subject to an enforcement action for failure to comply with certain Title V permit requirements. This paper considers the basic definition of the designated representative under EPA`s Title IV and Title V regulations, identifies the responsibilities assigned to the designated representative, and then analyzes the enforcement mechanisms that may be applied to the designated representative if a regulatory responsibility has not been satisfied.
Fairag, Faisal
in engines and drag reduction), aerodynamics (maneuvering flight of jet aircraft) and biophysical a practical engineering point of view, the study of Ladyzhenskaya equations and of proprieties
Combined Wronskian solutions to the 2D Toda molecule equation
Ma, Wen-Xiu
partic- ular solutions [14, 15], and thus possess linear subspaces of solutions. Therefore, though soliton equations are nonlinear, they are good neighbors to linear equations. However, given
From the Boltzmann equation to fluid mechanics on a manifold
Peter J. Love; Donato Cianci
2012-08-27
We apply the Chapman-Enskog procedure to derive hydrodynamic equations on an arbitrary surface from the Boltzmann equation on the surface.
A new nonlinear generalization of the Dirac equation
Nikolay Marchuk
2013-07-24
We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.
Two standard methods for solving the Ito equation
Alvaro Salas Salas
2008-05-21
In this paper we show some exact solutions for the Ito equation. These solutions are obtained by two methods: the tanh method and the projective Riccati equation method.
Hyperinstantons, the Beltrami Equation, and Triholomorphic Maps
Fré, P; Sorin, A S
2015-01-01
We consider the Beltrami equation for hydrodynamics and we show that its solutions can be viewed as instanton solutions of a more general system of equations. The latter are the equations of motion for an ${\\cal N}=2$ sigma model on 4-dimensional worldvolume (which is taken locally HyperK\\"ahler) with a 4-dimensional HyperK\\"ahler target space. By means of the 4D twisting procedure originally introduced by Witten for gauge theories and later generalized to 4D sigma-models by Anselmi and Fr\\'e, we show that the equations of motion describe triholomophic maps between the worldvolume and the target space. Therefore, the classification of the solutions to the 3-dimensional Beltrami equation can be performed by counting the triholomorphic maps. The counting is easily obtained by using several discrete symmetries. Finally, the similarity with holomorphic maps for ${\\cal N}=2$ sigma on Calabi-Yau space prompts us to reformulate the problem of the enumeration of triholomorphic maps in terms of a topological sigma mod...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
AFDC Printable Version Share this resource Send a link to EERE: Alternative Fuels Data Center Home Page to someone by E-mail Share EERE: Alternative Fuels Data Center Home Page on Facebook Tweet about EERE: Alternative Fuels Data Center Home Page on Twitter Bookmark EERE: Alternative Fuels Data Center Home Page on Google Bookmark EERE: Alternative Fuels Data Center Home Page on Delicious Rank EERE:FinancingPetroleum12, 2015Executive Order14, 20111,FY 2007 FeeFederalFirst2 DOEMeetingExperience |
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
AFDC Printable Version Share this resource Send a link to EERE: Alternative Fuels Data Center Home Page to someone by E-mail Share EERE: Alternative Fuels Data Center Home Page on Facebook Tweet about EERE: Alternative Fuels Data Center Home Page on Twitter Bookmark EERE: Alternative Fuels Data Center Home Page on Google Bookmark EERE: Alternative Fuels Data Center Home Page on Delicious Rank EERE:FinancingPetroleum12, 2015Executive Order14, 20111,FY 2007 FeeFederalFirst2 DOEMeetingExperience
Fourier transform of the 3d NS equations The 3d NS equations are
Salmon, Rick
1 Fourier transform of the 3d NS equations The 3d NS equations are (1) vi t + vj vi xj = - p xi easily add it in at the end. Our interest is in the advection and pressure terms. Introducing the Fourier transforms (2) vi x( ) = ui k( )eikx k p x( ) = p k( )eikx k we obtain the Fourier transform of (1
Differential Equations I Lab #8: Differential Equations and Linear Algebra with Mathematica
Peckham, Bruce B.
and NDSolve for differential equations, and LinearSolve, Eigenvector, Eigen- value, NullSpace, Inverse/instructor each output line generated by Mathematica. If you elect to write a report, your report should include an analytical solution to y + 3y + 2y = 3e4t. #12;2. The logistic differential equation (again). Consider
H. Kleinert; V. Zatloukal
2015-03-05
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Electromagnetic field with constraints and Papapetrou equation
Z. Ya. Turakulov; A. T. Muminov
2006-01-12
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end the entire functional space of electromagnetic fields must be reduced to its subspace of locally plane monochromatic waves. We have formulated the constraints under which the entire functional space of electromagnetic fields reduces to its subspace of locally plane monochromatic waves. These constraints introduce variables of another kind which specify a field of local frames associated to the wave and contain some congruence of null-curves. The Lagrangian for constrained electromagnetic field contains variables of two kinds, namely, a congruence of null-curves and the field itself. This yields two kinds of Euler-Lagrange equations. Equations of first kind are trivial due to the constraints imposed. Variation of the curves yields the Papapetrou equations for a classical massless particle with helicity 1.
Chemical potential and the gap equation
Huan Chen; Wei Yuan; Lei Chang; Yu-Xin Liu; Thomas Klahn; Craig D. Roberts
2008-07-17
In general the kernel of QCD's gap equation possesses a domain of analyticity upon which the equation's solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the single-quark number- and scalar-density distribution functions are mu-independent. This is illustrated via two models for the gap equation's kernel. The models are alike in concentrating support in the infrared. They differ in the form of the vertex but qualitatively the results are largely insensitive to the Ansatz. In vacuum both models realise chiral symmetry in the Nambu-Goldstone mode and in the chiral limit, with increasing chemical potential, exhibit a first-order chiral symmetry restoring transition at mu~M(0), where M(p^2) is the dressed-quark mass function. There is evidence to suggest that any associated deconfinement transition is coincident and also of first-order.
Bulk equations of motion from CFT correlators
Daniel Kabat; Gilad Lifschytz
2015-07-27
To O(1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk microcausality. This requires adding an infinite tower of smeared higher-dimension double-trace operators to the CFT definition of a bulk field, with coefficients that we explicitly compute. By summing the contribution of the higher-dimension operators we derive the equations of motion satisfied by these uplifted CFT operators and show that we precisely recover the expected bulk equations of motion. We exhibit the freedom in the CFT construction which corresponds to bulk field redefinitions.
Bulk equations of motion from CFT correlators
Kabat, Daniel
2015-01-01
To O(1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk microcausality. This requires adding an infinite tower of smeared higher-dimension double-trace operators to the CFT definition of a bulk field, with coefficients that we explicitly compute. By summing the contribution of the higher-dimension operators we derive the equations of motion satisfied by these uplifted CFT operators and show that we precisely recover the expected bulk equations of motion. We exhibit the freedom in the CFT construction which corresponds to bulk field redefinitions.
R. A. Soltz
2009-09-14
We present results from recent calculations of the QCD equation of state by the HotQCD Collaboration and review the implications for hydrodynamic modeling. The equation of state of QCD at zero baryon density was calculated on a lattice of dimensions $32^3 \\times 8$ with $m_l = 0.1 m_s$ (corresponding to a pion mass of $\\sim$220 MeV) using two improved staggered fermion actions, p4 and asqtad. C alculations were performed along lines of constant physics using more than 100M cpu-hours on BG/L supercomputers at LLNL, NYBlue, and SDSC. We present paramete rizations of the equation of state suitable for input into hydrodynamics models of heavy ion collisions.
Some Wave Equations for Electromagnetism and Gravitation
Zi-Hua Weng
2010-08-11
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that in conventional electromagnetic theory with vector terminology. By means of the octonion exponential function, we can draw out that the electromagnetic waves are transverse waves in a vacuum, and rephrase the law of reflection, Snell's law, Fresnel formula, and total internal reflection etc. The study claims that the theoretical results of wave equations for electromagnetic strength keep unchanged in the case for coexistence of gravitational and electromagnetic fields. Meanwhile the electric and magnetic components of electromagnetic waves can not be determined simultaneously in electromagnetic fields.
Interplay of Boltzmann equation and continuity equation for accelerated electrons in solar flares
Codispoti, Anna
2015-01-01
During solar flares a large amount of electrons are accelerated within the plasma present in the solar atmosphere. Accurate measurements of the motion of these electrons start becoming available from the analysis of hard X-ray imaging-spectroscopy observations. In this paper, we discuss the linearized perturbations of the Boltzmann kinetic equation describing an ensemble of electrons accelerated by the energy release occurring during solar flares. Either in the limit of high energy or at vanishing background temperature such an equation reduces to a continuity equation equipped with an extra force of stochastic nature. This stochastic force is actually described by the well known energy loss rate due to Coulomb collision with ambient particles, but, in order to match the collision kernel in the linearized Boltzmann equation it needs to be treated in a very specific manner. In the second part of the paper the derived continuity equation is solved with some hyperbolic techniques, and the obtained solution is wr...
Relativistic Wave Equations: An Operational Approach
G. Dattoli; E. Sabia; K. Górska; A. Horzela; K. A. Penson
2015-02-02
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schr\\"odinger, Klein-Gordon and Dirac. We discuss the free particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
Changing the Equation in STEM Education
Broader source: Energy.gov [DOE]
Editor's Note: This is a cross post of an announcement that the White House featured on its blog last week. Check out the video below for Secretary Chu's thoughts on how an education in math and science helps students understand the world and deal with the pressing issues of our time. Today, President Obama announced the launch of Change the Equation, a CEO-led effort to dramatically improve education in science, technology, engineering, and math (STEM), as part of his “Educate to Innovate” campaign. Change the Equation is a non-profit organization dedicated to mobilizing the business community to improve the quality of STEM education in the United States.
4Q CY2008 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from October to December 2008. Data for these indicators are gathered by Field...
