Analysis of fuel shares in the industrial sector
Roop, J.M.; Belzer, D.B.
1986-06-01
These studies describe how fuel shares have changed over time; determine what factors are important in promoting fuel share changes; and project fuel shares to the year 1995 in the industrial sector. A general characterization of changes in fuel shares of four fuel types - coal, natural gas, oil and electricity - for the industrial sector is as follows. Coal as a major fuel source declined rapidly from 1958 to the early 1970s, with oil and natural gas substituting for coal. Coal's share of total fuels stabilized after the oil price shock of 1972-1973, and increased after the 1979 price shock. In the period since 1973, most industries and the industrial sector as a whole appear to freely substitute natural gas for oil, and vice versa. Throughout the period 1958-1981, the share of electricity as a fuel increased. These observations are derived from analyzing the fuel share patterns of more than 20 industries over the 24-year period 1958 to 1981.
DOE R&D Accomplishments [OSTI]
1998-09-21
In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
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.
Set Equation Transformation System.
Energy Science and Technology Software Center (OSTI)
2002-03-22
Version 00 SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protectionmore » requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system. Two auxiliary programs, SEP and FTD, are included. SEP performs the quantitative analysis of reduced Boolean equations (minimal cut sets) produced by SETS. The user can manipulate and evaluate the equations to find the probability of occurrence of any desired event and to produce an importance ranking of the terms and events in an equation. FTD is a fault tree drawing program which uses the proprietary ISSCO DISSPLA graphics software to produce an annotated drawing of a fault tree processed by SETS. The DISSPLA routines are not included.« less
Parallel Multigrid Equation Solver
Energy Science and Technology Software Center (OSTI)
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
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.
Menikoff, Ralph
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Generalizing the cosmic energy equation
Shtanov, Yuri; Sahni, Varun
2010-11-15
We generalize the cosmic energy equation to the case when massive particles interact via a modified gravitational potential of the form {phi}(a,r), which is allowed to explicitly depend upon the cosmological time through the expansion factor a(t). Using the nonrelativistic approximation for particle dynamics, we derive the equation for the cosmological expansion which has the form of the Friedmann equation with a renormalized gravitational constant. The generalized Layzer-Irvine cosmic energy equation and the associated cosmic virial theorem are applied to some recently proposed modifications of the Newtonian gravitational interaction between dark-matter particles. We also draw attention to the possibility that the cosmic energy equation may be used to probe the expansion history of the universe thereby throwing light on the nature of dark matter and dark energy.
Friedmann equations from entropic force
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
2010-03-15
In this paper, by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.
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.
Nonextensive Boltzmann Equation and Hadronization
Biro, T.S.; Purcsel, G.
2005-10-14
We present a novel nonextensive generalization of the Boltzmann equation. We investigate the evolution of the one-particle distribution in this framework. The stationary solution is exponential in a nonlinear function of the original energy. The total energy is composed using a general, associative nonextensive rule. We propose that for describing the hadronization of quark matter such rules may apply.
Ordinary Differential Equation System Solver
Energy Science and Technology Software Center (OSTI)
1992-03-05
LSODE is a package of subroutines for the numerical solution of the initial value problem for systems of first order ordinary differential equations. The package is suitable for either stiff or nonstiff systems. For stiff systems the Jacobian matrix may be treated in either full or banded form. LSODE can also be used when the Jacobian can be approximated by a band matrix.
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.
ADVANCED WAVE-EQUATION MIGRATION
L. HUANG; M. C. FEHLER
2000-12-01
Wave-equation migration methods can more accurately account for complex wave phenomena than ray-tracing-based Kirchhoff methods that are based on the high-frequency asymptotic approximation of waves. With steadily increasing speed of massively parallel computers, wave-equation migration methods are becoming more and more feasible and attractive for imaging complex 3D structures. We present an overview of several efficient and accurate wave-equation-based migration methods that we have recently developed. The methods are implemented in the frequency-space and frequency-wavenumber domains and hence they are called dual-domain methods. In the methods, we make use of different approximate solutions of the scalar-wave equation in heterogeneous media to recursively downward continue wavefields. The approximations used within each extrapolation interval include the Born, quasi-Born, and Rytov approximations. In one of our dual-domain methods, we use an optimized expansion of the square-root operator in the one-way wave equation to minimize the phase error for a given model. This leads to a globally optimized Fourier finite-difference method that is a hybrid split-step Fourier and finite-difference scheme. Migration examples demonstrate that our dual-domain migration methods provide more accurate images than those obtained using the split-step Fourier scheme. The Born-based, quasi-Born-based, and Rytov-based methods are suitable for imaging complex structures whose lateral variations are moderate, such as the Marmousi model. For this model, the computational cost of the Born-based method is almost the same as the split-step Fourier scheme, while other methods takes approximately 15-50% more computational time. The globally optimized Fourier finite-difference method significantly improves the accuracy of the split-step Fourier method for imaging structures having strong lateral velocity variations, such as the SEG/EAGE salt model, at an approximately 30% greater
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.
Germanium multiphase equation of state
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Crockett, Scott D.; Lorenzi-Venneri, Giulia De; Kress, Joel D.; Rudin, Sven P.
2014-05-07
A new SESAME multiphase germanium equation of state (EOS) has been developed using the best available experimental data and density functional theory (DFT) calculations. The equilibrium EOS includes the Ge I (diamond), the Ge II (β-Sn) and the liquid phases. The foundation of the EOS is based on density functional theory calculations which are used to determine the cold curve and the Debye temperature. Results are compared to Hugoniot data through the solid-solid and solid-liquid transitions. We propose some experiments to better understand the dynamics of this element
The equation of state of nuclear matter
Gandolfi, Stefano; Carlson, Joseph Allen
2015-06-30
A brief status report of research on equation of state (EOS) of nuclear matter is provided, along with two graphs.
Product equation of state for polysulfone
Ticknor, Christopher
2015-09-30
Here we review the new polysulfone product equation of state (EOS) made with magpie, a chemical equilibrium code.
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.
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.
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.
Double distributions and evolution equations
A.V. Radyushkin
1998-05-01
Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements < p{prime} {vert_bar}O(0,z){vert_bar}p > of quark and gluon light-cone operators. In their previous papers the authors used two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{sub {zeta}}(X;t). Here they discuss in more detail the double distributions (DD's) and evolution equations which they satisfy. They propose simple models for F(x,y;t=0) DD's with correct spectral and symmetry properties which also satisfy the reduction relations connecting them to the usual parton densities f(x). In this way, they obtain self-consistent models for the {zeta}-dependence of nonforward distributions. They show that, for small {zeta}, one can easily obtain nonforward distributions (in the X > {zeta} region) from the parton densities: F{sub {zeta}} (X;t=0) {approx} f(X{minus}{zeta}/2).
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.
The Boltzmann equation in the difference formulation
Szoke, Abraham; Brooks III, Eugene D.
2015-05-06
First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.
The generalized SchrdingerLangevin equation
Bargueo, Pedro; Miret-Arts, Salvador
2014-07-15
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called SchrdingerLangevin 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 systembath coupling. This generalization is developed both in the Schrdinger and Bohmian formalisms. We write the generalized Kostin equation for two measurement problems. We reformulate the generalized uncertainty principle in terms of this equation.
Fokker-Planck equation in mirror research
Post, R.F.
1983-08-11
Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror.
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.
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.
Probability Density Function Method for Langevin Equations with...
Office of Scientific and Technical Information (OSTI)
Language: English Subject: PDF method, uncertainty quantification, Langevin equation, Fokker-Planck equation, colored-noise, Large-Eddy-Diffusivity approximation Word Cloud More ...
Equation of State Measurements by Radiography Provide Evidence...
Office of Scientific and Technical Information (OSTI)
Equation of State Measurements by Radiography Provide Evidence for a Liquid-Liquid Phase Transition in Cerium Citation Details In-Document Search Title: Equation of State ...
Nonparametric reconstruction of the dark energy equation of state...
Office of Scientific and Technical Information (OSTI)
energy equation of state from diverse data sets Citation Details In-Document Search Title: Nonparametric reconstruction of the dark energy equation of state from diverse data ...
Equation of State from Lattice QCD Calculations (Conference)...
Office of Scientific and Technical Information (OSTI)
Conference: Equation of State from Lattice QCD Calculations Citation Details In-Document Search Title: Equation of State from Lattice QCD Calculations You are accessing a...
Probability Density Function Method for Langevin Equations with...
Office of Scientific and Technical Information (OSTI)
Probability Density Function Method for Langevin Equations with Colored Noise Citation Details In-Document Search Title: Probability Density Function Method for Langevin Equations ...
Iterative solution of Hermite boundary integral equations (Journal...
Office of Scientific and Technical Information (OSTI)
Iterative solution of Hermite boundary integral equations Citation Details In-Document Search Title: Iterative solution of Hermite boundary integral equations An efficient ...
An Acoustic Wave Equation for Tilted Transversely Isotropic Media...
Office of Scientific and Technical Information (OSTI)
An Acoustic Wave Equation for Tilted Transversely Isotropic Media Citation Details In-Document Search Title: An Acoustic Wave Equation for Tilted Transversely Isotropic Media ...
Solves the Multigroup Neutron Diffusion Equation
Energy Science and Technology Software Center (OSTI)
1995-06-23
GNOMER is a program which solves the multigroup neutron diffusion equation in 1D, 2D and 3D cartesian geometry. The program is designed to calculate the global core power distributions (with thermohydraulic feedbacks), as well as power distribution and homogenized cross sections over a fuel assembly.
Ultra Deep Wave Equation Imaging and Illumination
Alexander M. Popovici; Sergey Fomel; Paul Sava; Sean Crawley; Yining Li; Cristian Lupascu
2006-09-30
In this project we developed and tested a novel technology, designed to enhance seismic resolution and imaging of ultra-deep complex geologic structures by using state-of-the-art wave-equation depth migration and wave-equation velocity model building technology for deeper data penetration and recovery, steeper dip and ultra-deep structure imaging, accurate velocity estimation for imaging and pore pressure prediction and accurate illumination and amplitude processing for extending the AVO prediction window. Ultra-deep wave-equation imaging provides greater resolution and accuracy under complex geologic structures where energy multipathing occurs, than what can be accomplished today with standard imaging technology. The objective of the research effort was to examine the feasibility of imaging ultra-deep structures onshore and offshore, by using (1) wave-equation migration, (2) angle-gathers velocity model building, and (3) wave-equation illumination and amplitude compensation. The effort consisted of answering critical technical questions that determine the feasibility of the proposed methodology, testing the theory on synthetic data, and finally applying the technology for imaging ultra-deep real data. Some of the questions answered by this research addressed: (1) the handling of true amplitudes in the downward continuation and imaging algorithm and the preservation of the amplitude with offset or amplitude with angle information required for AVO studies, (2) the effect of several imaging conditions on amplitudes, (3) non-elastic attenuation and approaches for recovering the amplitude and frequency, (4) the effect of aperture and illumination on imaging steep dips and on discriminating the velocities in the ultra-deep structures. All these effects were incorporated in the final imaging step of a real data set acquired specifically to address ultra-deep imaging issues, with large offsets (12,500 m) and long recording time (20 s).
Dark soliton solution of Sasa-Satsuma equation
Ohta, Y.
2010-03-08
The Sasa-Satsuma equation is a higher order nonlinear Schroedinger type equation which admits bright soliton solutions with internal freedom. We present the dark soliton solutions for the equation by using Gram type determinant. The dark solitons have no internal freedom and exist for both defocusing and focusing equations.