1Q CY2009 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from January to March 2009. Data for these indicators are gathered by Field...
3Q CY2007 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from July to September 2007. Data for these indicators are gathered by Field...
1Q CY2003 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative Program Performance Indicators (PIs) Quarterly Report Covering the Period from January to March 2003. Data for these indicators are gathered by Field...
3Q C&2008 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from July to September 2008. Data for these indicators aregathered by Field...
2Q CY2009 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from April to June 2009. Data for these indicators are gathered by Field elements...
2Q CY2008 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators QuarterlyReport covering the period from April to June 2008. Data for these indicators aregathered by Field elements...
3Q CY2006 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from July to September 2006. Data for these indicators are gathered by Field...
4Q CY2006 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Office of Energy Efficiency and Renewable Energy (EERE)
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from October to December 2006. Data for these indicators are gathered by Field...
1Q CY2010 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from January to March2010. Data for these indicators are gathered by Field...
1Q CY2006 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from January to March 2006. Data for these indicators are gathered by Field...
2Q CY2007 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from April to June 2007. Data for these indicators are gathered by field elements...
4Q CY2005 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from October to December 2005. Data for these indicators are gathered by Field...
2Q CY2006 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from April to June 2006. Data for these indicators are gathered by Field elements...
3Q CY2009 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from July to September 2009. Data for these indicators are gathered by Field...
2Q CY2010 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
This memorandum summarizes the highlight of, and announces the availablity on-line of, the Facility Representative (FR) Program Performance Indicators are gathered by Field elements quarterly per...
3Q CY2000 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
The Facility Representative Program Indicators (Pis) Quarterly Report attached, covering the period from July to September 2000. Data for these indicators are gathered by the Field elements...
1Q CY2012 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
This memorandum summarizes the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from January through March 2012. Data for these indicators were...
2Q CY2011 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"This memorandum summarizes the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period April through June 20 1 1. Data for these indicators were gathered...
4Q CY2011 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"This memorandum summarizes the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from October through December 2011. Data for these indicators were...
3Q CY2010 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
This memorandum summarizes the highlights of the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period of July through September 2010. Data for these...
4Q CY2010 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"This memorandum summarizes the highlights of the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period October through December 2010. Data for these...
1Q CY2011 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
This memorandum summarizes the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the Period January through March 2011. Data for these indicators were gathered...
4Q CY2009 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"Attached is the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from October to December 2009. Data for these indicators are gathered by Field...
3Q CY2011 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
This memorandum summarizes the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the Period July through September 2011. Data for these indicators were gathered...
2Q CY2012 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"This memorandum summarizes the Facility Representative (FR) Program Performance Indicators Quarterly Report covering the period from April through June 2012. Data for these indicators were...
4Q CY2007 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Office of Energy Efficiency and Renewable Energy (EERE)
"Attached is the Facility Representative (FR) Program Performance Indicators QuarterlyReport covering the period from October to December 2007. Data for these indicators aregathered by Field...
Academic Council Representatives 2009-2010 Title/Committee 2009/2010 Members
Maurer, Frank
Taryn Lenders ELECTED REPRESENTATIVES Management & Professional Staff Council Kathy Drewes General) John Wright (L) Travel Committee Taryn Lenders Shawna Sadler #12;
Principle of Least Squares Regression Equations Residuals Correlation and Regression
Watkins, Joseph C.
Principle of Least Squares Regression Equations Residuals Topic 3 Correlation and Regression Linear Regression I 1 / 15 #12;Principle of Least Squares Regression Equations Residuals Outline Principle of Least Squares Regression Equations Residuals 2 / 15 #12;Principle of Least Squares Regression Equations
Kinetic equation for a soliton gas Chernogolovka, July 2009
Fominov, Yakov
Kinetic equation for a soliton gas Gennady El Chernogolovka, July 2009 Gennady El Kinetic equation, Kinetic equation for solitons, JETP (1971) Here we consider only strongly integrable systems (like KdV, NLS etc.) Gennady El Kinetic equation for a soliton gas #12;From N-solitons/N-gap potentials
Lecture by John F. Nash Jr. An Interesting Equation
Babu, G. Jogesh
Lecture by John F. Nash Jr. An Interesting Equation The equation that we have discovered is a 4th order covariant tensor partial differential equation applicable to the metric tensor of a spaceRp a s b - 1 2 gab Rps = 0 And this equation is formally divergence free in the same way
An energy estimate for a perturbed Hasegawa--Mima equation
Grauer, Rainer
An energy estimate for a perturbed Hasegawa--Mima equation Rainer Grauer Institut fÂ¨ur Theoretische transport at the plasma edge of a tokamak fusion reactor. A oneÂfield equation describing the electrostatic potential fluctuations in this regime is the soÂcalled Hasegawa--Mima equation. If this equation is driven
Evolution equations: Frobenius integrability, conservation laws and travelling waves
Geoff Prince; Naghmana Tehseen
2015-06-07
We give new results concerning the Frobenius integrability and solution of evolution equations admitting travelling wave solutions. In particular, we give a powerful result which explains the extraordinary integrability of some of these equations. We also discuss "local" conservations laws for evolution equations in general and demonstrate all the results for the Korteweg de Vries equation.
Karczewska, Anna; Infeld, Eryk
2015-01-01
It is well known that the KdV equation has an infinite set of conserved quantities. The first three are often considered to represent mass, momentum and energy. Here we try to answer the question of how this comes about, and also how these KdV quantities relate to those of the Euler shallow water equation. Here Luke's Lagrangian is helpful. We also consider higher order extensions of KdV. Though in general not integrable, in some sense they are almost so.
Energy-Momentum Distribution in Weyl Metrics
M. Sharif; Tasnim Fatima
2005-07-16
In this paper, we evaluate energy and momentum density distributions for the Weyl metric by using the well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and M$\\ddot{o}$ller. The metric under consideration is the static axisymmetric vacuum solution to the Einstein field equations and one of the field equations represents the Laplace equation. Curzon metric is the special case of this spacetime. We find that the energy density is different for each prescription. However, momentum turns out to be constant in each case.
Cubic Nonlinear Schrodinger Equation with vorticity
Caliari, Marco
) Equation, plays a fundamental role in describing the hydrodynamics of a BoseEinstein condensate [4] (see Bose particles, as recently described within Stochastic Quantization by Lagrangian Variational the general one-particle Bose dynamics out of dynamical equilibrium. We observe that in the most simple
Pointwise Fourier Inversion: a Wave Equation Approach
Pointwise Fourier Inversion: a Wave Equation Approach Mark A. Pinsky1 Michael E. Taylor2. A general criterion for pointwise Fourier inversion 2. Pointwise Fourier inversion on Rn (n = 3) 3. Fourier inversion on R2 4. Fourier inversion on Rn (general n) 5. Fourier inversion on spheres 6. Fourier inversion
Differential Equations Math 125 Name Quiz Section
Burdzy, Krzysztof "Chris"
-trivial applications of Differential Equations. Forensic Mathematics A detective discovers a murder victim in a hotel the murder took place. Let u(t) be the temperature of the body after t hours. By Newton's Law of Cooling we = 98.6 F and solve for t. At what time did the murder take place? #12;Spread of a Rumor The Xylocom
The Kinematic Algebras from the Scattering Equations
Monteiro, Ricardo
2013-01-01
We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears natur...
Nonlocal kinetic equation: integrable hydrodynamic reductions, symmetries
, Troitsk, Moscow Region, Russia Lebedev Physical Institute, Russian Academy of Sciences, Moscow § SISSA, Trieste, Italy, and Institute of Metal Physics, Urals Division of Russian Academy of Sciences, Ekaterinburg, Russia We study a new class of nonlinear kinetic equations recently derived in the context
Evolution equations in QCD and QED
M. Slawinska
2008-05-12
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions. Finally, comparison of solutions obtained numerically are presented.
SYSTEMS OF FUNCTIONAL EQUATIONS MICHAEL DRMOTA
Drmota, Michael
of planted plane trees. Hence the corresponding generating function y(x) satis#12;es the functional equation the asymptotic properties of the coeÃ?cients of generating functions which satisfy a system of functional a recursive description then the generating function y(x) = P o2Y x joj = P n#21;0 yn x n satis#12;es
Conservation of Energy Thermodynamic Energy Equation
Hennon, Christopher C.
, is derived beginning with an alternative form of the 1st Law of Thermodynamics, the internal energy formConservation of Energy Thermodynamic Energy Equation The previous two sections dealt addresses the conservation of energy. The first law of thermodynamics, of which you should be very familiar
Optimal polarisation equations in FLRW universes
Tram, Thomas; Lesgourgues, Julien, E-mail: thomas.tram@epfl.ch, E-mail: Julien.Lesgourgues@cern.ch [Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland)
2013-10-01
This paper presents the linearised Boltzmann equation for photons for scalar, vector and tensor perturbations in flat, open and closed FLRW cosmologies. We show that E- and B-mode polarisation for all types can be computed using only a single hierarchy. This was previously shown explicitly for tensor modes in flat cosmologies but not for vectors, and not for non-flat cosmologies.
Thermodynamics of viscoelastic fluids: the temperature equation.
Wapperom, Peter
Thermodynamics of viscoelastic fluids: the temperature equation. Peter Wapperom Martien A. Hulsen and Hydrodynamics Rotterdamseweg 145 2628 AL Delft (The Netherlands) Abstract From the thermodynamics with internal. The well- known stress differential models that fit into the thermodynamic theory will be treated
MULTIVARIATE PUBLIC KEY CRYPTOSYSTEMS FROM DIOPHANTINE EQUATIONS
Gao, Shuhong
MULTIVARIATE PUBLIC KEY CRYPTOSYSTEMS FROM DIOPHANTINE EQUATIONS SHUHONG GAO AND RAYMOND HEINDL for multivariate public key cryptosystems, which combines ideas from both triangular and oil-vinegar schemes. We the framework. 1. Introduction 1.1. Multivariate Public Key Cryptography. Public key cryptography plays
The general solution of Schrodigers differential equation
Nikos Bagis
2009-10-31
In this note we solve theoretically the Schrodingers differential equation using results based on our previous work which concern semigroup operators. Our method does not use eigenvectors or eigenvalues and the solution depends only from the selected base of the Hilbert space.