Wang, Chi-Jen
2013-01-01
In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.
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.
The quasicontinuum Fokker-Plank equation
Alexander, Francis J
2008-01-01
We present a regularized Fokker-Planck equation with more accurate short-time and high-frequency behavior for continuous-time, discrete-state systems. The regularization preserves crucial aspects of state-space discreteness lost in the standard Kramers-Moyal expansion. We apply the method to a simple example of biochemical reaction kinetics and to a two-dimensional symmetric random walk, and suggest its application to more complex systerns.
Development of surface mine cost estimating equations
Not Available
1980-09-26
Cost estimating equations were developed to determine capital and operating costs for five surface coal mine models in Central Appalachia, Northern Appalachia, Mid-West, Far-West, and Campbell County, Wyoming. Engineering equations were used to estimate equipment costs for the stripping function and for the coal loading and hauling function for the base case mine and for several mines with different annual production levels and/or different overburden removal requirements. Deferred costs were then determined through application of the base case depreciation schedules, and direct labor costs were easily established once the equipment quantities (and, hence, manpower requirements) were determined. The data points were then fit with appropriate functional forms, and these were then multiplied by appropriate adjustment factors so that the resulting equations yielded the model mine costs for initial and deferred capital and annual operating cost. (The validity of this scaling process is based on the assumption that total initial and deferred capital costs are proportional to the initial and deferred costs for the primary equipment types that were considered and that annual operating cost is proportional to the direct labor costs that were determined based on primary equipment quantities.) Initial capital costs ranged from $3,910,470 in Central Appalachia to $49,296,785; deferred capital costs ranged from $3,220,000 in Central Appalachia to $30,735,000 in Campbell County, Wyoming; and annual operating costs ranged from $2,924,148 in Central Appalachia to $32,708,591 in Campbell County, Wyoming. (DMC)
Efficient solution of the simplified PN equations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Hamilton, Steven P.; Evans, Thomas M.
2014-12-23
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. Moreover, 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. These 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.
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.
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 equation of motion of an electron
Kim, K.; Sessler, A.M.
1999-07-01
We review the current status of understanding of the equation of motion of an electron. Classically, a consistent, linearized theory exists for an electron of finite extent, as long as the size of the electron is larger than the classical electron radius. Nonrelativistic quantum mechanics seems to offer a fine theory even in the point particle limit. Although there is as yet no convincing calculation, it is probable that a quantum electrodynamical result will be at least as well-behaved as is the nonrelativistic quantum mechanical results. {copyright} {ital 1999 American Institute of Physics.}
Sandia Equation of State Model Library
Energy Science and Technology Software Center (OSTI)
2013-08-29
The software provides a general interface for querying thermodynamic states of material models along with implementation of both general and specific equation of state models. In particular, models are provided for the IAPWS-IF97 and IAPWS95 water standards as well as the associated water standards for viscosity, thermal conductivity, and surface tension. The interface supports implementation of models in a variety of independent variable spaces. Also, model support routines are included that allow for coupling ofmore » models and determination and representation of phase boundaries.« less
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.
Equations for plutonium and americium-241 decay corrections ...
Office of Scientific and Technical Information (OSTI)
PLUTONIUM; ACCOUNTING; CORRECTIONS; DIFFERENTIAL EQUATIONS; ISOTOPE RATIO; NUCLEAR MATERIALS MANAGEMENT; TIME DEPENDENCE; ACTINIDE ISOTOPES; ACTINIDE NUCLEI; ACTINIDES; ALPHA ...
Differential form of the Skornyakov-Ter-Martirosyan Equations
Pen'kov, F. M.; Sandhas, W.
2005-12-15
The Skornyakov-Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.
Thermal equation of state and spin transition of magnesiosiderite...
Office of Scientific and Technical Information (OSTI)
Citation Details In-Document Search Title: Thermal equation of ... Subject: catalysis (heterogeneous), solar (photovoltaic), phonons, thermoelectric, energy storage (including ...
Conservation properties and potential systems of vorticity-type equations
Cheviakov, Alexei F.
2014-03-15
Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Favalli, Andrea; Croft, Stephen; Santi, Peter
2015-06-15
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclearmore » data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.« less
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
Favalli, Andrea; Croft, Stephen; Santi, Peter
2015-06-15
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclear data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.
The Raychaudhuri equation in homogeneous cosmologies
Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A. E-mail: cembra@fis.ucm.es E-mail: dobado@fis.ucm.es
2014-03-01
In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories.
Equations determine coiled tubing collapse pressure
Avakov, V.; Taliaferro, W.
1995-07-24
A set of equations has been developed for calculating pipe collapse pressure for oval tubing such as coiled tubing. When coiled tubing is placed onto a reel, the tubing is forced into an oval shape and never again returns to perfect roundness because the coiling process exceeds the plasticity limits of the tubing. Straightening the tubing for the trip into the well does not restore roundness. The consequence of this physical property is that all coiled tubing collapse pressure calculations should be made considering oval tubing, not round tubing. Tubing collapse can occur when formation pressure against the coiled tubing exceeds the collapse resistance inherent in the coiled tubing. As coiled tubing becomes more oval in shape, it becomes more oval in shape, it becomes more susceptible to collapse from outside pressure.
Assessment of UF6 Equation of State
Brady, P; Chand, K; Warren, D; Vandersall, J
2009-02-11
A common assumption in the mathematical analysis of flows of compressible fluids is to treat the fluid as a perfect gas. This is an approximation, as no real fluid obeys the perfect gas relationships over all temperature and pressure conditions. An assessment of the validity of treating the UF{sub 6} gas flow field within a gas centrifuge with perfect gas relationships has been conducted. The definition of a perfect gas is commonly stated in two parts: (1) the gas obeys the thermal equation of state, p = {rho}RT (thermally perfect), and, (2) the gas specific heats are constant (calorically perfect). Analysis indicates the thermally perfect assumption is valid for all flow conditions within the gas centrifuge, including shock fields. The low operating gas pressure is the primary factor in the suitability of the thermally perfect equation of state for gas centrifuge computations. UF{sub 6} is not calorically perfect, as the specific heats vary as a function of temperature. This effect is insignificant within the bulk of the centrifuge gas field, as gas temperatures vary over a narrow range. The exception is in the vicinity of shock fields, where temperature, pressure, and density gradients are large, and the variation of specific heats with temperature should be included in the technically detailed analyses. Results from a normal shock analysis incorporating variable specific heats is included herein, presented in the conventional form of shock parameters as a function of inlet Mach Number. The error introduced by assuming constant specific heats is small for a nominal UF{sub 6} shock field, such that calorically perfect shock relationships can be used for scaling and initial analyses. The more rigorous imperfect gas analysis should be used for detailed analyses.
Complete Mie-Gruneisen Equation of State
Menikoff, Ralph
2012-06-28
The Mie-Gruneisen equation of state (EOS) is frequently used in hydro simulations to model solids at high pressure (up to a few Mb). It is an incomplete EOS characterized by a Gruneisen coefficient, {Lambda} = -V({partial_derivative}{sub e}P){sub V}, that is a function of only V. Expressions are derived for isentropes and isotherms. This enables the extension to a complete EOS. Thermodynamic consistency requires that the specific heat is a function of a single scaled temperature. A complete extension is uniquely determined by the temperature dependence of the specific heat at a fixed reference density. In addition we show that if the domain of the EOS extends to T = 0 and the specific heat vanishes on the zero isotherm then {Lambda} a function of only V is equivalent to a specific heat with a single temperature scale. If the EOS domain does not include the zero isotherm, then a specific heat with a single temperature scale leads to a generalization of the Mie-Gruneisen EOS in which the pressure is linear in both the specific energy and the temperature. Such an EOS has previously been used to model liquid nitromethane.
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E.
2013-10-15
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
Validity of ELTB Equation for Suitable Description of BEC
Kim, Dooyoung; Kim, Jinguanghao; Yoon, Jin-Hee
2005-10-17
The Bose-Einstein condensation (BEC) has been found for various alkali-metal gases such as 7Li, 87Rb, Na, and H. For the description of atoms in this condensate state, the Gross-Pitaevskii (GP) equation has been widely used. However, the GP equation contains the nonlinear term, which makes this equation hard to solve. Therefore, physical quantities are usually obtained numerically, and sometimes it is difficult to extract a physical meaning from the calculated results. The nuclear theory group at Purdue University in the U.S. developed a new simple equation, the equivalent linear two-body (ELTB) equation, using the hyper-radius coordinates and tested it for one-dimensional BEC system. Their results are consistent with the numerical values from the GP equation within 4.5%.We test the validity of the ELTB equation for three-dimensional BEC system by calculating the energies per particle and the wave functions for 87Rb gas and for 7Li gas. We use the quantum-mechanical variational method for the BEC energy. Our result for 87Rb gas agrees with a numerical calculation based on the GP equation, with a relative error of 12% over a wide range of N from 100 to 10,000. The relative distances between particles for 7Li gas are consistent within a relative error of 17% for N {<=} 1300. The relatively simple form of the ELTB equation, compared with the GP equation, enables us to treat the N-body system easily and efficiently. We conclude that the ELTB equation is a powerful equation for describing BEC system because it is easy to treat.
A new least-squares transport equation compatible with voids
Hansen, J. B.; Morel, J. E.
2013-07-01
We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)
Scientists compose complex math equations to replicate behaviors...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Climate Models: Rob Jacob Scientists compose complex math equations to replicate behaviors ... It's math in action. A global model depends on submodels Submodels can be broken into two ...
Felix Bloch, Nuclear Induction, Bloch Equations, Bloch Theorem...
Office of Scientific and Technical Information (OSTI)
... Landmarks: NMR-- Grandmother of MRI, American Physical Society (APS) Chronology - Bloch (Felix) Papers; Online Archive of California, Stanford University Archives Bloch Equations ...
Covariant functional diffusion equation for Polyakov's bosonic string
Botelho, L. C. L.
1989-07-15
I write a covariant functional diffusion equation for Polyakov's bosonic string with the string's world-sheet area playing the role of proper time.
Penetration equations Young, C.W. [Applied Research Associates...
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45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEFENSE; EARTH PENETRATORS; EQUATIONS; NUCLEAR WEAPONS; SOILS; ICE; ROCKS; CONCRETES; PERMAFROST; SCALING LAWS In 1967, Sandia...
An Acoustic Wave Equation for Tilted Transversely Isotropic Media...
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Citation Details In-Document Search Title: An Acoustic Wave Equation for Tilted Transversely Isotropic Media A finite-difference method for computing the first arrival traveltimes ...
Adjoint Fokker-Planck equation and runaway electron dynamics...
Office of Scientific and Technical Information (OSTI)
This content will become publicly available on January 13, 2017 Title: Adjoint Fokker-Planck equation and runaway electron dynamics Authors: Liu, Chang 1 ; Brennan, Dylan P. 1 ...
Solving the power flow equations: a monotone operator approach...
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Technical Report: Solving the power flow equations: a monotone operator approach Citation ... In this paper, we solve this problem using the theory of monotone operators. We show that ...
SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics...
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SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics in Understanding Tsunami" Professor J. Douglas Wright, Associate Professor Department of Mathematics, Drexel ...
A Least-Squares Transport Equation Compatible with Voids
Hansen, Jon; Peterson, Jacob; Morel, Jim; Ragusa, Jean; Wang, Yaqi
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
Slyusarchuk, V. E. E-mail: V.Ye.Slyusarchuk@NUWM.rv.ua
2014-06-01
The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the H-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the H-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated. Bibliography: 24 titles. (paper)
Stochastic differential equations and numerical simulation for pedestrians
Garrison, J.C.
1993-07-27
The mathematical foundation of the Ito interpretation of stochastic ordinary and partial differential equations is briefly explained. This provides the basis for a review of simple difference approximations to stochastic differential equations. An example arising in the theory of optical switching is discussed.
Stable Difference Schemes for the Neutron Transport Equation
Ashyralyev, Allaberen; Taskin, Abdulgafur
2011-09-22
The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.
The modified equation for spinless particles and superalgebra
Sadeghi, J.; Rostami, M.; Sadeghi, Z.
2013-09-15
In this paper we consider modified wave equations for spinless particles in an external magnetic field. We consider 4-potentials which guarantee Lorentz' and Coulomb's conditions. The new variable for modified wave equation leads us to consider the associated Laguerre differential equation. We take advantage of the factorization method in Laguerre differential equation and solve the modified equation. In order to obtain the wave function, energy spectrum and its quantization, we will establish conditions for the orbital quantum number. We account such orbital quantum number and obtain the raising and lowering operators. If we want to have supersymmetry partners, we need to apply the shape invariance condition. This condition for the partner potential will help us find the limit of ρ as ρ=±√(l)
BHR equations re-derived with immiscible particle effects
Schwarzkopf, John Dennis; Horwitz, Jeremy A.
2015-05-01
Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied to the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.
New Dirac equation from the view point of particle
Ozaydin, Fatih; Altintas, Azmi Ali; Susam, Lidya Amon; Arik, Metin; Yarman, Tolga
2012-09-06
According to the classical approach, especially the Lorentz Invariant Dirac Equation, when particles are bound to each other, the interaction term appears as a quantity belonging to the 'field'. In this work, as a totally new approach, we propose to alter the rest masses of the particles due to their interaction, as much as their respective contributions to the static binding energy. Thus we re-write and solve the Dirac Equation for the hydrogen atom, and amazingly, obtain practically the same numerical results for the ground states, as those obtained from the Dirac Equation.
The fundamental solution of the unidirectional pulse propagation equation
Babushkin, I.; Bergé, L.
2014-03-15
The fundamental solution of a variant of the three-dimensional wave equation known as “unidirectional pulse propagation equation” (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented as a projection of a fundamental solution of the wave equation to some functional subspace. We discuss the degree of equivalence of the UPPE and the wave equation in this respect. In particular, we show that the UPPE, in contrast to the common belief, describes wave propagation in both longitudinal and temporal directions, and, thereby, its fundamental solution possesses a non-causal character.
Exact solution of the self-consistent Vlasov equation
Morawetz, K.
1997-03-01
An analytical solution of the self-consistent Vlasov equation is presented. The time evolution is entirely determined by the initial distribution function. The largest Lyapunov exponent is calculated analytically. For special parameters of the potential a positive Lyapunov exponent is possible. This model may serve as a check for numerical codes solving self-consistent Vlasov equations. The here presented method is also applicable for any system with an analytical solution of the Hamilton equation for the form factor of the potential. {copyright} {ital 1997} {ital The American Physical Society}
Time-dependent closure relations for relativistic collisionless fluid equations
Bendib-Kalache, K.; Bendib, A.; El Hadj, K. Mohammed
2010-11-15
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space ({omega},k), where {omega} and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter {omega}/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc{sup 2}/T, where m is the particle rest mass and T, the plasma temperature in energy units.
Variational principles for eigenvalues of the Klein-Gordon equation
Langer, Matthias; Tretter, Christiane
2006-10-15
In this paper variational principles for eigenvalues of an abstract model of the Klein-Gordon equation with electromagnetic potential are established. They are used to characterize and estimate eigenvalues in cases where the essential spectrum has a gap around 0, even in the presence of complex eigenvalues. As a consequence, a comparison between eigenvalues of the Klein-Gordon equation in R{sup d} and eigenvalues of certain Schroedinger operators is obtained. The results are illustrated on examples including the Klein-Gordon equation with Coulomb and square-well potential.
Constraining the equation of state of superhadronic matter from...
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The equation of state of QCD matter for temperatures near and above the quark-hadron transition (165 MeV) is inferred within a Bayesian framework through the comparison of data ...
Green Computing Helps in Zero Energy Equation - News Feature...
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Green Computing Helps in Zero Energy Equation April 14, 2010 Photo of two men watching as a third man goes over blueprints in the data center of NREL's Research Support Facility. ...
Numerical solution of control problems governed by nonlinear differential equations
Heinkenschloss, M.
1994-12-31
In this presentation the author investigates an iterative method for the solution of optimal control problems. These problems are formulated as constrained optimization problems with constraints arising from the state equation and in the form of bound constraints on the control. The method for the solution of these problems uses the special structure of the problem arising from the bound constraint and the state equation. It is derived from SQP methods and projected Newton methods and combines the advantages of both methods. The bound constraint is satisfied by all iterates using a projection, the nonlinear state equation is satisfied in the limit. Only a linearized state equation has to be solved in every iteration. The solution of the linearized problems are done using multilevel methods and GMRES.
Equator Appliance: ENERGY STAR Referral (EZ 3720 CEE)
Broader source: Energy.gov [DOE]
DOE referred the matter of Equator clothes washer model EZ 3720 CEE to the EPA for appropriate action after DOE testing showed that the model does not meet the ENERGY STAR specification.
Accuracy-based time step criteria for solving parabolic equations
Mohtar, R.; Segerlind, L.
1995-12-31
Parabolic equations govern many transient engineering problems. Space integration using finite element or finite difference methods changes the parabolic partial differential equation into an ordinary differential equation. Time integration schemes are needed to solve the later equation. In order to accurately perform the later integration a proper time step must be provided. Time step estimates based on a stability criteria have been prescribed in the literature. The following paper presents time step estimates that satisfy stability as well as accuracy criteria. These estimates were correlated to the Froude and Courant Numbers. The later criteria were found to be overly conservative for some integration schemes. Suggestions as to which time integration scheme is the best to use are also presented.
Electrolux Gibson Air Conditioner and Equator Clothes Washer...
Broader source: Energy.gov (indexed) [DOE]
ENERGY STAR program has revealed that an Electrolux Gibson air conditioner (model GAH105Q2T1) and an Equator clothes washer (model EZ 3720 CEE), both of which claimed ENERGY STAR...
Development of one-equation transition/turbulence models
Edwards, J.R.; Roy, C.J.; Blottner, F.G.; Hassan, H.A.
2000-01-14
This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity--transport equation for nonturbulent fluctuation growth based on that proposed by Warren and Hassan is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittency function based on the work of Dhawan and Narasimha. The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the grid-dependence of selected predictions is analyzed.
Multibump solutions for quasilinear elliptic equations with critical growth
Liu, Jiaquan; Wang, Zhi-Qiang; Wu, Xian
2013-12-15
The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrdinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 12171269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 40404102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions.
Absorbing boundary conditions for relativistic quantum mechanics equations
Antoine, X.; Sater, J.; Fillion-Gourdeau, F.; Bandrauk, A.D.
2014-11-15
This paper is devoted to the derivation of absorbing boundary conditions for the Klein–Gordon and Dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields. Microlocal analysis is the main ingredient in the derivation of these boundary conditions, which are obtained in the form of pseudo-differential equations. Basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.
Multifractal analysis of time series generated by discrete Ito equations
Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele
2015-06-15
In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.
Optimization of High-order Wave Equations for Multicore CPUs
Energy Science and Technology Software Center (OSTI)
2011-11-01
This is a simple benchmark to guage the performance of a high-order isotropic wave equation grid. The code is optimized for both SSE and AVX and is parallelized using OpenMP (see Optimization section). Structurally, the benchmark begins, reads a few command-line parameters, allocates and pads the four arrays (current, last, next wave fields, and the spatially varying but isotropic velocity), initializes these arrays, then runs the benchmark proper. The code then benchmarks the naive, SSEmore » (if supported), and AVX (if supported implementations) by applying the wave equation stencil 100 times and taking the average performance. Boundary conditions are ignored and would noiminally be implemented by the user. THus, the benchmark measures only the performance of the wave equation stencil and not a full simulation. The naive implementation is a quadruply (z,y,x, radius) nested loop that can handle arbitrarily order wave equations. The optimized (SSE/AVX) implentations are somewhat more complex as they operate on slabs and include a case statement to select an optimized inner loop depending on wave equation order.« less
Handbook of Industrial Engineering Equations, Formulas, and Calculations
Badiru, Adedeji B; Omitaomu, Olufemi A
2011-01-01
The first handbook to focus exclusively on industrial engineering calculations with a correlation to applications, Handbook of Industrial Engineering Equations, Formulas, and Calculations contains a general collection of the mathematical equations often used in the practice of industrial engineering. Many books cover individual areas of engineering and some cover all areas, but none covers industrial engineering specifically, nor do they highlight topics such as project management, materials, and systems engineering from an integrated viewpoint. Written by acclaimed researchers and authors, this concise reference marries theory and practice, making it a versatile and flexible resource. Succinctly formatted for functionality, the book presents: Basic Math Calculations; Engineering Math Calculations; Production Engineering Calculations; Engineering Economics Calculations; Ergonomics Calculations; Facility Layout Calculations; Production Sequencing and Scheduling Calculations; Systems Engineering Calculations; Data Engineering Calculations; Project Engineering Calculations; and Simulation and Statistical Equations. It has been said that engineers make things while industrial engineers make things better. To make something better requires an understanding of its basic characteristics and the underlying equations and calculations that facilitate that understanding. To do this, however, you do not have to be computational experts; you just have to know where to get the computational resources that are needed. This book elucidates the underlying equations that facilitate the understanding required to improve design processes, continuously improving the answer to the age-old question: What is the best way to do a job?
Bifurcations of traveling wave solutions for an integrable equation
Li Jibin; Qiao Zhijun
2010-04-15
This paper deals with the following equation m{sub t}=(1/2)(1/m{sup k}){sub xxx}-(1/2)(1/m{sup k}){sub x}, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.
Properties of the Boltzmann equation in the classical approximation
Tanji, Naoto; Epelbaum, Thomas; Gelis, Francois; Wu, Bin
2014-12-30
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.
Properties of the Boltzmann equation in the classical approximation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin
2014-12-30
We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore » has also access to the non-approximated result for comparison.« less
Non-stochastic matrix Schrdinger equation for open systems
Joubert-Doriol, Loc; Ryabinkin, Ilya G.; Izmaylov, Artur F.
2014-12-21
We propose an extension of the Schrdinger equation for a quantum system interacting with environment. This extension describes dynamics of a collection of auxiliary wavefunctions organized as a matrix m, from which the system density matrix can be reconstructed as ?{sup ^}=mm{sup }. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy loss in the time-dependent variational principle applied to mixed states of closed systems.
Properties of the Boltzmann equation in the classical approximation
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin
2014-12-30
We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.
Multi-time Schrdinger equations cannot contain interaction potentials
Petrat, Sren; Tumulka, Roderich
2014-03-15
Multi-time wave functions are wave functions that have a time variable for every particle, such as ?(t{sub 1},x{sub 1},...,t{sub N},x{sub N}). They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrdinger equations, one for each time variable. These Schrdinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schrdinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, Multi-time wave functions for quantum field theory, Ann. Physics (to be published)]. We also prove the following result: When a cut-off length ? > 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schrdinger equations with interaction potentials of range ? are consistent; however, in the desired limit ? ? 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.
Ideal solar cell equation in the presence of photon recycling
Lan, Dongchen Green, Martin A.
2014-11-07
Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.