NOTES ON THE JACOBI EQUATION ALEXANDER LYTCHAK
Lytchak, Alexander
NOTES ON THE JACOBI EQUATION ALEXANDER LYTCHAK Abstract. We discuss some properties of Jacobi spaces of Jacobi fields and give some applica- tions to Riemannian geometry. 1. Introduction This note is essentially a collection of results about conjugate points of Jacobi fields for which we could not find
Partial Differential Equations of Electrostatic MEMS
Fournier, John J.F.
Partial Differential Equations of Electrostatic MEMS by Yujin Guo B.Sc., China Three Gorges) The University of British Columbia July 2007 c Yujin Guo 2007 #12;Abstract Micro-Electromechanical Systems (MEMS their initial development in the 1980s, MEMS has revolutionized numerous branches of science and industry
Equation of State of Uranium and Plutonium
Barroso, Dalton Ellery Girão
2015-01-01
The objective of this work is to define the parameters of the three-term equation of state for uranium and plutonium, appropriate for conditions in which these materials are subjected to strong shock compressions, as in cylindrical and spherical implosions. The three-term equation of state takes into account the three components of the pressure that resist to compression in the solid: the elastic or "cold" pressure (coulombian repulsion between atoms), the thermal pressure due to vibratory motion of atoms in the lattice of the solid and the thermal pressure of electrons thermally excited. The equation of state defined here permits also to take into account the variation of the specific heat with the transition of the solid to the liquid or gaseous state due to continued growth of temperature in strong shock compressions. In the definition of uranium equation of state, experimental data on the uranium compression, available in the open scientific literature, are used. In the plutonium case, this element was co...
Equation of State of Uranium and Plutonium
Dalton Ellery Girão Barroso
2015-07-13
The objective of this work is to define the parameters of the three-term equation of state for uranium and plutonium, appropriate for conditions in which these materials are subjected to strong shock compressions, as in cylindrical and spherical implosions. The three-term equation of state takes into account the three components of the pressure that resist to compression in the solid: the elastic or "cold" pressure (coulombian repulsion between atoms), the thermal pressure due to vibratory motion of atoms in the lattice of the solid and the thermal pressure of electrons thermally excited. The equation of state defined here permits also to take into account the variation of the specific heat with the transition of the solid to the liquid or gaseous state due to continued growth of temperature in strong shock compressions. In the definition of uranium equation of state, experimental data on the uranium compression, available in the open scientific literature, are used. In the plutonium case, this element was considered initially in the alpha-phase or stabilized in the delta-phase. In the last case, an abrupt and instantaneous transition to the alpha-phase was considered when the delta-phase plutonium is submitted to strong compressions.
Wave function derivation of the JIMWLK equation
Alexey V. Popov
2008-12-16
Using the stationary lightcone perturbation theory, we propose the complete and careful derivation the JIMWLK equation. We show that the rigorous treatment requires the knowledge of a boosted wave function with second order accuracy. Previous wave function approaches are incomplete and implicitly used the time ordered perturbation theory, which requires a usage of an external target field.
Construction of tree volume tables from integration of taper equations
Coffman, Jerry Gale
1973-01-01
) were used as a basis for comparison. The integrated taper equation appears to be as accurate as the tradi- 2 tional volume equation V a + bD H, but somewhat less accurate than volume equations involving form class measurements. A computer program... and help throughout my graduate career. TABLE OF CONTENTS CHAPTER Page I INTRODUCTION AND OBJECTIVES II REVIEW OF LITERATURE III METHODS Sample Data Procedure Analysis 1 Analysis 2 13 Integration of Taper Equations to Volume Equations Tests...
Master equation for a quantum particle in a gas
Klaus Hornberger
2006-09-05
The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts non-perturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.
Equation of state and singularities in FLRW cosmological models
L. Fernandez-Jambrina; R. Lazkoz
2010-01-18
We consider FLRW cosmological models with standard Friedmann equations, but leaving free the equation of state. We assume that the dark energy content of the universe is encoded in an equation of state $p=f(\\rho)$, which is expressed with most generality in the form of a power expansion. The inclusion of this expansion in Friedmann equations allows us to construct a perturbative solution and to relate the coefficients of the equation of state with the formation of singularities of different types.
The Swing Equation: Power Form, PerUnit, Error 1.0 Power Form of Swing Equation
McCalley, James D.
1 The Swing Equation: Power Form, PerUnit, Error 1.0 Power Form of Swing Equation Recall from when the swing equation is written in perunit, the numerical value of the torque version) to analyze error in the power form of the swing equation. But before we do that, we need to define pu speed
REDUCTION OF THE EQUATION FOR LOWER HYBRID WAVES IN A PLASMA TO A NONLINEAR SCH~DINGER EQUATION
Karney, Charles
REDUCTION OF THE EQUATION FOR LOWER HYBRID WAVES IN A PLASMA TO A NONLINEAR SCH~DINGER EQUATION C h Equation* by Charles F. F. Karney Research Laboratory of Electronics and Plasma Fusion Center and Development Administration (Contract E(l1-11-3070) #12;Reduction sf the Equation for Lower Hybrid Waves
The Semiclassical Einstein Equation on Cosmological Spacetimes
Daniel Siemssen
2015-03-06
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the stress-energy tensor and the semiclassical Einstein equation. Basic notions of differential geometry, topology, functional and microlocal analysis, causality and general relativity will be summarised, and the algebraic approach to QFT on curved spacetime will be reviewed. Apart from these foundations, the original research of the author and his collaborators will be presented: Together with Fewster, the author studied the up and down structure of permutations using their decomposition into so-called atomic permutations. The relevance of these results to this thesis is their application in the calculation of the moments of quadratic quantum fields. In a work with Pinamonti, the author showed the local and global existence of solutions to the semiclassical Einstein equation in flat cosmological spacetimes coupled to a scalar field by solving simultaneously for the quantum state and the Hubble function in an integral-functional equation. The theorem is proved with a fixed-point theorem using the continuous functional differentiability and boundedness of the integral kernel of the integral-functional equation. In another work with Pinamonti the author proposed an extension of the semiclassical Einstein equations which couples the moments of a stochastic Einstein tensor to the moments of the quantum stress-energy tensor. In a toy model of a Newtonianly perturbed exponentially expanding spacetime it is shown that the quantum fluctuations of the stress-energy tensor induce an almost scale-invariant power spectrum for the perturbation potential and that non-Gaussianties arise naturally.
Representing liquid-vapor equilibria of Ternary systems using neural networks
Swisher, Mathew M
2015-01-01
We develop a method based on neural networks for efficiently interpolating equations of state (EOS) for liquid-vapor equilibria of ternary mixtures. We investigate the performance of neural networks both when experimental ...
Detecting and Representing Relevant Web Deltas in Whoweda Sourav S Bhowmick1
Bhowmick, Sourav S.
Detecting and Representing Relevant Web Deltas in Whoweda Sourav S Bhowmick1 Sanjay Madria2 Wee given the old and new versions of a set of interlinked Web documents, retrieved in response to a user's query. In particular, we show how to detect and represent web deltas, i.e., changes in the Web documents
Zaniolo, Carlo
Representing and Querying the Evolution of Databases and their Schemas in XML Fusheng Wang surprisingly effective solutions to the problem of representing and querying the evolution of databases for evolution [20, 19, 13]. Meanwhile, there is much current interest in publishing and viewing database
Representative Subsets For Big Data Learning using k-NN Graphs
Representative Subsets For Big Data Learning using k-NN Graphs Raghvendra Mall, Vilen Jumutc, Rocco a deterministic method to obtain subsets from big data which are a good representative of the inherent structure a subset for this big data network. The FURS selection technique selects nodes from different dense regions
April 21, 2014 2014-15 NON-REPRESENTED STAFF SALARY PROGRAM/
Leistikow, Bruce N.
April 21, 2014 2014-15 NON-REPRESENTED STAFF SALARY PROGRAM/ CALL FOR PERFORMANCE APPRAISALS JULY 1, 2013-JUNE 30, 2014 Salary Program The 2014-15 salary program is a 3% salary program for non-represented career staff. Individual employee's increases will vary due to the Salary Program Parameters listed below
A SOFTWARE SYSTEM FOR ANALYSING CERAMIC ARTEFACTS REPRESENTED BY 2D DRAWINGS
Borissova, Daniela
A SOFTWARE SYSTEM FOR ANALYSING CERAMIC ARTEFACTS REPRESENTED BY 2D DRAWINGS Gennady Agre1.hristov@gmail.com Abstract: The paper describes a part of an extensible system for analysing ceramic artefacts represented this function and using it for comparing artefacts are described. Key words: ceramics classification, curvature
Kovalyov, Mikhail [Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1 (Canada)
2010-06-15
In this article the sets of solutions of the sine-Gordon equation and its linearization the Klein-Gordon equation are discussed and compared. It is shown that the set of solutions of the sine-Gordon equation possesses a richer structure which partly disappears during linearization. Just like the solutions of the Klein-Gordon equation satisfy the linear superposition principle, the solutions of the sine-Gordon equation satisfy a nonlinear superposition principle.