Levinson theorem for the Dirac equation in D+1 dimensions
Gu Xiaoyan; Ma Zhongqi; Dong Shihai
2003-06-01
In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E={+-}M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.
Equation of State measurements of hydrogen isotopes on Nova
Collins, G. W., LLNL
1997-11-01
High intensity lasers can be used to perform measurements of materials at extremely high pressures if certain experimental issues can be overcome. We have addressed those issues and used the Nova laser to shock-compress liquid deuterium and obtain measurements of density and pressure on the principal Hugoniot at pressures from 300 kbar to more than 2 Mbar. The data are compared with a number of equation of state models. The data indicate that the effect of molecular dissociation of the deuterium into a monatomic phase may have a significant impact on the equation of state near 1 Mbar.
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.
Equation of state of liquid Indium under high pressure
Li, Huaming E-mail: mo.li@gatech.edu; Li, Mo E-mail: mo.li@gatech.edu; Sun, Yongli
2015-09-15
We apply an equation of state of a power law form to liquid Indium to study its thermodynamic properties under high temperature and high pressure. Molar volume of molten indium is calculated along the isothermal line at 710K within good precision as compared with the experimental data in an externally heated diamond anvil cell. Bulk modulus, thermal expansion and internal pressure are obtained for isothermal compression. Other thermodynamic properties are also calculated along the fitted high pressure melting line. While our results suggest that the power law form may be a better choice for the equation of state of liquids, these detailed predictions are yet to be confirmed by further experiment.
Equations of state and phase diagrams of hydrogen isotopes
Urlin, V. D.
2013-11-15
A new form of the semiempirical equation of state proposed for the liquid phase of hydrogen isotopes is based on the assumption that its structure is formed by cells some of which contain hydrogen molecules and others contain hydrogen atoms. The values of parameters in the equations of state of the solid (molecular and atomic) phases as well as of the liquid phase of hydrogen isotopes (protium and deuterium) are determined. Phase diagrams, shock adiabats, isentropes, isotherms, and the electrical conductivity of compressed hydrogen are calculated. Comparison of the results of calculations with available experimental data in a wide pressure range demonstrates satisfactory coincidence.
Hamiltonian time integrators for Vlasov-Maxwell equations
He, Yang; Xiao, Jianyuan; Zhang, Ruili; Liu, Jian; Qin, Hong; Sun, Yajuan
2015-12-15
Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.
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.
Gravitational lens equation for embedded lenses; magnification and ellipticity
Chen, B.; Kantowski, R.; Dai, X.
2011-10-15
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with standard linear lensing theory. We also compute analytic expressions for the lowest order corrections to image amplifications and distortions caused by incorporating the lensing mass into the mean. We use these results to estimate the effect of embedding on strong lensing magnifications and ellipticities and find only small effects, <1%, contrary to what we have found for time delays and for weak lensing, {approx}5%.
Mass distribution from a quark matter equation of state
Biro, T. S.; Levai, P.; Van, P.; Zimanyi, J.
2007-03-15
We analyze the equation of state in terms of quasiparticles with continuously distributed mass. We seek for a description of the entire pressure-temperature curve at vanishing chemical potential in terms of a temperature independent mass distribution. We point out properties indicating a mass gap in this distribution, conjectured to be related to confinement.
National Lab Uses OGJ Data to Develop Cost Equations
Brown, Daryl R.; Cabe, James E.; Stout, Tyson E.
2011-01-03
For the past 30 years, the Oil and Gas Journal (OGJ) has published data on the costs of onshore and offshore oil and gas pipelines and related equipment. This article describes the methodology employed and resulting equations developed for conceptual capital cost estimating of onshore pipelines. Also described are cost trends uncovered during the course of the analysis.
Dirac equation in low dimensions: The factorization method
Snchez-Monroy, J.A.; Quimbay, C.J.
2014-11-15
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two KleinGordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: The low-dimensional Dirac equation in the presence of static potentials is solved. The factorization method is generalized for energy-dependent Hamiltonians. The shape invariance is generalized for energy-dependent Hamiltonians. The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.
Non-commutative relativistic equation with a Coulomb potential
Zaim, Slimane; Khodja, Lamine; Delenda, Yazid
2012-06-27
We improve the previous study of the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the secondorder corrections in the non-commutativity parameter. Phenomenologically we show that noncommutativity plays the role of spin.
Solves Poisson's Equation in Axizymmetric Geometry on a Rectangular Mesh
Energy Science and Technology Software Center (OSTI)
1996-09-10
DATHETA4.0 computes the magnetostatic field produced by multiple point current sources in the presence of perfect conductors in axisymmetric geometry. DATHETA4.0 has an interactive user interface and solves Poisson''s equation using the ADI method on a rectangular finite-difference mesh. DATHETA4.0 uncludes models specific to applied-B ion diodes.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-04-15
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
Development of a One-Equation Transition/Turbulence Model
EDWARDS,JACK R.; ROY,CHRISTOPHER J.; BLOTTNER,FREDERICK G.; HASSAN,HASSAN A.
2000-09-26
This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.
Quantum Markovian master equation for scattering from surfaces
Li, Haifeng; Shao, Jiushu; Azuri, Asaf; Pollak, Eli Alicki, Robert
2014-01-07
We propose a semi-phenomenological Markovian Master equation for describing the quantum dynamics of atom-surface scattering. It embodies the Lindblad-like structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface. As a numerical test, we apply it to a model of an Ar atom scattered from a LiF surface, allowing for interaction only in the vertical direction. At low temperatures, we find that the quantum mechanical average energy loss is smaller than the classical energy loss. The numerical results obtained from the space dependent friction master equation are compared with numerical simulations for a discretized bath, using the multi-configurational time dependent Hartree methodology. The agreement between the two simulations is quantitative.
Boltzmann equation solver adapted to emergent chemical non-equilibrium
Birrell, Jeremiah; Wilkening, Jon; Rafelski, Johann
2015-01-15
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ?(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ?(t) such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e{sup }-annihilation)
Eternal inflation and a thermodynamic treatment of Einstein's equations
Ghersi, José Tomás Gálvez; Geshnizjani, Ghazal; Shandera, Sarah; Piazza, Federico E-mail: ggeshnizjani@perimeterinstitute.ca E-mail: sshandera@perimeterinstitute.ca
2011-06-01
In pursuing the intriguing resemblance of the Einstein equations to thermodynamic equations, most sharply seen in systems possessing horizons, we suggest that eternal inflation of the stochastic type may be a fruitful phenomenon to explore. We develop a thermodynamic first law for quasi-de Sitter space, valid on the horizon of a single observer's Hubble patch and explore consistancy with previous proposals for horizons of various types in dynamic and static situations. We use this framework to demonstrate that for the local observer fluctuations of the type necessary for stochastic eternal inflation fall within the regime where the thermodynamic approach is believed to apply. This scenario is interesting because of suggestive parallels with black hole evaporation.
Numerical solution of three-dimensional magnetic differential equations
Reiman, A.H.; Greenside, H.S.
1987-02-01
A computer code is described that solves differential equations of the form B . del f = h for a single-valued solution f, given a toroidal three-dimensional divergence-free field B and a single-valued function h. The code uses a new algorithm that Fourier decomposes a given function in a set of flux coordinates in which the field lines are straight. The algorithm automatically adjusts the required integration lengths to compensate for proximity to low order rational surfaces. Applying this algorithm to the Cartesian coordinates defines a transformation to magnetic coordinates, in which the magnetic differential equation can be accurately solved. Our method is illustrated by calculating the Pfirsch-Schlueter currents for a stellarator.
Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations
Lung, Tyler B.; Roe, Phil; Morgan, Nathaniel R.
2012-08-15
Long term research goals are to develop an improved cell-centered Lagrangian Hydro algorithm with the following qualities: 1. Utilizes Flux Corrected Transport (FCT) to achieve second order accuracy with multidimensional physics; 2. Does not rely on the one-dimensional Riemann problem; and 3. Implements a form of vorticity control. Short term research goals are to devise and implement a 2D vorticity preserving FCT solver for the acoustic equations on an Eulerian mesh: 1. Develop a flux limiting mechanism for systems of governing equations with symmetric wave speeds; 2. Verify the vorticity preserving properties of the scheme; and 3. Compare the performance of the scheme to traditional MUSCL-Hancock and other algorithms.
Disastrous Equations J. Douglas Wright Drexel University Department
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Disastrous Equations J. Douglas Wright Drexel University Department of Mathematics Science on Saturday 1 Earthquakes far out in the ocean gener- ate massive water waves called tsunami. When such waves hit coastlines they can cause massive damage. 2 The 2004 Indian Ocean Tsunami: 100' waves. 230,000 deaths. (photo by David Rydevik) 3 The 2011 T¯ ohoku Tsunami: 130' waves. 15,000 deaths + Nuclear accidents. (photo from National Geographic) 4 The 2011 T¯ ohoku Tsunami: 130' waves. 15,000 deaths +
Method of comparison equations for Schwarzschild black holes
Casadio, Roberto; Luzzi, Mattia
2006-10-15
We employ the method of comparison equations to study the propagation of a massless minimally coupled scalar field on the Schwarzschild background. In particular, we show that this method allows us to obtain explicit approximate expressions for the radial modes with energy below the peak of the effective potential which are fairly accurate over the whole region outside the horizon. This case can be of particular interest, for example, for the problem of black hole evaporation.
Felix Bloch, Nuclear Induction, Bloch Equations, Bloch Theorem, Bloch
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
States Felix Bloch, Nuclear Induction, and Bloch Equations Resources with Additional Information Stressing "the importance both of demonstrating the neutron's magnetic moment and of determining its magnitude", Felix Bloch began his research on neutron physics at Stanford [University] in early 1936. "Using mostly X-ray and microwave equipment from the physics labs, he and Norris Bradbury ... built [a neutron] source ... . (Bloch later pointed out that this equipment was more
Higher order matrix differential equations with singular coefficient matrices
Fragkoulis, V. C.; Kougioumtzoglou, I. A.; Pantelous, A. A.; Pirrotta, A.
2015-03-10
In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.
Time-periodic solutions of the Benjamin-Ono equation
Ambrose , D.M.; Wilkening, Jon
2008-04-01
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Toutounji, Mohamad
2015-02-15
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
Friedmann's equations in all dimensions and Chebyshev's theorem
Chen, Shouxin; Gibbons, Gary W.; Li, Yijun; Yang, Yisong E-mail: gwg1@damtp.cam.ac.uk E-mail: yisongyang@nyu.edu
2014-12-01
This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time t and conformal time η of the Friedmann equations in all dimensions and with an arbitrary cosmological constant Λ. More precisely, it is shown that for spatially flat universes an explicit integration in t may always be carried out, and that, in the non-flat situation and when Λ is zero and the ratio w of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension n of space and w obey some specific relations among an infinite family. The situation for explicit integration in η is complementary to that in t. More precisely, it is shown in the flat-universe case with Λ ≠ 0 that an explicit integration in η can be carried out if and only if w and n obey similar relations among a well-defined family which we specify, and that, when Λ = 0, an explicit integration can always be carried out whether the space is flat, closed, or open. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear.
Development and Application of Compatible Discretizations of Maxwell's Equations
White, D; Koning, J; Rieben, R
2005-05-27
We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we have designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.
On the vector Helmholtz equation in toroidal waveguides
Biro, Thomas
2005-02-15
A wave splitting method is proposed to solve the problem of propagation of microwaves in a circular waveguide bend of circular cross section. The splitting method, applied to the vector Helmholtz equation, gives a stable solution in terms of waves propagating to the right and to the left in the bend. The formulation is particularly transparent for analyzing the scattering properties of toroidal bends. The basis for the transparency of the method is that the wave splitting is formally exact as the exponential of the square root of a differential operator. The modal functions of the straight cylindrical waveguide are chosen as basis functions in the transverse quasi-toroidal variables.
Fire Intensity Data for Validation of the Radiative Transfer Equation
Blanchat, Thomas K.; Jernigan, Dann A.
2016-01-01
A set of experiments and test data are outlined in this report that provides radiation intensity data for the validation of models for the radiative transfer equation. The experiments were performed with lightly-sooting liquid hydrocarbon fuels that yielded fully turbulent fires 2 m diameter). In addition, supplemental measurements of air flow and temperature, fuel temperature and burn rate, and flame surface emissive power, wall heat, and flame height and width provide a complete set of boundary condition data needed for validation of models used in fire simulations.
On the Nonautonomous Nonlinear Schroedinger Equations and Soliton Management
Zhao Dun; Luo Honggang; He Xugang
2010-03-08
We present some novel results on the nonlinear Schroedinger equations with time- and space-dependent dispersion, nonlinearity, dissipation/gain and external potentials which read i(partial derivu(x,t)/partial derivt)+f(x,t)(partial deriv{sup 2}u(x,t)/partial derivx{sup 2})+g(x,t)|u(x,t)|{sup 2}u(x,t)+V(x,t)u(x,t)+igamma (x,t)u(x,t) = 0. Based on these results, we show some explicit ways to control the soliton dynamics in some physically interesting nonlinear systems like Bose-Einstein condensates and optical soliton transmission.
Integral equation for gauge invariant quark Green's function
Sazdjian, H.
2008-08-29
We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional relations between Green's functions with different numbers of segments of the polygonal lines are established. An integral equation is obtained for the Green's function having a phase factor along a single straight line. The related kernels involve Wilson loops with skew-polygonal contours and with functional derivatives along the sides of the contours.
Real-time nonlinear optimization as a generalized equation.
Zavala, V. M.; Anitescu, M. (Mathematics and Computer Science)
2010-11-11
We establish results for the problem of tracking a time-dependent manifold arising in real-time optimization by casting this as a parametric generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a single linear complementarity problem (LCP) at each time step. We derive sufficient conditions guaranteeing that the tracking error remains bounded to second order with the size of the time step even if the LCP is solved only approximately. We use these results to derive a fast, augmented Lagrangian tracking algorithm and demonstrate the developments through a numerical case study.
Heart simulation with surface equations for using on MCNP code
Rezaei-Ochbelagh, D.; Salman-Nezhad, S.; Asadi, A.; Rahimi, A.
2011-12-26
External photon beam radiotherapy is carried out in a way to achieve an 'as low as possible' a dose in healthy tissues surrounding the target. One of these surroundings can be heart as a vital organ of body. As it is impossible to directly determine the absorbed dose by heart, using phantoms is one way to acquire information around it. The other way is Monte Carlo method. In this work we have presented a simulation of heart geometry by introducing of different surfaces in MCNP code. We used 14 surface equations in order to determine human heart modeling. Those surfaces are borders of heart walls and contents.
CDF Solutions of Buckley-Leverett Equation with Uncertain Parameters
Wang, Peng; Tartakovsky, Daniel M.; Jarman, Kenneth D.; Tartakovsky, Alexandre M.
2013-01-15
The Buckley-Leverett (nonlinear advection) equation is often used to describe two-phase flow in porous media. We develop a new probabilistic method to quantify parametric uncertainty in the Buckley-Leverett model. Our approach is based on the concept of fine-grained cumulative density function (CDF) and provides a full statistical description of the system states. Hence, it enables one to obtain not only average system response but also the probability of rare events, which is critical for risk assessment. We obtain a closed-form, semi-analytical solution and test it against the results from Monte Carlo simulations.
Vortex equations governing the fractional quantum Hall effect
Medina, Luciano
2015-09-15
An existence theory is established for a coupled non-linear elliptic system, known as “vortex equations,” describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the existence and uniqueness of multiple vortices over a doubly periodic domain and the full plane. In the doubly periodic situation, explicit sufficient and necessary conditions are obtained that relate the size of the domain and the vortex numbers. For the full plane case, existence is established for all finite-energy solutions and exponential decay estimates are proved. Quantization phenomena of the magnetic flux are found in both cases.
A new high pressure and temperature equation of state of fcc...
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A new high pressure and temperature equation of state of fcc cobalt Citation Details In-Document Search Title: A new high pressure and temperature equation of state of fcc cobalt ...
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation...
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The Two-Phase Six-Equation Flow Model Citation Details In-Document Search Title: A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model We introduce a novel ...
Phase Diagram and Equation of State of Magnesium to High Pressures...
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Phase Diagram and Equation of State of Magnesium to High Pressures and High Temperatures Citation Details In-Document Search Title: Phase Diagram and Equation of State of Magnesium ...
Synthesis and equation of state of perovskite in the (Mg,Fe)...
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Synthesis and equation of state of perovskite in the (Mg,Fe)subscript 3Alsubscript ... Citation Details In-Document Search Title: Synthesis and equation of state of perovskite ...
The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyrazine...
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The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) Citation Details In-Document Search Title: The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyraz...
Wong's equations and the small x effective action in QCD (Journal...
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Wong's equations and the small x effective action in QCD Citation Details In-Document Search Title: Wong's equations and the small x effective action in QCD We propose a new form ...
Nonparametric reconstruction of the dark energy equation of state
Heitmann, Katrin; Holsclaw, Tracy; Alam, Ujjaini; Habib, Salman; Higdon, David; Sanso, Bruno; Lee, Herbie
2009-01-01
The major aim of ongoing and upcoming cosmological surveys is to unravel the nature of dark energy. In the absence of a compelling theory to test, a natural approach is to first attempt to characterize the nature of dark energy in detail, the hope being that this will lead to clues about the underlying fundamental theory. A major target in this characterization is the determination of the dynamical properties of the dark energy equation of state w. The discovery of a time variation in w(z) could then lead to insights about the dynamical origin of dark energy. This approach requires a robust and bias-free method for reconstructing w(z) from data, which does not rely on restrictive expansion schemes or assumed functional forms for w(z). We present a new non parametric reconstruction method for the dark energy equation of state based on Gaussian Process models. This method reliably captures nontrivial behavior of w(z) and provides controlled error bounds. We demollstrate the power of the method on different sets of simulated supernova data. The GP model approach is very easily extended to include diverse cosmological probes.
Vibrational properties of nanocrystals from the Debye Scattering Equation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Scardi, P.; Gelisio, L.
2016-02-26
One hundred years after the original formulation by Petrus J.W. Debije (aka Peter Debye), the Debye Scattering Equation (DSE) is still the most accurate expression to model the diffraction pattern from nanoparticle systems. A major limitation in the original form of the DSE is that it refers to a static domain, so that including thermal disorder usually requires rescaling the equation by a Debye-Waller thermal factor. The last is taken from the traditional diffraction theory developed in Reciprocal Space (RS), which is opposed to the atomistic paradigm of the DSE, usually referred to as Direct Space (DS) approach. Besides beingmore » a hybrid of DS and RS expressions, rescaling the DSE by the Debye-Waller factor is an approximation which completely misses the contribution of Temperature Diffuse Scattering (TDS). The present work proposes a solution to include thermal effects coherently with the atomistic approach of the DSE. Here, a deeper insight into the vibrational dynamics of nanostructured materials can be obtained with few changes with respect to the standard formulation of the DSE, providing information on the correlated displacement of vibrating atoms.« less
Possible ambiguities in the equation of state for neutron stars
Cheoun, Myung-Ki; Miyatsu, Tsuyoshi; Ryu, C. Y.; Deliduman, Cemsinan; Gngr, Can; Kele?, Vildan; Kajino, Toshitaka; Mathews, Grant J.
2014-05-02
We addressed possible ambiguities on the properties of neutron stars (NSs) estimated in theoretical sides. First, roles of hyperons inside the NS are discussed through various relativistic mean field (RMF) theories. In particular, the extension of SU(6) spin-flavor symmetry to SU(3) flavor symmetry is shown to give rise to the increase of hyperon threshold density, similarly to the Fock term effects in RMF theories. As a result, about 2.0 solar mass is obtained with the hyperons. Second, the effect by the modified f(R) gravity, which leaves a room for the dark energy in the Einstein equation to be taken into account, is discussed for the NS in a strong magnetic field (MF). Our results show that the modified gravity with the Kaluza-Klein electro-magnetism theory expanded in terms of a length scale parameter may reasonably describe the NS in strong MF, so called magnetar. Even the super-soft equation of state is shown to be revived by the modified f(R) gravity.
Richards Equation Solver; Rectangular Finite Volume Flux Updating Solution.
Energy Science and Technology Software Center (OSTI)
2002-01-18
Version: 00 POLYRES solves the transient, two-dimensional, Richards equation for water flow in unsaturated-saturated soils. The package is specifically designed to allow the user to easily model complex polygon-shaped regions. Flux, head, and unit gradient boundary conditions can be used. Spatial variation of the hydraulic properties can be defined across individual polygon-shaped subdomains, called objects. These objects combine to form a polygon-shaped model domain. Each object can have its own distribution of hydraulic parameters. Themore » resulting model domain and polygon-shaped internal objects are mapped onto a rectangular, finite-volume, computational grid by a preprocessor. This allows the user to specify model geometry independently of the underlying grid and greatly simplifies user input for complex geometries. In addition, this approach significantly reduces the computational requirements since complex geometries are actually modeled on a rectangular grid. This results in well-structured, finite difference-like systems of equations that require minimal storage and are very efficient to solve.« less
Crystal structure optimisation using an auxiliary equation of state
Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T.; Walsh, Aron
2015-11-14
Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy–volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other “beyond” density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu{sub 2}ZnSnS{sub 4} and the magnetic metal-organic framework HKUST-1.
Thermodynamics of the polaron master equation at finite bias
Krause, Thilo Brandes, Tobias; Schaller, Gernot; Esposito, Massimiliano
2015-04-07
We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system.
Luo Yousong
2010-06-15
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.
Higher-order Schrödinger and Hartree–Fock equations
Carles, Rémi; Lucha, Wolfgang; Moulay, Emmanuel
2015-12-15
The domain of validity of the higher-order Schrödinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then, the Cauchy theory for higher-order Hartree–Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Christov, Ivan C.
2015-08-20
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
Christov, Ivan C.
2015-08-20
We propose a hierarchy of nonlinearly dispersive generalized Kortewegde Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (peakompactons) are presented.
Equation of State for Supercooled Water at Pressures up to 400 MPa
Holten, Vincent; Sengers, Jan V.; Anisimov, Mikhail A.
2014-12-01
An equation of state is presented for the thermodynamic properties of cold and supercooled water. It is valid for temperatures from the homogeneous ice nucleation temperature up to 300 K and for pressures up to 400 MPa, and can be extrapolated up to 1000 MPa. The equation of state is compared with experimental data for the density, expansion coefficient, isothermal compressibility, speed of sound, and heat capacity. Estimates for the accuracy of the equation are given. The melting curve of ice I is calculated from the phase-equilibrium condition between the proposed equation and an existing equation of state for ice I.