Generalized kinetics of overall phase transition in terms of logistic equation
Avramov, I
2015-01-01
We summarize and to discuss briefly the geometrical practice of modeling attitudes so far popular in treating reaction kinetics of solid-state processes. The model equations existing in the literature have been explored to describe the thermal decomposition and crystallization data and are deeply questioned and analyzed showing that under such a simple algebraic representation, the reacting system is thus classified as a set of geometrical bodies (spheres) where each and every one reaction interface is represented by similar and smooth characteristics of reaction curve. It brings an unsolved question whether the sharp and even boundary factually exists or if it resides jointly just inside the global whole of the sample entirety preventing individual particles from having their individual reaction front. Most of the derived expressions are specified in an averaged generalization in terms of the three and two parameters equation (so called JMAK and SB models) characterized by a combination of power exponents m,...
E. V. Shiryaeva; M. Yu. Zhukov
2014-10-10
In paper [S.I. Senashov, A. Yakhno. 2012. SIGMA. Vol.8. 071] the variant of the hodograph method based on the conservation laws for two hyperbolic quasilinear equations of the first order is described. Using these results we propose a method which allows to reduce the Cauchy problem for the two quasilinear PDE's to the Cauchy problem for ODE's. The proposed method is actually some similar method of characteristics for a system of two hyperbolic quasilinear equations. The method can be used effectively in all cases, when the linear hyperbolic equation in partial derivatives of the second order with variable coefficients, resulting from the application of the hodograph method, has an explicit expression for the Riemann-Green function. One of the method's features is the possibility to construct a multi-valued solutions. In this paper we present examples of method application for solving the classical shallow water equations.
Celso de Araujo Duarte
2015-10-15
Traditionally, the electromagnetic theory dictates the well-known second order differential equation for the components of the scalar and the vector potentials, or in other words, for the four-vector electromagnetic potential $\\phi^{\\mu}$. But the second order is not obligatory at least with respect to the electromagnetic radiation fields: actually, a heuristic first order differential equation can be constructed to describe the electromagnetic radiation, supported on the phenomenology of its electric and magnetic fields. Due to a formal similarity, such an equation suggests a direct comparative analysis with Dirac's equation for half spin fermions, conducting to the finding that the Dirac's spinor field $\\Psi$ for massive or massless fermions is equivalent to a set of two potential-like four vector fields $\\psi^{\\mu}$ and $\\chi^{\\mu}$. Under this point of view, striking similarities with the electromagnetic theory emerge with a category of "pseudo electric'' and "pseudo magnetic'' vector fermionic fields.
Summation formula for solutions of Riccati-Abel equation
Robert M. Yamaleev
2012-10-08
The generalized Riccati equation defined as an equation between first order derivative and the cubic polynomial is named Riccati-Abel equation. Unlike solutions of ordinary Riccati equation, the solutions of Riccati-Abel equation do not admit an addition formula. In the present paper we explain a nature of this fault and elaborate a method of solution of this problem. We show that the addition formula for Riccati-Abel equation can be established only for pair of solutions. Furthermore, it is shown that analogously with ordinary Riccati equation, the relationships with linear differential equations and the general complex algebra of third order can be established only for the pair of solutions of Riccati-Abel equation.
Fundamental Equation of State for Deuterium
Richardson, I. A.; Leachman, J. W., E-mail: jacob.leachman@wsu.edu [HYdrogen Properties for Energy Research (HYPER) Laboratory, School of Mechanical and Materials Engineering, Washington State University, P.O. Box 642920, Pullman, Washington 99164 (United States); Lemmon, E. W. [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)] [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)
2014-03-15
World utilization of deuterium is anticipated to increase with the rise of fusion-energy machines such as ITER and NIF. We present a new fundamental equation of state for the thermodynamic properties of fluid deuterium. Differences between thermodynamic properties of orthodeuterium, normal deuterium, and paradeuterium are described. Separate ideal-gas functions were fitted for these separable forms together with a single real-fluid residual function. The equation of state is valid from the melting line to a maximum pressure of 2000 MPa and an upper temperature limit of 600 K, corresponding to available experimental measurements. The uncertainty in predicted density is 0.5% over the valid temperature range and pressures up to 300 MPa. The uncertainties of vapor pressures and saturated liquid densities are 2% and 3%, respectively, while speed-of-sound values are accurate to within 1% in the liquid phase.
Euler's fluid equations: Optimal Control vs Optimization
Darryl D. Holm
2009-09-28
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the \\emph {same} Euler fluid equations, although their Lagrangian parcel dynamics are \\emph{different}. This is a result of the \\emph{gauge freedom} in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.
Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
Noble, J H
2015-01-01
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\\"{o}dinger--Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive, and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
J. H. Noble; U. D. Jentschura
2015-06-05
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\\"{o}dinger--Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive, and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
Correction to Solution of Dirac Equation
Rui Chen
2015-10-11
Using the Chen unitary principle to test the Dirac theoryfor the hydrogen atomic spectrum shows that the standard Dirac function withthe Dirac energy levels is only one the formal solutions of theDirac-Coulomb equation, which conceals some pivotal mathematicalcontradictions. The theorem of existence of solution of the Dirac equationrequires an important modification to the Dirac angular momentum constantthat was defined by Dirac's algebra. It derives the modified radial Diracequation which has the consistency solution involving the quantum neutronradius and the neutron binding energy. The inevitable solution for otheratomic energy states is only equivalent to the Bohr solution. It concludesthat the Dirac equation is more suitable to describe the structure ofneutron. How to treat the difference between the unitary energy levels andthe result of the experimental observation of the atomic spectrums for thehydrogen atom needs to be solved urgently.
Correction to Solution of Dirac Equation
Rui Chen
2015-10-13
Using the China unitary principle to test the Dirac theoryfor the hydrogen atomic spectrum shows that the standard Dirac function withthe Dirac energy levels is only one the formal solutions of theDirac-Coulomb equation, which conceals some pivotal mathematicalcontradictions. The theorem of existence of solution of the Dirac equationrequires an important modification to the Dirac angular momentum constantthat was defined by Dirac's algebra. It derives the modified radial Diracequation which has the consistency solution involving the quantum neutronradius and the neutron binding energy. The inevitable solution for otheratomic energy states is only equivalent to the Bohr solution. It concludesthat the Dirac equation is more suitable to describe the structure ofneutron. How to treat the difference between the unitary energy levels andthe result of the experimental observation of the atomic spectrums for thehydrogen atom needs to be solved urgently.
Equation of State for Parallel Rigid Spherocylinders
Masashi Torikai
2012-08-06
The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto's method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto's original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto's original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2.
Financial Derivatives and Partial Differential Equations
Almgren, Robert F.
at which trades actually occured; this picture contains 5400 data points. The fastest oscillations, on scales of a few seconds, represent "bounce" between bid and ask prices. But complicated structure half-hour time intervals, for 1999 (about 3000 data values). Although the direction of the changes
Semirelativistic Bound-State Equations: Trivial Considerations
Wolfgang Lucha; Franz F. Schöberl
2014-07-17
Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the nonsingular Woods-Saxon potential and the singular Hulth\\'en potential, recall elementary tools that practitioners looking for analytic albeit approximate solutions might find useful in their quest.
Weakly nonlocal fluid mechanics - the Schrodinger equation
P. Van; T. Fulop
2004-06-09
A weakly nonlocal extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit the additional pressure term can be derived from a potential. The requirement of the additivity of the specific entropy function determines the quantum potential uniquely. The relation to other known derivations of Schr\\"odinger equation (stochastic, Fisher information, exact uncertainty) is clarified.
Bosonic Fradkin-Tseytlin equations unfolded
Oleg Shaynkman
2014-12-30
We test series of infinite-dimensional algebras as the candidates for higher spin extension of su(k,k). Adjoint and twisted-adjoint representations of su(k,k) on spaces of these algebras are carefully explored. For k=2 corresponding unfolded systems are analyzed and they shown to encode Fradkin-Tseytlin equations for some set of integer spins. In each case spectrum of spins is found.
High order difference methods for parabolic equations
Matuska, Daniel Alan
1971-01-01
HIGH ORDER DIFFERENCE METHODS FOR PARABOLIC E(PATIONS A Thesis by Daniel Alan Matuska Submitted to the Graduate College of Texas A&M University in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE May 1971 Ma...)or Sub]ect: Mathematics HIGH ORDER DIFFERENCE METHODS FOR PARABOLIC EQUATIONS A Thesis by Daniel Alan Matuska Approved as to style and content by: Pc~ &~ (Chairman of Committee) (Head of Department) (Member) C . (Member) (Member) (Member...
Commuting Matrix Solutions of PQCD Evolution Equations
Mehrdad Goshtasbpour; Seyed Ali Shafiei
2013-03-16
A method of obtaining parton distributions directly from data is revealed in this series. In the process, the first step would be developing appropriate matrix solutions of the evolution equations in $x$ space. A division into commuting and non-commuting matrix solutions has been made. Here, well-developed commuting matrix solutions are presented. Results for finite LO evolution match those of standard LO sets. There is a real potential of doing non-parametric data analysis.
Global evolution of random vortex filament equation
Z. Brze?niak; M. Gubinelli; M. Neklyudov
2013-07-04
We prove the existence of a global solution for the filament equation with inital condition given by a geometric rough path in the sense of Lyons (1998).Our work gives a positive answer to a question left open in recent publications: Berselli and Gubinelli (2007) showed the existence of global solution for a smooth initial condition while Bessaih, Gubinelli, Russo (2005) proved the existence of a local solution for a general initial condition given by a rough path.
Quantum Potential Via General Hamilton - Jacobi Equation
Maedeh Mollai; Mohammad Razavi; Safa Jami; Ali Ahanj
2011-10-29
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The interpretation of QP in terms of independent entity is discussed along with the introduction of quantum kinetic energy. The method has been extended to relativistic regime, and same results have been concluded.
Lyapunov Functionals for the Enskog Equation
Zhenglu Jiang
2006-08-27
Two Lyapunov functionals are presented for the Enskog equation. One is to describe interactions between particles with various velocities and another is to measure the $L^1$ distance between two classical solutions. The former yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the verification of the $L^1$ stability of global classical solutions.