Levinson theorem for the Dirac equation in one dimension
Ma Zhongqi; Dong Shihai; Wang Luya
2006-07-15
The Levinson theorem for the (1+1)-dimensional Dirac equation with a symmetric potential is proved with the Sturm-Liouville theorem. The half-bound states at the energies E={+-}M, whose wave function is finite but does not decay at infinity fast enough to be square integrable, are discussed. The number n{sub {+-}} of bound states is equal to the sum of the phase shifts at the energies E={+-}M:{delta}{sub {+-}}(M)+{delta}{sub {+-}}(-M)=(n{sub {+-}}+a){pi}, where the subscript {+-} denotes the parity and the constant a is equal to -1/2 when no half-bound state occurs, to 0 when one half-bound state occurs at E=M or at E=-M, and to 1/2 when two half-bound states occur at both E={+-}M.
Regular perturbation solution of the Elenbaas-Heller equation
Shaw, B.D.
2006-02-01
The Elenbaas-Heller equation is nondimensionalized and solved using regular perturbation theory to provide closed-form analytical solutions to describe structures of cylindrically symmetrical steady electric arc discharges with negligible radiant heat transfer. Based on available data, it is assumed that the electrical conductivity varies with the heat-flux potential in an Arrhenius fashion. The leading-order solution is equivalent to an asymptotic solution proposed by Kuiken [J. Appl. Phys. 58, 1833 (1991)]. Higher-order terms are also derived in the present paper, and it is shown that quantitatively accurate analytical solutions can be developed when higher-order terms are included. Analysis shows that appreciable Joule heating is restricted to an inner zone when a dimensionless parameter is large relative to unity, leading to arc-channel models suggested by previous investigators.
The isobaric multiplet mass equation for A?71 revisited
Lam, Yi Hua; Blank, Bertram; Smirnova, Nadezda A.; Bueb, Jean Bernard; Antony, Maria Susai
2013-11-15
Accurate mass determination of short-lived nuclides by Penning-trap spectrometers and progress in the spectroscopy of proton-rich nuclei have triggered renewed interest in the isobaric multiplet mass equation (IMME). The energy levels of the members of T=1/2,1,3/2, and 2 multiplets and the coefficients of the IMME are tabulated for A?71. The new compilation is based on the most recent mass evaluation (AME2011) and it includes the experimental results on energies of the states evaluated up to end of 2011. Taking into account the error bars, a significant deviation from the quadratic form of the IMME for the A=9,35 quartets and the A=32 quintet is observed.
Stochastic Liouville equations for femtosecond stimulated Raman spectroscopy
Agarwalla, Bijay Kumar; Ando, Hideo; Dorfman, Konstantin E.; Mukamel, Shaul
2015-01-14
Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a nonstationary state and after a variable delay period T, probing them with a Raman process induced by a combination of a broadband and a narrowband pulse. This technique, known as femtosecond stimulated Raman spectroscopy (FSRS), can effectively probe time resolved vibrational resonances. We show how FSRS signals can be modeled and interpreted using the stochastic Liouville equations (SLE), originally developed for NMR lineshapes. The SLE provide a convenient simulation protocol that can describe complex dynamics caused by coupling to collective bath coordinates at much lower cost than a full dynamical simulation. The origin of the dispersive features that appear when there is no separation of timescales between vibrational variations and the dephasing time is clarified.
SESAME 7363: A new Li(6)D equation of state
Sheppard, Daniel Glen; Kress, Joel David; Crockett, Scott; Collins, Lee A.; Greeff, Carl William
2015-09-21
A new Equation of State (EOS) for Lithium 6 Deuteride (^{6}LiD) was created, sesame 7363. This EOS was released to the user community under “eos-developmental” as sesame 97363. The construction of this new EOS is a modification of a previously released EOS, sesame 7360^{1}. Sesame 7360 is too stiff (5-10% excess pressure) at high compressions and high temperatures (ρ = 4-110g/cm^{3}, T = 30-10,000 eV) compared to orbital-free density-functional theory. Sesame 7363 is softer and gives a better representation of the physics over this range without compromising the agreement with the experimental and simulation data that sesame 7360 was based on.
Line Soliton Interactions of the Kadomtsev-Petviashvili Equation
Biondini, Gino
2007-08-10
We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u{sub t}+6uu{sub x}+3u{sub xxx}){sub x}+u{sub yy}=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y{yields}{infinity} coincide with those of the N asymptotic line solitons as y{yields}-{infinity}. We also show that the (2N-1){exclamation_point}{exclamation_point} types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.
INTERACTING QUARK MATTER EQUATION OF STATE FOR COMPACT STARS
Fraga, Eduardo S.; Kurkela, Aleksi; Vuorinen, Aleksi
2014-02-01
Lattice quantum chromodynamics (QCD) studies of the thermodynamics of hot quark-gluon plasma demonstrate the importance of accounting for the interactions of quarks and gluons if one wants to investigate the phase structure of strongly interacting matter. Motivated by this observation and using state-of-the-art results from perturbative QCD, we construct a simple, effective equation of state (EOS) for cold quark matter that consistently incorporates the effects of interactions and furthermore includes a built-in estimate of the inherent systematic uncertainties. This goes beyond the MIT bag model description in a crucial way, yet leads to an EOS that is equally straightforward to use. We also demonstrate that, at moderate densities, our EOS can be made to smoothly connect to hadronic EOSs, with the two exhibiting very similar behavior near the matching region. The resulting hybrid stars are seen to have masses similar to those predicted by the purely nucleonic EOSs.
Polynomial solutions of the Monge-Ampre equation
Aminov, Yu A
2014-11-30
The question of the existence of polynomial solutions to the Monge-Ampre equation z{sub xx}z{sub yy}?z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is apolynomial. It is proved that if f is apolynomial of the second degree, which is positive for all values of its arguments and has apositive squared part, then no polynomial solution exists. On the other hand, asolution which is not polynomial but is analytic in the whole of the x,y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.
The one-dimensional Gross-Pitaevskii equation and its some excitation states
Prayitno, T. B.
2015-04-16
We have derived some excitation states of the one-dimensional Gross-Pitaevskii equation coupled by the gravitational potential. The methods that we have used here are taken by pursuing the recent work of Kivshar et. al. by considering the equation as a macroscopic quantum oscillator. To obtain the states, we have made the appropriate transformation to reduce the three-dimensional Gross-Pitaevskii equation into the one-dimensional Gross-Pitaevskii equation and applying the time-independent perturbation theory in the general solution of the one-dimensional Gross-Pitaevskii equation as a linear superposition of the normalized eigenfunctions of the Schrödinger equation for the harmonic oscillator potential. Moreover, we also impose the condition by assuming that some terms in the equation should be so small in order to preserve the use of the perturbation method.
Wavevortex interactions in the nonlinear Schrdinger equation
Guo, Yuan Bhler, Oliver
2014-02-15
This is a theoretical study of wavevortex interaction effects in the two-dimensional nonlinear Schrdinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wavevortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wavevortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.
Concerning the equation of state for partially ionized system
Baker, Jr, George A
2008-01-01
I will discuss the expansion of various thermodynamic quantities about the ideal gas in powers of the electric charge, and I will discuss some cellular models. The first type of cellular model is appropriate for hydrogen. The second type is for Z > 1. It has the independent electron approximation within the atoms. These models are cross compared and minimal regions of validity are determined. The actual region of validity is expected to be larger. In the cellular models, the phase boundaries for liquid-gas transitions are found. For the second type of cellular model, in the part of the low-temperature, low-density region where there is not much expectation of validity of these methods, a non-thermodynamic region is found. I have devised a construction, similar in spirit to the Maxwell construction, to bridge this region so as to leave a thermodynamically valid equation of state. The non-thermodynamic region does not occur in hydrogen and it seems to be due to the inadequacy of the aforementioned approximation in that region.
A Schamel equation for ion acoustic waves in superthermal plasmas
Williams, G. Kourakis, I.; Verheest, F.; Hellberg, M. A.; Anowar, M. G. M.
2014-09-15
An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u{sub 0}. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation.
Opal equation-of-state tables for astrophysical applications
Rogers, F.J.; Swenson, F.J.; Iglesias, C.A.
1996-01-01
OPAL opacities have recently helped to resolve a number of long-standing discrepancies between theory and observation. This success has made it important to provide the associated equation-of-state (EOS) data. The OPAL EOS is based on an activity expansion of the grand canonical partition function of the plasma in terms of its fundamental constituents (electrons and nuclei). The formation of composite particles and many-body effects on the internal bound states occur naturally in this approach. Hence, pressure ionization is a consequence of the theory. In contrast, commonly used approaches, all of which are based on minimization of free energy, are forced to assert the effect of the plasma on composite particles and must rely on an ad hoc treatment of pressure ionization. Another advantage of the OPAL approach is that it provides a systematic expansion in the Coulomb coupling parameter that includes subtle quantum effects generally not considered in other EOS calculations. Tables have been generated that provide pressure, internal energy, entropy, and a variety of derivative quantities. These tables cover a fairly broad range of conditions and compositions applicable to general stellar-evolution calculations for stars more massive than {approximately}0.8 {ital M}{sub {circle_dot}}. An interpolation code is provided along with the tables to facilitate their use. {copyright} {ital 1996 The American Astronomical Society.}
Test plan for validation of the radiative transfer equation.
Ricks, Allen Joseph; Grasser, Thomas W.; Kearney, Sean Patrick; Jernigan, Dann A.; Blanchat, Thomas K.
2010-09-01
As the capabilities of numerical simulations increase, decision makers are increasingly relying upon simulations rather than experiments to assess risks across a wide variety of accident scenarios including fires. There are still, however, many aspects of fires that are either not well understood or are difficult to treat from first principles due to the computational expense. For a simulation to be truly predictive and to provide decision makers with information which can be reliably used for risk assessment the remaining physical processes must be studied and suitable models developed for the effects of the physics. A set of experiments are outlined in this report which will provide soot volume fraction/temperature data and heat flux (intensity) data for the validation of models for the radiative transfer equation. In addition, a complete set of boundary condition measurements will be taken to allow full fire predictions for validation of the entire fire model. The experiments will be performed with a lightly-sooting liquid hydrocarbon fuel fire in the fully turbulent scale range (2 m diameter).
Nuclear processing - a simple cost equation or a complex problem?
Banfield, Z.; Banford, A.W.; Hanson, B.C.; Scully, P.J.
2007-07-01
BNFL has extensive experience of nuclear processing plant from concept through to decommissioning, at all stages of the fuel cycle. Nexia Solutions (formerly BNFL's R and D Division) has always supported BNFL in development of concept plant, including the development of costed plant designs for the purpose of economic evaluation and technology selection. Having undertaken such studies over a number of years, this has enabled Nexia Solutions to develop a portfolio of costed plant designs for a broad range of nuclear processes, throughputs and technologies. This work has led to an extensive understanding of the relationship of the cost of nuclear processing plant, and how this can be impacted by scale of process, and the selection of design philosophy. The relationship has been seen to be non linear and so simplistic equations do not apply, the relationship is complex due to the variety of contributory factors. This is particularly evident when considering the scale of a process, for example how step changes in design occurs with increasing scale, how the applicability of technology options can vary with scale etc... This paper will explore the contributory factor of scale to nuclear processing plant costs. (authors)
Equations of state and phase transitions in stellar matter
Raduta, Ad. R. [IFIN-HH, Bucharest POB-MG 6 (Romania); Gulminelli, F.; Aymard, F. [CNRS, UMR6534, LPC and ENSICAEN, UMR6534, LPC, F-14050 Caen cedex (France); Oertel, M. [LUTH, CNRS, Observatoire de Paris, Universite Paris Diderot, 92195 Meudon (France); Margueron, J. [IPN, IN2P3-CNRS, Universite Paris-Sud, F-91406 Orsay cedex (France)
2014-05-09
Realistic description of core-collapsing supernovae evolution and structure of proto-neutron stars chiefly depends on microphysics input in terms of equations of state, chemical composition and weak interaction rates. At sub-saturation densities the main uncertainty comes from the symmetry energy. Within a nuclear statistical equilibrium (NSE) model with consistent treatment of clusterized and unbound components we investigate the meaning of symmetry energy in the case of dis-homogeneous systems, as the one thought to constitute the neutron star crust, and its sensitivity to the isovector properties of the effective interaction. At supra-saturation densities the situation is much more difficult because of the poor knowledge of nucleon-hyperon and hyperon-hyperon interactions and thermodynamic behavior in terms of phase transitions. Within a simple (np?) model we show that compressed baryonic matter with strangeness manifests a complex phase diagram with first and second order phase transitions. The fact that both are explored under strangeness chemical equilibrium and survive Coulomb suggests that they might have sizable consequences on star evolution. An example in this sense is the drastic reduction of the neutrino-mean free path in the vicinity of the critical point obtained within RPA which would lead to a less rapid star cooling.