Freeze Out and the Boltzmann Transport Equation
L. P. Csernai; V. K. Magas; E. Molnar; A. Nyiri; K. Tamosiunas
2005-02-20
Recently several works have appeared in the literature that addressed the problem of Freeze Out in energetic heavy ion reaction and aimed for a description based on the Boltzmann Transport Equation (BTE). In this paper we develop a dynamical Freeze-Out description, starting from the BTE, pointing out the basic limitations of the BTE approach, and the points where the BTE approach should be modified.
Modified Boltzmann Transport Equation and Freeze Out
Csernai, L P; Molnár, E; Nyiri, A; Tamosiunas, K
2005-01-01
We study Freeze Out process in high energy heavy ion reaction. The description of the process is based on the Boltzmann Transport Equation (BTE). We point out the basic limitations of the BTE approach and introduce Modified BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a layer of finite thickness, and we employ Modified BTE for the realistic Freeze Out description.
Modified Boltzmann Transport Equation and Freeze Out
L. P. Csernai; V. K. Magas; E. Molnar; A. Nyiri; K. Tamosiunas
2005-05-26
We study Freeze Out process in high energy heavy ion reaction. The description of the process is based on the Boltzmann Transport Equation (BTE). We point out the basic limitations of the BTE approach and introduce Modified BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a layer of finite thickness, and we employ Modified BTE for the realistic Freeze Out description.
Dilatonic Equation of Hydrostatic Equilibrium and Neutron Star Structure
S. H. Hendi; G. H. Bordbar; B. Eslam Panah; M. Najafi
2015-06-30
In this paper, we present a new hydrostatic equilibrium equation related to dilaton gravity. We consider a spherical symmetric metric to obtain the hydrostatic equilibrium equation of stars in $4$-dimensions, and generalize TOV equation to the case of regarding a dilaton field. Then, we calculate the structure properties of neutron star using our obtained hydrostatic equilibrium equation employing the modern equations of state of neutron star matter derived from microscopic calculations. We show that the maximum mass of neutron star depends on the parameters of dilaton field and cosmological constant. In other words, by setting the parameters of new hydrostatic equilibrium equation, we calculate the maximum mass of neutron star.
Stochastic semiclassical equations for weakly inhomogeneous cosmologies
Antonio Campos; Enric Verdaguer
1995-11-28
Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman and Vernon influence functional which describes the effect of the ``environment'', the quantum field which is coarse grained here, on the ``system'', the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be viewed now as mean field equations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.
Nonholonomic Hamilton-Jacobi equation and Integrability
Tomoki Ohsawa; Anthony M. Bloch
2009-12-18
We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton--Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton-Jacobi theory for unconstrained systems. The proof also helps us identify a geometric meaning of the conditions on the solutions of the Hamilton-Jacobi equation that arise from nonholonomic constraints. The major advantage of our result is that it provides us with a method of integrating the equations of motion just as the unconstrained Hamilton--Jacobi theory does. In particular, we build on the work by Iglesias-Ponte, de Leon, and Martin de Diego so that the conventional method of separation of variables applies to some nonholonomic mechanical systems. We also show a way to apply our result to systems to which separation of variables does not apply.
Total Operators and Inhomogeneous Proper Values Equations
Jose G. Vargas
2015-07-09
Kaehler's two-sided angular momentum operator, K + 1, is neither vector-valued nor bivector-valued. It is total in the sense that it involves terms for all three dimensions. Constant idempotents that are "proper functions" of K+1's components are not proper functions of K+1. They rather satisfy "inhomogeneous proper-value equations", i.e. of the form (K + 1)U = {\\mu}U + {\\pi}, where {\\pi} is a scalar. We consider an equation of that type with K+1 replaced with operators T that comprise K + 1 as a factor, but also containing factors for both space and spacetime translations. We study the action of those T's on linear combinations of constant idempotents, so that only the algebraic (spin) part of K +1 has to be considered. {\\pi} is now, in general, a non-scalar member of a Kaehler algebra. We develop the system of equations to be satisfied by the combinations of those idempotents for which {\\pi} becomes a scalar. We solve for its solutions with {\\mu} = 0, which actually also makes {\\pi} = 0: The solutions with {\\mu} = {\\pi} = 0 all have three constituent parts, 36 of them being different in the ensemble of all such solutions. That set of different constituents is structured in such a way that we might as well be speaking of an algebraic representation of quarks. In this paper, however, we refrain from pursuing this identification in order to emphasize the purely mathematical nature of the argument.
Guiding Center Equations for Ideal Magnetohydrodynamic Modes
Roscoe B. White
2013-02-21
Guiding center simulations are routinely used for the discovery of mode-particle resonances in tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions caused by a given spectrum of modes, including large scale avalanches during events with a number of large amplitude modes. One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through ?~B = ? X (? X B) however perturbs the magnetic topology, introducing extraneous magnetic islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian displacement of the field due to the perturbation and conserves magnetic topology as it should. In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories the guiding center equations should include a correct Lagrangian treatment. Guiding center equations for an ideal displacement ? are derived which perserve the magnetic topology and are used to examine mode particle resonances in toroidal confinement devices. These simulations are compared to others which are identical in all respects except that they use the linear representation for the field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding center equations does not result in extraneous mode particle resonances.
Guiding center equations for ideal magnetohydrodynamic modes
White, R. B. [Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543 (United States)
2013-04-15
Guiding center simulations are routinely used for the discovery of mode-particle resonances in tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions caused by a given spectrum of modes, including large scale avalanches during events with a number of large amplitude modes. One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through {delta}B-vector={nabla} Multiplication-Sign ({xi}-vector Multiplication-Sign B-vector), however, perturbs the magnetic topology, introducing extraneous magnetic islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian displacement of the field due to the perturbation and conserves magnetic topology as it should. In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories, the guiding center equations should include a correct Lagrangian treatment. Guiding center equations for an ideal displacement {xi}-vector are derived which preserve the magnetic topology and are used to examine mode particle resonances in toroidal confinement devices. These simulations are compared to others which are identical in all respects except that they use the linear representation for the field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding center equations does not result in extraneous mode particle resonances.
Solution generating theorems for the TOV equation
Petarpa Boonserm; Matt Visser; Silke Weinfurtner
2007-07-17
The Tolman-Oppenheimer-Volkov [TOV] equation constrains the internal structure of general relativistic static perfect fluid spheres. We develop several "solution generating" theorems for the TOV, whereby any given solution can be "deformed" to a new solution. Because the theorems we develop work directly in terms of the physical observables -- pressure profile and density profile -- it is relatively easy to check the density and pressure profiles for physical reasonableness. This work complements our previous article [Phys. Rev. D71 (2005) 124307; gr-qc/0503007] wherein a similar "algorithmic" analysis of the general relativistic static perfect fluid sphere was presented in terms of the spacetime geometry -- in the present analysis the pressure and density are primary and the spacetime geometry is secondary. In particular, our "deformed" solutions to the TOV equation are conveniently parameterized in terms of delta rho_c and delta p_c, the finite shift in the central density and central pressure. We conclude by presenting a new physical and mathematical interpretation of the TOV equation -- as an integrability condition on the density and pressure profiles.
Measuring the dark matter equation of state
Ana Laura Serra; Mariano Javier de León Domínguez Romero
2011-05-30
The nature of the dominant component of galaxies and clusters remains unknown. While the astrophysics community supports the cold dark matter (CDM) paradigm as a clue factor in the current cosmological model, no direct CDM detections have been performed. Faber and Visser 2006 have suggested a simple method for measuring the dark matter equation of state that combines kinematic and gravitational lensing data to test the widely adopted assumption of pressureless dark matter. Following this formalism, we have measured the dark matter equation of state for first time using improved techniques. We have found that the value of the equation of state parameter is consistent with pressureless dark matter within the errors. Nevertheless, the measured value is lower than expected because typically the masses determined with lensing are larger than those obtained through kinematic methods. We have tested our techniques using simulations and we have also analyzed possible sources of error that could invalidate or mimic our results. In the light of this result, we can now suggest that the understanding of the nature of dark matter requires a complete general relativistic analysis.
Spin crossover equation of state and sound velocities of (Mg0.65Fe0.35)O ferropericlase to 140 GPa
Jackson, Jennifer M.
Spin crossover equation of state and sound velocities of (Mg0.65Fe0.35)O ferropericlase to 140 GPa.65Fe0.35)O ("FP35"), a composition representative of deep mantle "pyrolite" or chondrite in diamond-anvil cells at 300 K. Combining with in situ XRD measurements, the Debye sound velocity of FP35
105TH CONGRESS REPORT " !HOUSE OF REPRESENTATIVES2d Session 105796
Hollaar, Lee A.
69006 105TH CONGRESS REPORT " !HOUSE OF REPRESENTATIVES2d Session 105796 DIGITAL MILLENNIUM the following CONFERENCE REPORT [To accompany H.R. 2281] The committee of conference on the disagreeing votes
105TH CONGRESS REPORT " !HOUSE OF REPRESENTATIVES2d Session 105452
Hollaar, Lee A.
59006 105TH CONGRESS REPORT " !HOUSE OF REPRESENTATIVES2d Session 105452 COPYRIGHT TERM EXTENSION, having considered the same, report favorably thereon with an amendment and recommend that the bill do
2Q CY2000 (PDF), Facility Representative Program Performance Indicators Quarterly Report
Broader source: Energy.gov [DOE]
"The Facility Representative Program Performance Indicators (PIs) Quarterly Report is attached, covering the period from April 2000 to June 2000. Data for these indicators are gathered by the Field...
112TH CONGRESS REPORT " !HOUSE OF REPRESENTATIVES1st Session 112
Efficiency and Renewable Energy ................................. 22 84 Electricity Delivery and Energy Reliability ............................... 22 93 Nuclear Energy66387 112TH CONGRESS REPORT " !HOUSE OF REPRESENTATIVES1st Session 112 ENERGY AND WATER
Broader source: Energy.gov [DOE]
Slide Presentation by Tom McQuiston, Dr. P.H., United Steelworkers - Tony Mazzocchi Center for Health, Safety and Environmental Education. Lessons Learned in Optimizing Workers’ and Worker Representatives’ Input in Work Planning and Control.
Gregory H. Friedman: Before The U.S. House of Representatives...
Office of Environmental Management (EM)
The U.S. House of Representatives Committee on Government Reform Subcommittee on the Federal Workforce and Agency Organization Gregory H. Friedman: Before The U.S. House of...
A characterization of causal automorphisms by wave equations
Do-Hyung Kim
2011-11-07
A characterization of causal automorphism on Minkowski spacetime is given by use of wave equation. The result shows that causal analysis of spacetime may be replaced by studies of wave equation on manifolds.
Solutions of Lattice Differential Equations over Inhomogeneous Media
Brucal Hallare, Maila
2012-12-31
nontrivial examples of lattice differential equations (LDEs) on Z that are related to the (homogeneous) lattice Nagumo equation. The LDEs that we consider are used to model natural phenomena defined over an inhomogeneous medium, namely: (1) a lattice Nagumo...
Weighted Energy Decay for 1D Dirac Equation
E. Kopylova
2011-02-10
We obtain a dispersive long-time decay in weighted energy norms for solutions of the 1D Dirac equation with generic potential. The decay extends the results obtained by Jensen, Kato and Murata for the Schr\\"odinger equations.
On the invariant thermal Proca - Klein - Gordon equation
Magdalena Pelc
2007-10-14
In this paper we discuss the invariant thermal Proca - Klein - Gordon equation (PKG). We argue that for the thermal PKG equation the absolute velocity is equal v = alpha*c, where alpha is the fine stucture constant for electromagnetic interaction.
Self-adjointness of a generalized Camassa-Holm equation
N. H. Ibragimov; R. Khamitova; A. Valenti
2011-04-01
It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, Ibragimov has shown that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization of the Camassa-Holm equation, we prove that the Camassa-Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa-Holm equation using its symmetries.
Outline for Linear Equations and Inequalities of 2 variables
charlotb
2010-04-15
Outline for Linear Equations and Inequalities of 2 variables. A. 1. Substitute any value for x in the equation and solve for y. This results in a point (x, y). OR.
Stochastic partial differential equations with singular terminal condition
Popier, Alexandre
Stochastic partial differential equations with singular terminal condition A Matoussi, Lambert Piozin, A Popier To cite this version: A Matoussi, Lambert Piozin, A Popier. Stochastic partial differential equations with singular terminal condition. 2015. HAL Id: hal-01152687 https
Pad\\'e interpolation for elliptic Painlev\\'e equation
Noumi, Masatoshi; Yamada, Yasuhiko
2012-01-01
An interpolation problem related to the elliptic Painlev\\'e equation is formulated and solved. A simple form of the elliptic Painlev\\'e equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also given.
Propagation of ultra-short solitons in stochastic Maxwell's equations
Kurt, Levent; Schäfer, Tobias
2014-01-15
We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.
EFFECTIVE MACROSCOPIC DYNAMICS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN PERFORATED
Duan, Jinqiao
EFFECTIVE MACROSCOPIC DYNAMICS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN PERFORATED DOMAINS equation defined on a domain perforated with small holes or heterogeneities. The homogenized effective, effective macroscopic model, stochastic homogenization, white noise, probability distribution, perforated
Derivation of the Camassa-Holm equations for elastic waves
H. A. Erbay; S. Erbay; A. Erkip
2015-02-10
In this paper we provide a formal derivation of both the Camassa-Holm equation and the fractional Camassa-Holm equation for the propagation of small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic medium. We first show that the equation of motion for the nonlocally and nonlinearly elastic medium reduces to the improved Boussinesq equation for a particular choice of the kernel function appearing in the integral-type constitutive relation. We then derive the Camassa-Holm equation from the improved Boussinesq equation using an asymptotic expansion valid as nonlinearity and dispersion parameters tend to zero independently. Our approach follows mainly the standard techniques used widely in the literature to derive the Camassa-Holm equation for shallow water waves. The case where the Fourier transform of the kernel function has fractional powers is also considered and the fractional Camassa-Holm equation is derived using the asymptotic expansion technique.
Mathematics of Fluids and Plasmas 1+2 -Outline February 9, 2007
Dundee, University of
., Euler Eq. Â· Conservation of mass, energy, equation of state. 3. Common approximations (2 lectures] Â· Linearised MHD equations, Â· Sound waves, Alfven waves, magnetoacoustic waves 6. Solar applications: [5) Â· Incompressible, irrotational, potential flow Â· Bernoulli's theorem 4. Laplace's equation (3 lectures) Â· Laplace
Nonlinear Integral Equations for the Inverse Problem in Corrosion ...
2012-06-15
Nonlinear Integral Equations for the Inverse. Problem in Corrosion Detection from Partial. Cauchy Data. Fioralba Cakoni. Department of Mathematical Sciences, ...
Soliton Solutions of Fractional order KdV-Burger's Equation
Muhammad Younis
2013-08-31
In this article, the new exact travelling wave solutions of the time-and space-fractional KdV-Burgers equation has been found. For this the fractional complex transformation have been implemented to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations, in the sense of the Jumarie's modified Riemann-Liouville derivative. Afterwards, the improved (G'/G)-expansion method can be implemented to celebrate the soliton solutions of KdV-Burger's equation of fractional order.
Direct Experimental Simulation of the Yang-Baxter Equation
Chao Zheng; Jun-lin Li; Si-yu Song; Gui Lu Long
2013-05-27
Introduced in the field of many-body statistical mechanics, Yang-Baxter equation has become an important tool in a variety fields of physics. In this work, we report the first direct experimental simulation of the Yang-Baxter equation using linear quantum optics. The equality between the two sides of the Yang-Baxter equation in two dimension has been demonstrated directly, and the spectral parameter transformation in the Yang-Baxter equation is explicitly confirmed.
221A Lecture Notes 1 HamiltonJacobi Equation
Murayama, Hitoshi
221A Lecture Notes WKB Method 1 HamiltonJacobi Equation We start from the Schr¨odinger equation this equation by using (x, t) = eiS(x,t)/¯h : - S t = 1 2m ( S)2 - i¯h 2m ( 2 S) + V . (2) Assuming = 0, this leads to an equation - S t = 1 2m ( S)2 - i¯h 2m ( 2 S) + V. (3) Now taking the formal limit ¯h 0
Transformations of Heun's equation and its integral relations
Léa Jaccoud El-Jaick; Bartolomeu D. B. Figueiredo
2011-01-26
We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erd\\'elyi-type). Such kernels, by a limiting process, also afford new kernels for the confluent Heun equation.
ARTICULATORY SYNTHESIS: NUMERICAL SOLUTION OF A HYPERBOLIC DIFFERENTIAL EQUATION
into the context of finite-difference approximations to a differential equation describing acoustic wave-that of solving the differ- ential equation describing acoustic (small amplitude), one-dimensional propagationARTICULATORY SYNTHESIS: NUMERICAL SOLUTION OF A HYPERBOLIC DIFFERENTIAL EQUATION Richard S. Mc
Theory Revision in Equation Discovery Ljupco Todorovski and Saso Dzeroski
Dzeroski, Saso
.Dzeroski@ijs.si Abstract. State of the art equation discovery systems start the discov- ery process from scratch, rather the accuracy of the model. 1 Introduction Most of the existing equation discovery systems make use of a very neglected by the equation discovery systems are the existing models in the domain. Rather than starting
The Whitham Equation as a Model for Surface Water Waves
Daulet Moldabayev; Henrik Kalisch; Denys Dutykh
2014-10-30
The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of the water wave problem, it is thought to provide a more faithful description of shorter waves of small amplitude than traditional long wave models such as the KdV equation. In this work, we identify a scaling regime in which the Whitham equation can be derived from the Hamiltonian theory of surface water waves. The Whitham equation is integrated numerically, and it is shown that the equation gives a close approximation of inviscid free surface dynamics as described by the Euler equations. The performance of the Whitham equation as a model for free surface dynamics is also compared to two standard free surface models: the KdV and the BBM equation. It is found that in a wide parameter range of amplitudes and wavelengths, the Whitham equation performs on par with or better than both the KdV and BBM equations.
Two-component equations modelling water waves with constant vorticity
Joachim Escher; David Henry; Boris Kolev; Tony Lyons
2014-09-30
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to recast this equation as a geodesic flow on an infinite dimensional manifold. Finally, we provide a criteria for global existence.
French-Chinese School on Differential and Functional Equations
Pouyanne, Nicolas
French-Chinese School on Differential and Functional Equations Wuhan University Wuhan, China, April 16th-27th, 2012 #12;French-Chinese School on Differential and Functional Equations, Wuhan, China, April 16th-27th, 2012 French-Chinese School on Differential and Functional Equations Wuhan, China, April
Radon transform and kinetic equations in tomographic representation
V. N. Chernega; V. I. Man'ko; B. I. Sadovnikov
2009-11-01
Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for classical systems with tomographic probability distributions is elucidated. Examples of simple kinetic equations like Liouville equations for one and many particles are studied in detail.