Solving the power flow equations: a monotone operator approach
Dvijotham, Krishnamurthy; Low, Steven; Chertkov, Michael
2015-07-21
The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. These methods work well given a good initial “guess” for the solution, which is always available in normal system operations. However, with the increase in levels of intermittent generation, the assumption of a good initial guess always being available is no longer valid. In this paper, we solve this problem using the theory of monotone operators. We show that it is possible to compute (using an offline optimization) a “monotonicity domain” in the space of voltage phasors. Given this domain, there is a simple efficient algorithm that will either find a solution in the domain, or provably certify that no solutions exist in it. We validate the approach on several IEEE test cases and demonstrate that the offline optimization can be performed tractably and the computed “monotonicity domain” includes all practically relevant power flow solutions.
Murphy, M J
2010-03-08
We describe an improved reaction rate equation for simulating ignition and growth of reaction in high explosives. It has been implemented into CALE and ALE3D as an alternate to the baseline the Lee-Tarver reactive flow model. The reactive flow model treats the explosive in two phases (unreacted/reactants and reacted/products) with a reaction rate equation to determine the fraction reacted, F. The improved rate equation has fewer parameters, is continuous with continuous derivative, results in a unique set of reaction rate parameters for each explosive while providing the same functionality as the baseline rate equation. The improved rate equation uses a cosine function in the ignition term and a sine function in the growth and completion terms. The improved rate equation is simpler with fewer parameters.
An Asymptotic Study of Discretized Transport Equations in the Fokker-Planck Limit
Pautz, Shawn D.; Adams, Marvin L.
2002-01-15
Recent analyses have shown that the Fokker-Planck equation is an asymptotic limit of the transport equation given a forward-peaked scattering kernel satisfying certain constraints. Discretized transport equations in the same limit are studied, both by asymptotic analysis and by numerical testing. It is shown that spatially discretized discrete ordinates transport solutions can be accurate in this limit if and only if the scattering operator is handled in a certain nonstandard way.
An asymptotic expansion of the solution of amatrix difference equation of general form
Sgibnev, M S
2014-12-31
An asymptotic expansion of the solution of an inhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. An integral estimate with asubmultiplicative weight is established for the remainder in terms of the submultiplicative moment of the free term of the equation. Bibliography: 14 titles.
Validity of equation-of-motion approach to kondo problem in the...
Office of Scientific and Technical Information (OSTI)
Visit OSTI to utilize additional information resources in energy science and technology. A ... equation for the one-particle Green function is derived and numerically solved ...
Solitary waves in nonlinear Dirac equation. From field theory to Dirac materials
Saxena, Avadh
2015-11-02
This report describes the implementation of nonlinear Dirac equations in the calculation of solitary waves. Conclusions and comments on quantum elasticity are also included.
Equation of state of pyrite to 80 GPa and 2400 K (Journal Article...
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Title: Equation of state of pyrite to 80 GPa and 2400 K Authors: Thompson, Elizabeth C. ; Chidester, Bethany A. ; Fischer, Rebecca A. ; Myers, Gregory I. ; Heinz, Dion L. ; ...
Validity of equation-of-motion approach to kondo problem in the large N
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limit (Journal Article) | SciTech Connect Validity of equation-of-motion approach to kondo problem in the large N limit Citation Details In-Document Search Title: Validity of equation-of-motion approach to kondo problem in the large N limit The Anderson impurity model for Kondo problem is investigated for arbitrary orbit-spin degeneracy N of the magnetic impurity by the equation of motion method (EOM). By employing a new decoupling scheme, a self-consistent equation for the one-particle
A Bme Solution Of The Stochastic Three-Dimensional Laplace Equation...
Solution Of The Stochastic Three-Dimensional Laplace Equation Representing A Geothermal Field Subject To Site-Specific Information Abstract This work develops a model of the...
The thermal equation of state of (Mg, Fe)SiO[subscript 3] bridgmanite...
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thermal equation of state of (Mg, Fe)SiOsubscript 3 bridgmanite (perovskite) and implications for lower mantle structures Citation Details In-Document Search Title: The thermal ...
Ayyoubzadeh, Seyed Mohsen; Vosoughi, Naser
2011-09-14
Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning.
A parametric approach to supersymmetric quantum mechanics in the solution of Schrdinger equation
Tezcan, Cevdet; Sever, Ramazan
2014-03-15
We study exact solutions of the Schrdinger equation for some potentials. We introduce a parametric approach to supersymmetric quantum mechanics to calculate energy eigenvalues and corresponding wave functions exactly. As an application we solve Schrdinger equation for the generalized Morse potential, modified Hulthen potential, deformed Rosen-Morse potential and Poschl-Teller potential. The method is simple and effective to get the results.
Symmetry operators for Dirac's equation on two-dimensional spin manifolds
Fatibene, Lorenzo; McLenaghan, Raymond G.; Smith, Shane N.; Rastelli, Giovanni
2009-05-15
It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence 2 Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.
Explicit solutions of the radiative transport equation in the P{sub 3} approximation
Liemert, André Kienle, Alwin
2014-11-01
Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.
Two Soliton Interactions of BD.I Multicomponent NLS Equations and Their Gauge Equivalent
Gerdjikov, V. S.; Grahovski, G. G.
2010-11-25
Using the dressing Zakharov-Shabat method we re-derive the effects of the two-soliton interactions for the MNLS equations related to the BD.I-type symmetric spaces. Next we generalize this analysis for the Heisenberg ferromagnet type equations, gauge equivalent to MNLS.
Horowitz, Jordan M.
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Nakatsuji, Hiroshi Nakashima, Hiroyuki
2015-02-28
The free-complement (FC) method is a general method for solving the Schrdinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrdinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrdinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrdinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and H{sup T}Q methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hookes atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the worlds most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the Schrdinger equation of general atoms and molecules.
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.
Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A.
2012-07-01
Finite-difference time-dependent equations of Surface Harmonics method have been obtained for plane geometry. Verification of these equations has been carried out by calculations of tasks from 'Benchmark Problem Book ANL-7416'. The capacity and efficiency of the Surface Harmonics method have been demonstrated by solution of the time-dependent neutron transport equation in diffusion approximation. The results of studies showed that implementation of Surface Harmonics method for full-scale calculations will lead to a significant progress in the efficient solution of the time-dependent neutron transport problems in nuclear reactors. (authors)
Error propagation equations for estimating the uncertainty in high-speed wind tunnel test results
Clark, E.L.
1994-07-01
Error propagation equations, based on the Taylor series model, are derived for the nondimensional ratios and coefficients most often encountered in high-speed wind tunnel testing. These include pressure ratio and coefficient, static force and moment coefficients, dynamic stability coefficients, and calibration Mach number. The error equations contain partial derivatives, denoted as sensitivity coefficients, which define the influence of free-steam Mach number, M{infinity}, on various aerodynamic ratios. To facilitate use of the error equations, sensitivity coefficients are derived and evaluated for five fundamental aerodynamic ratios which relate free-steam test conditions to a reference condition.
Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential
Zhang Ying [State Key Lab Nucl. Phys. and Tech., School of Physics, Peking University, Beijing 100871 (China); Liang Haozhao [State Key Lab Nucl. Phys. and Tech., School of Physics, Peking University, Beijing 100871 (China); Institut de Physique Nucleaire, IN2P3-CNRS and Universite Paris-Sud, F-91406 Orsay France (France); Meng Jie [State Key Lab Nucl. Phys. and Tech., School of Physics, Peking University, Beijing 100871 (China); Department of Physics, University of Stellenbosch, Stellenbosch (South Africa)
2009-08-26
The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus {sup 12}C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.
Daeva, S.G.; Setukha, A.V.
2015-03-10
A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.
A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise
Hong, Jialin; Zhang, Liying
2014-07-01
In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with additive noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with additive noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.
Equation of state and phase diagram of Fe-16Si alloy as a candidate...
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SciTech Connect Search Results Journal Article: Equation of state and phase diagram of Fe-16Si alloy as a candidate component of Earths core Citation Details In-Document Search ...
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
Webb, G. M.; Brio, M.; Zank, G. P.
1996-07-20
A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in {beta}{approx}1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a{sub g}{sup 2}=V{sub A}{sup 2} where a{sub g} is the gas sound speed and V{sub A} is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation.
Equations of state in the Fe-FeSi system at high pressures and...
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SciTech Connect Search Results Journal Article: Equations of state in the Fe-FeSi system ... Country of Publication: United States Language: ENGLISH Word Cloud More Like This Full ...
Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma
Yasmin, S.; Asaduzzaman, M.; Mamun, A. A.
2012-10-15
There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).
A UQ Enabled Aluminum Tabular Multiphase Equation-of-State Model
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1325C A UQ Enabled Aluminum Tabular Multiphase Equation-of-State Model Allen C. Robinson, John H. Carpenter0, Bert J. Debusschere*, Ann E. Mattsson0 t Computational Multiphysics, ...
First-principles high-pressure unreacted equation of state and...
Office of Scientific and Technical Information (OSTI)
Title: First-principles high-pressure unreacted equation of state and heat of formation of crystal 2,6-diamino-3, 5-dinitropyrazine-1-oxide (LLM-105) Authors: Manaa, M R ; Kuo, I W ...
New Improved Equations For Na-K, Na-Li And Sio2 Geothermometers...
Improved Equations For Na-K, Na-Li And Sio2 Geothermometers By Outlier Detection And Rejection Jump to: navigation, search OpenEI Reference LibraryAdd to library Journal Article:...
Thermal equation of state and stability of (Mg[subscript 0.06...
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SciTech Connect Search Results Journal Article: Thermal equation of state and stability of (Mgsubscript 0.06Fesubscript 0.94)O Citation Details In-Document Search Title: ...
Fa, Kwok Sau
2015-02-15
An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems. - Highlights: • Calculation of the correlation function. • The correlation function is connected to the survival probability. • The model can be applied to the internal dynamics of proteins.
Electrolux Gibson Air Conditioner and Equator Clothes Washer Fail DOE Energy Star Testing
Broader source: Energy.gov [DOE]
DOE testing in support of the ENERGY STAR program has revealed that an Electrolux Gibson air conditioner (model GAH105Q2T1) and an Equator clothes washer (model EZ 3720 CEE), both of which claimed...
Brett, Tobias Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation...
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A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model Citation Details In-Document Search Title: A Novel Hyperbolization Procedure for The Two-Phase...
Quasiparticle description of (2+1)- flavor lattice QCD equation of state
Chandra, Vinod; Ravishankar, V.