Long-wave instabilities and saturation in thin film equations
Pugh, Mary
to shorter wavelengths which then dissipate the energy. The nonlinearity in the KS equation is advective.2) The equation arises as an interface model in bio-fluids [15], solar convec- tion [19], and binary alloys [48Long-wave instabilities and saturation in thin film equations A. L. Bertozzi Department
Longwave instabilities and saturation in thin film equations
Pugh, Mary
then dissipate the energy. The nonlinearity in the KS equation is advective, and a#ects the dyÂ namics di.2) The equation arises as an interface model in bioÂfluids [15], solar convecÂ tion [19], and binary alloys [48LongÂwave instabilities and saturation in thin film equations A. L. Bertozzi Department
Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanal-
International Association for Cryptologic Research (IACR)
Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanal- ysis. In this paper, we apply similar graph theory techniques to systems of multivariate polynomial equations to a system of multivariate polynomial equations is an NP-complete problem [7, Ch. 3.9]. A variety of solution
EXISTENCE OF INSENSITIZING CONTROLS FOR A SEMILINEAR HEAT EQUATION WITH
González Burgos, Manuel
EXISTENCE OF INSENSITIZING CONTROLS FOR A SEMILINEAR HEAT EQUATION WITH A SUPERLINEAR NONLINEARITY system of heat equations, the first one of semilinear type. In addition, the control enters on the second by D.G.E.S. (Spain), Grant PB981134. Abstract In this paper we consider a semilinear heat equation (in
September 2011 Discrete Wheeler-DeWitt Equation
Hamber, Herbert W.
September 2011 Discrete Wheeler-DeWitt Equation Herbert W. Hamber 1 Institut des Hautes Etudes, Cambridge CB3 0JG, United Kingdom. ABSTRACT We present a discrete form of the Wheeler-DeWitt equation, with the solutions to the lattice equations providing a suitable approximation to the continuum wave functional
On linearization of super sine-Gordon equation
M. Siddiq; M. Hassan
2006-05-09
Two sets of super Riccati equations are presented which result in two linear problems of super sine-Gordon equation. The linear problems are then shown to be related to each other by a super gauge transformation and to the super B\\"{a}cklund transformation of the equation.
Differential Equations Lectures INF2320 p. 1/6
Stølen, Ketil
of Calculus, we get the solution r(t) = r(0)+ t 0 f(s)ds (3) · The integral can then be calculated as accurateDifferential Equations Lectures INF2320 p. 1/6 #12;Differential equations · A differential be determined · In practice, differential equations typically describe quantities that changes in relation
UNCONDITIONALLY STABLE METHODS FOR HAMILTON-JACOBI EQUATIONS
UNCONDITIONALLY STABLE METHODS FOR HAMILTON-JACOBI EQUATIONS KENNETH HVISTENDAHL KARLSEN AND NILS to the Cauchy problem for Hamilton-Jacobi equations of the form u t + H(Dxu) = 0. The methods are based stable numerical methods for the Cauchy problem for multi-dimensional Hamilton-Jacobi equations ( u t +H
Reasoning About Systems of Physics Equations Chun Wai Liew1
Liew, Chun Wai
Reasoning About Systems of Physics Equations Chun Wai Liew1 and Donald E. Smith2 1 Department Physics require the student to enter a system of algebraic equations as the answer. Tutoring systems must presents an approach that accepts from the student a system of equations describing the physics
Developments of the Price equation and natural selection under uncertainty
Grafen, Alan
success, following Darwin (1859). Here, this project is pursued by developing the Price equation, ¢rstDevelopments of the Price equation and natural selection under uncertainty Alan Grafen Department to employ these approaches. Here, a new theore- tical development arising from the Price equation provides
Heavy tailed K distributions imply a fractional advection dispersion equation
Meerschaert, Mark M.
Dispersion Equation (FADE) to model contaminant transport in porous media. This equation characterizes, and Particle Jumps Equations of contaminant transport in porous media are based on assumptions about hydraulic governing groundwater flow (e.g., Freeze and Cherry, 1979): h K v - = (1) where v is average velocity
Lagrangian Reduction, the EulerPoincare Equations, and Semidirect Products
Marsden, Jerrold
reduction for semidirect products, which applies to examples such as the heavy top, com- pressible fluids equations for a fluid or a rigid body, namely Lie-Poisson systems on the dual of a Lie algebra and their Lagrangian counterpart, the "pure" Euler-Poincar´e equations on a Lie algebra. The Lie-Poisson Equations
On Gaussian Beams Described by Jacobi's Equation
Steven Thomas Smith
2014-04-18
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the \\v{C}erven\\'y equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton-Jacobi theory with Jacobi's equation that connects Riemannian curvature to geodesic flow. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gaussian curvature in which the geometry of ducts corresponds to great circles on a sphere and convergence zones correspond to antipodes. The distance between caustics $\\pi(c/c")^{1/2}$ is equated with an ideal hyperbolic cosine SSP duct. (4) An "intrinsic" version of \\v{C}erven\\'y's formulae for the amplitude and phase of Gaussian beams is derived that does not depend on an "extrinsic" arbitrary choice of coordinates such as range and depth. Direct comparisons are made between the computational frameworks used by the three different approaches to Gaussian beams: Snell's law, the extrinsic Frenet-Serret formulae, and the intrinsic Jacobi methods presented here. The relationship of Gaussian beams to Riemannian curvature is explained with an overview of the modern covariant geometric methods that provide a general framework for application to other special cases.
Stochastic evolution equations with random generators
Leon, Jorge A.; Nualart, David
1998-05-01
maximal inequality for the Skorohod integral deduced from the It ˆ o’s formula for this anticipating stochastic integral. 1. Introduction. In this paper we study nonlinear stochastic evolution equations of the form X t = ? + ? t 0 #3;A#3;s#4;X s +F#3;s#7;X.... The functions F#3;s#7;?#7; x#4; and B#3;s#7;?#7; x#4; are predictable processes satisfying suitable Lipschitz–type conditions and taking values in H and L 2 #3;U#7;H#4;, respectively. We will assume that A#3;s#7;?#4; is a random family of unbounded operators...
Canonical equations of ideal magnetic hydrodynamics
Gorskii, V.B.
1987-07-01
Ideal magnetohydrodynamics is used to consider a general class of adiabatic flow in magnetic liquids. Two invariants of the canonical equations of motion--Hamiltonian and Lagrangian--are determined in terms of the canonical variables by using the approximate variational formulations. The resulting model describes adiabatic three-dimensional flow of a nonviscous compressible liquid with ideal electric conductivity and zero heat conductivity. A Clebsch transformation is used to arrive at a form of the Lagrange-Cauchy integral for a vortex flow.
An Interesting Class of Partial Differential Equations
Wen-an Yong
2007-08-28
This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a direct relation of irreversible processes to the entropy change. We show that the properties imply various entropy dissipation conditions for hyperbolic relaxation problems. As an application of the observation, we propose an approximation method to solve relaxation problems. Moreover, the observation is interpreted physically and verified with eight (sets of) systems from different fields.
Solving the Schroedinger equation using Smolyak interpolants
Avila, Gustavo; Carrington, Tucker Jr.
2013-10-07
In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased.
The Schrodinger Equation as a Volterra Problem
Mera, Fernando Daniel
2011-08-08
is obtained from Chapter IV of Lawrence C. Evans?s book on partial di erential equations [5]. Let y = x+ z, where 2 = 2~tm ; then we can rewrite the Poisson integral as u(x; t) = 1 i n=2 Z Rn eijzj 2 f(x+ z) dz (II.18) where jzj = jx yj . Let... implies that 8 > 0 9 > 0 such that 8x 2 Rn with jx yj 0, then there exists a t so small such that jf(x + z) f(x)j < for all z...
Efficient Solution of the Simplified PN Equations
Hamilton, Steven P [ORNL; Evans, Thomas M [ORNL
2015-01-01
In this paper we show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. Our results show that the most ecient approach is the generalized Davidson method, that is 30{40 times faster than traditional power iteration and 6{10 times faster than Arnoldi's method.
Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem
Albert Schwarz
2000-04-27
We analyze the perturbation series for noncommutative eigenvalue problem $AX=X\\lambda$ where $\\lambda$ is an element of a noncommutative ring, $ A$ is a matrix and $X$ is a column vector with entries from this ring. As a corollary we obtain a theorem about the structure of perturbation series for Tr $x^r$ where $x$ is a solution of noncommutative algebraic equation (for $r=1$ this theorem was proved by Aschieri, Brace, Morariu, and Zumino, hep-th/0003228, and used to study Born-Infeld lagrangian for the gauge group $U(1)^k$).
Reducing differential equations for multiloop master integrals
Roman N. Lee
2015-04-21
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter $\\epsilon$. We consider linear transformations of the functions column which are rational in the variable and in $\\epsilon$. Apart from some degenerate cases described below, the algorithm allows one to obtain the required transformation or to ascertain irreducibility to the form required. Degenerate cases are quite anticipated and likely to correspond to irreducible systems.
Generalized Ideal Gas Equations for Structureful Universe
Shahid N. Afridi; Khalid Khan
2006-09-04
We have derived generalized ideal gas equations for a structureful universe consisting of all forms of matters. We have assumed a universe that contains superclusters. Superclusters are then made of clusters. Each cluster can be further divided into smaller ones and so on. We have derived an expression for the entropy of such a universe. Our model is rather independent of the geometry of the intermediate clusters. Our calculations are valid for a non-interacting universe within non-relativistic limits. We suggest that structure formation can reduce the expansion rate of the universe.
On the multivariate Burgers equation and the incompressible Navier-Stokes equation (Part I)
Joerg Kampen
2011-03-14
We provide a constructive global existence proof for the multivariate viscous Burgers equation system defined on the whole space or on a domain isomorphic to the n-torus and with time horizon up to infinity and C^{\\infty}- data (satisfying some growth conditions if the problem is posed on the whole space). The proof is by a time discretized semiexplicit perturbative expansion in transformed coordinates where the convergence is guaranteed by certain a priori estimates. The scheme is useful in order to define computation for related equation systems of fluid dynamics.
Schrödinger-Pauli Equation for the Standard Model Extension CPT-Violating Dirac Equation
Thomas D. Gutierrez
2015-04-06
It is instructive to investigate the non-relativistic limit of the simplest Standard Model Extension (SME) CPT-violating Dirac-like equation but with minimal coupling to the electromagnetic fields. In this limit, it becomes an intuitive Schr\\"odinger-Pauli-like equation. This is comparable to the free particle treatment as explored by Kostelecky and Lane, but this exercise only considers the $a$ and $b$ CPT-violating terms and $\\vec{p}/m$ terms to first order. Several toy systems are discussed.
Calculating work in weakly driving quantum master equations: backward and forward equations
Fei Liu
2015-06-28
We present a technical report that the two methods of calculating characteristic functions for the work distribution in the weakly driven quantum master equations are equivalent. One is obtained by the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014)], while the other is based on the two time energy measurements on the combined system and reservoir [Silaev, et al., Phys. Rev. E 90, 022103 (2014)]. They are indeed the backward and forward methods, respectively, which is very similar to the case of the Kolmogorov backward and forward equations in classical stochastic theory. The microscopic basis of the former method is also clarified.
Craig, Walter
The Boltzmann equation Global existence results Uniqueness Properties of propagation Main ideas of the proof On the Boltzmann equation: global solutions in one spatial dimension Walter Craig Department 11, 2005 Walter Craig McMaster University Global solutions of the Boltzmann equation #12;The
Integral equations for the H- X- and Y-functions
B. Rutily; L. Chevallier; J. Bergeat
2006-01-16
We come back to a non linear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex plane using the method of residues. Then its counterpart in a finite slab is derived; it consists in two series of integral equations for the X- and Y-functions. These integral equations are finally applied to the solution of the albedo problem in a slab.
Topography influence on the Lake equations in bounded domains
Christophe Lacave; Toan T. Nguyen; Benoit Pausader
2013-06-10
We investigate the influence of the topography on the lake equations which describe the two-dimensional horizontal velocity of a three-dimensional incompressible flow. We show that the lake equations are structurally stable under Hausdorff approximations of the fluid domain and $L^p$ perturbations of the depth. As a byproduct, we obtain the existence of a weak solution to the lake equations in the case of singular domains and rough bottoms. Our result thus extends earlier works by Bresch and M\\'etivier treating the lake equations with a fixed topography and by G\\'erard-Varet and Lacave treating the Euler equations in singular domains.
Integer Algorithms to Solver Diophantine Linear Equations and Systems
Florentin Smarandache
2007-11-28
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to Diophantine linear equations with $n$ unknowns and then to Diophantine linear systems. The proprieties of the general integer solution are determined (both for a Diophantine linear equation and for a Diophantine linear system). Seven original integer algorithms (two for Diophantine linear equations, and five for Diophantine linear systems) are exposed. The algorithms are strictly proved and an example for each of them is given. These algorithms can be easily implemented on the computer.
Modulated wave trains in generalized Kuramoto-Sivashinksi equations
Noble, Pascal
2010-01-01
This paper is concerned with the stability of periodic wave trains in a generalized Kuramoto-Sivashinski (gKS) equation. This equation is useful to describe the weak instability of low frequency perturbations for thin film flows down an inclined ramp. We provide a set of equations, namely Whitham's modulation equations, that determines the behaviour of low frequency perturbations of periodic wave trains. As a byproduct, we relate the spectral stability in the small wavenumber regime to properties of the modulation equations. This stability is always critical since 0 is a 0-Floquet number eigenvalue associated to translational invariance.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)] [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)
2013-08-15
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
Using the scalable nonlinear equations solvers package
Gropp, W.D.; McInnes, L.C.; Smith, B.F.
1995-02-01
SNES (Scalable Nonlinear Equations Solvers) is a software package for the numerical solution of large-scale systems of nonlinear equations on both uniprocessors and parallel architectures. SNES also contains a component for the solution of unconstrained minimization problems, called SUMS (Scalable Unconstrained Minimization Solvers). Newton-like methods, which are known for their efficiency and robustness, constitute the core of the package. As part of the multilevel PETSc library, SNES incorporates many features and options from other parts of PETSc. In keeping with the spirit of the PETSc library, the nonlinear solution routines are data-structure-neutral, making them flexible and easily extensible. This users guide contains a detailed description of uniprocessor usage of SNES, with some added comments regarding multiprocessor usage. At this time the parallel version is undergoing refinement and extension, as we work toward a common interface for the uniprocessor and parallel cases. Thus, forthcoming versions of the software will contain additional features, and changes to parallel interface may result at any time. The new parallel version will employ the MPI (Message Passing Interface) standard for interprocessor communication. Since most of these details will be hidden, users will need to perform only minimal message-passing programming.
Wave Equations for Discrete Quantum Gravity
Gudder, Stan
2015-01-01
This article is based on the covariant causal set ($c$-causet) approach to discrete quantum gravity. A $c$-causet $x$ is a finite partially ordered set that has a unique labeling of its vertices. A rate of change on $x$ is described by a covariant difference operator and this operator acting on a wave function forms the left side of the wave equation. The right side is given by an energy term acting on the wave function. Solutions to the wave equation corresponding to certain pairs of paths in $x$ are added and normalized to form a unique state. The modulus squared of the state gives probabilities that a pair of interacting particles is at various locations given by pairs of vertices in $x$. We illustrate this model for a few of the simplest nontrivial examples of $c$-causets. Three forces are considered, the attractive and repulsive electric forces and the strong nuclear force. Large models get much more complicated and will probably require a computer to analyze.
Wave Equations for Discrete Quantum Gravity
Stan Gudder
2015-08-29
This article is based on the covariant causal set ($c$-causet) approach to discrete quantum gravity. A $c$-causet $x$ is a finite partially ordered set that has a unique labeling of its vertices. A rate of change on $x$ is described by a covariant difference operator and this operator acting on a wave function forms the left side of the wave equation. The right side is given by an energy term acting on the wave function. Solutions to the wave equation corresponding to certain pairs of paths in $x$ are added and normalized to form a unique state. The modulus squared of the state gives probabilities that a pair of interacting particles is at various locations given by pairs of vertices in $x$. We illustrate this model for a few of the simplest nontrivial examples of $c$-causets. Three forces are considered, the attractive and repulsive electric forces and the strong nuclear force. Large models get much more complicated and will probably require a computer to analyze.
Alberto Barchielli
2015-06-24
The quantum stochastic Schroedinger equation or Hudson-Parthasareathy (HP) equation is a powerful tool to construct unitary dilations of quantum dynamical semigroups and to develop the theory of measurements in continuous time via the construction of output fields. An important feature of such an equation is that it allows to treat not only absorption and emission of quanta, but also scattering processes, which however had very few applications in physical modelling. Moreover, recent developments have shown that also some non-Markovian dynamics can be generated by suitable choices of the state of the quantum noises involved in the HP-equation. This paper is devoted to an application involving these two features, non-Markovianity and scattering process. We consider a micro-mirror mounted on a vibrating structure and reflecting a laser beam, a process giving rise to a radiation-pressure force on the mirror. We show that this process needs the scattering part of the HP-equation to be described. On the other side, non-Markovianity is introduced by the dissipation due to the interaction with some thermal environment which we represent by a phonon field, with a nearly arbitrary excitation spectrum, and by the introduction of phase noise in the laser beam. Finally, we study the full power spectrum of the reflected light and we show how the laser beam can be used as a temperature probe.
Multiscale functions, Scale dynamics and Applications to partial differential equations
Jacky Cresson; Frédéric Pierret
2015-09-03
Modeling phenomena from experimental data, always begin with a \\emph{choice of hypothesis} on the observed dynamics such as \\emph{determinism}, \\emph{randomness}, \\emph{derivability} etc. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following : \\emph{"With a finite set of data concerning a phenomenon, can we recover its underlying nature ?} From this problem, we introduce in this paper the definition of \\emph{multi-scale functions}, \\emph{scale calculus} and \\emph{scale dynamics} based on the \\emph{time-scale calculus} (see \\cite{bohn}). These definitions will be illustrated on the \\emph{multi-scale Okamoto's functions}. The introduced formalism explains why there exists different continuous models associated to an equation with different \\emph{scale regimes} whereas the equation is \\emph{scale invariant}. A typical example of such an equation, is the \\emph{Euler-Lagrange equation} and particularly the \\emph{Newton's equation} which will be discussed. Notably, we obtain a \\emph{non-linear diffusion equation} via the \\emph{scale Newton's equation} and also the \\emph{non-linear Schr\\"odinger equation} via the \\emph{scale Newton's equation}. Under special assumptions, we recover the classical \\emph{diffusion} equation and the \\emph{Schr\\"odinger equation}.
Poincare-invariant equations with a rising mass spectrum
Wilhelm I. Fushchych
2002-06-21
In this note we shall construct, in the framework of relativistic quantum mechanics, the Poincare-invariant motion equations with realistic mass spectra. These equations describe a system with mass spectra of the form $m^2=a^2+b^2 s(s+1)$, where a and b are arbitrary parameters. Such equations are obtained by a reduction of the motion equation for two particles to a one-particle equation which describes the particle in various mass and spin states. It we impose a certain condition on the wave function of the derived equation, such an equation describes the free motion of a fixed-mass particle with arbitrary (but fixed) spin s.
Nonlinear Integral-Equation Formulation of Orthogonal Polynomials
Carl M. Bender; E. Ben-Naim
2006-11-15
The nonlinear integral equation P(x)=\\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial solutions is orthogonal with respect to the measure x w(x). The nonlinear integral equation can be used to specify all orthogonal polynomials in a simple and compact way. This integral equation provides a natural vehicle for extending the theory of orthogonal polynomials into the complex domain. Generalizations of the integral equation are discussed.
The Master Equation for Two-Level Accelerated Systems at Finite Temperature
Jeferson Tomazelli; Renan Cunha
2015-12-05
In this work we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a \\emph{reservoir} in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a \\emph{reservoir}, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.