2011-10-01
A quasiparticle model has been employed to describe the (2+1)-flavor lattice QCD equation of state with physical quark masses. The interaction part of the equation of state has been mapped to the effective fugacities of otherwise noninteracting quasigluons and quasiquarks. The mapping is found to be exact for the equation of state. The model leads to nontrivial dispersion relations for quasipartons. The dispersion relations, effective quasiparticle number densities, and trace anomaly have been investigated employing the model. A virial expansion for the equation of state has further been obtained to investigate the role of interactions in quark-gluon plasma. Finally, Debye screening in quark-gluon plasma has been studied employing the model.
Thermal equation of state and stability of (Mg0.06Fe0.94)O (Journal...
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Thermal equation of state and stability of (Mg0.06Fe0.94)O This content will become publicly available on November 8, 2017 Title: Thermal equation of state and stability of ...
Exact solutions of the Fokker-Planck equations with moving boundaries
Lo, C.F. . E-mail: cflo@phy.cuhk.edu.hk
2005-10-01
By means of time-dependent similarity transformations, we derive exact solutions of the Fokker-Planck equations with moving boundaries in the presence of: (1) a time-dependent linear force and (2) a time-dependent nonlinear force. The method of similarity transformation is simple and can be easily applied to more general Fokker-Planck equations. Furthermore, the knowledge of the exact solutions in closed form can be useful as a benchmark to test approximate numerical or analytical procedures.
Fokker-Planck equations and density of states in disordered quantum wires
Titov, M.; Brouwer, P. W.; Furusaki, A.; Mudry, C.
2001-06-15
We propose a general scheme to construct scaling equations for the density of states in disordered quantum wires for all ten pure Cartan symmetry classes. The anomalous behavior of the density of states near the Fermi level {var_epsilon}=0 for the three chiral and four Bogoliubov{endash}de Gennes universality classes is analyzed in detail by means of a mapping to a scaling equation for the reflection from a quantum wire in the presence of an imaginary potential.
Mikami, T.
2000-07-01
R. Jordan, D. Kinderlehrer, and F. Otto proposed the discrete-time approximation of the Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional, and the Gibbs-Boltzmann entropy functional. In this paper we study the asymptotic behavior of the dynamical systems which describe their approximation of the Fokker-Planck equation and characterize the limit as a solution to a class of variational problems.
Investigating the Nuclear Equation of State through N/Z Equilibration
Yennello, S.; Keksis, A.; Bell, E.
2007-10-26
The equilibration of the N/Z degree of freedom during heavy-ion collisions can be a discriminating observables for helping to understand the nuclear equation of state. Equilibration can be investigated by examining the ratios of isotopes produced in these reactions. The isotope ratio method and the tracer method yield consistent results. The quasiprojectiles produced in deep inelastic collisions are predicted to be sensitive to the density dependence of the equation of state.
Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential
Iacob, Felix; Lute, Marina
2015-12-15
We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.
Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle
Barletti, Luigi
2014-08-15
The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.
ANALYSIS OF TWO-PHASE FLOW MODELS WITH TWO MOMENTUM EQUATIONS.
KROSHILIN,A.E.KROSHILIN,V.E.KOHUT,P.
2004-03-15
An analysis of the standard system of differential equations describing multi-speed flows of multi-phase media is performed. It is proved that the Cauchy problem, as posed in most best-estimate thermal-hydraulic codes, results in unstable solutions and potentially unreliable description of many physical phenomena. A system of equations, free from instability effects, is developed allowing more rigorous numerical modeling.
H–J–B Equations of Optimal Consumption-Investment and Verification Theorems
Nagai, Hideo
2015-04-15
We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H–J–B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings.
Equations Governing Space-Time Variability of Liquid Water Path in Stratus Clouds
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Equations Governing Space-Time Variability of Liquid Water Path in Stratus Clouds K. Ivanova Pennsylvania State University University Park, Pennsylvania T. P. Ackerman Pacific Northwest National Laboratory Richland, Washington M. Ausloos University of Liège B-4000 Liège, Belgium Abstract We present a method on how to derive an underlying mathematical (statistical or model free) equation for a liquid water path (LWP) signal directly from empirical data. The evolution of the probability density
Solutions of Boltzmann`s Equation for Mono-energetic Neutrons in an Infinite Homogeneous Medium
DOE R&D Accomplishments [OSTI]
Wigner, E. P.
1943-11-30
Boltzman's equation is solved for the case of monoenergetic neutrons created by a plane or point source in an infinite medium which has spherically symmetric scattering. The customary solution of the diffusion equation appears to be multiplied by a constant factor which is smaller than 1. In addition to this term the total neutron density contains another term which is important in the neighborhood of the source. It varies as 1/r{sup 2} in the neighborhood of a point source. (auth)
A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation
Larsen, Edward
2013-06-17
The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltz- mann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new “2D/1D” approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable itera- tion scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.
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.
Cari, C. Suparmi, A.
2014-09-30
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations
Sun, Wenjun; Jiang, Song; Xu, Kun
2015-03-15
The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.
Mukherjee, Abhik Janaki, M. S. Kundu, Anjan
2015-07-15
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
Dynamics of the Zakharov-Kuznetsov-Burgers equations in dusty plasmas
Zhen, Hui-Ling; Tian, Bo; Zhong, Hui; Sun, Wen-Rong; Li, Min
2013-08-15
In this paper, we investigate the Zakharov-Kuznetsov-Burgers (ZKB) equations for the dust-ion-acoustic waves in dusty plasmas. Shock-like and soliton solutions are both constructed through the introduction of an auxiliary function and variable. ZKB-soliton propagation is plotted, and from those figures, we find that energy of the solitons increases when the number of electrons in a dust particle decreases or the mass of such dust particle becomes larger. Considering the external perturbations in the dusty plasmas, we study the perturbed ZKB equation via some qualitative and quantitative methods. To corroborate that the perturbed ZKB equation can indeed give rise to the chaos, we make use of the power spectrum and Lyapunov exponents. Then, we investigate the phase projections, and find that both the weak and developed chaos can be observed. Weak chaos occur when the absolute value of damped coefficient (l{sub 1}) is stronger than the strength of perturbed term (g{sub 1}), or else, the developed one occurs. Ranges of l{sub 1} and g{sub 1} are given via the largest Lyapunov exponents when the perturbed ZKB equation is in different chaotic states. Therefore, we can find that the chaotic motion of the perturbed ZKB equation will be enhanced with the number of electrons in a dust particle or the mass of such a dust particle decreasing.
Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.
1997-03-01
The distributed approximating functional method is applied to the solution of the Fokker{endash}Planck equations. The present approach is limited to the standard eigenfunction expansion method. Three typical examples, a Lorentz Fokker{endash}Planck equation, a bistable diffusion model and a Henon{endash}Heiles two-dimensional anharmonic resonating system, are considered in the present numerical testing. All results are in excellent agreement with those of established methods in the field. It is found that the distributed approximating functional method yields the accuracy of a spectral method but with a local method{close_quote}s simplicity and flexibility for the eigenvalue problems arising from the Fokker{endash}Planck equations. {copyright} {ital 1997 American Institute of Physics.}
Stability and error analysis of nodal expansion method for convection-diffusion equation
Deng, Z.; Rizwan-Uddin; Li, F.; Sun, Y.
2012-07-01
The development, and stability and error analyses of nodal expansion method (NEM) for one dimensional steady-state convection diffusion equation is presented. Following the traditional procedure to develop NEM, the discrete formulation of the convection-diffusion equation, which is similar to the standard finite difference scheme, is derived. The method of discrete perturbation analysis is applied to this discrete form to study the stability of the NEM. The scheme based on the NEM is found to be stable for local Peclet number less than 4.644. A maximum principle is proved for the NEM scheme, followed by an error analysis carried out by applying the Maximum principle together with a carefully constructed comparison function. The scheme for the convection diffusion equation is of second-order. Numerical experiments are carried and the results agree with the conclusions of the stability and error analyses. (authors)
Equation of state of hot polarized nuclear matter and heavy-ion fusion reactions
Ghodsi, O. N.; Gharaei, R.
2011-08-15
We employ the equation of state of hot polarized nuclear matter to simulate the repulsive force caused by the incompressibility effects of nuclear matter in the fusion reactions of heavy colliding ions. The results of our studies reveal that temperature effects of compound nuclei have significant importance in simulating the repulsive force on the fusion reactions for which the temperature of the compound nucleus increases up to about 2 MeV. Since the equation of state of hot nuclear matter depends upon the density and temperature of the nuclear matter, it has been suggested that, by using this equation of state, one can simulate simultaneously both the effects of the precompound nucleons' emission and the incompressibility of nuclear matter to calculate the nuclear potential in fusion reactions within a static formalism such as the double-folding (DF) model.
Multi-time Schrödinger equations cannot contain interaction potentials
Petrat, Sören; Tumulka, Roderich
2014-03-15
Multi-time wave functions are wave functions that have a time variable for every particle, such as ϕ(t{sub 1},x{sub 1},...,t{sub N},x{sub N}). They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, “Multi-time wave functions for quantum field theory,” Ann. Physics (to be published)]. We also prove the following result: When a cut-off length δ > 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schrödinger equations with interaction potentials of range δ are consistent; however, in the desired limit δ → 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.
Constraining the equation of state of superhadronic matter from heavy-ion collisions
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Pratt, Scott; Sorensen, Paul; Sangaline, Evan; Wang, Hui
2015-05-19
The equation of state of QCD matter for temperatures near and above the quark-hadron transition (~165 MeV) is inferred within a Bayesian framework through the comparison of data from the Relativistic Heavy Ion Collider and from the Large Hadron Collider to theoretical models. State-of-the-art statistical techniques are applied to simultaneously analyze multiple classes of observables while varying 14 independent model parameters. Thus, the resulting posterior distribution over possible equations of state is consistent with results from lattice gauge theory.
Arnold, J.; Kosson, D.S.; Garrabrants, A.; Meeussen, J.C.L.; Sloot, H.A. van der
2013-02-15
A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.
Soliton solutions of the 3D Gross-Pitaevskii equation by a potential control method
Fedele, R.; Eliasson, B.; Shukla, P. K.; Haas, F.; Jovanovic, D.; De Nicola, S.
2010-12-14
We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.
Verification of the history-score moment equations for weight-window variance reduction
Solomon, Clell J; Sood, Avneet; Booth, Thomas E; Shultis, J. Kenneth
2010-12-06
The history-score moment equations that describe the moments of a Monte Carlo score distribution have been extended to weight-window variance reduction, The resulting equations have been solved deterministically to calculate the population variance of the Monte Carlo score distribution for a single tally, Results for one- and two-dimensional one-group problems are presented that predict the population variances to less than 1% deviation from the Monte Carlo for one-dimensional problems and between 1- 2% for two-dimensional problems,
Moawad, S. M.
2015-02-15
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
Temperature-dependent isovector pairing gap equations using a path integral approach
Fellah, M.; Allal, N. H.; Belabbas, M.; Oudih, M. R.; Benhamouda, N.
2007-10-15
Temperature-dependent isovector neutron-proton (np) pairing gap equations have been established by means of the path integral approach. These equations generalize the BCS ones for the pairing between like particles at finite temperature. The method has been numerically tested using the one-level model. It has been shown that the gap parameter {delta}{sub np} has a behavior analogous to that of {delta}{sub nn} and {delta}{sub pp} as a function of the temperature: one notes the presence of a critical temperature. Moreover, it has been shown that the isovector pairing effects remain beyond the critical temperature that corresponds to the pairing between like particles.
The One and Two Loops Renormalization Group Equations in the Standard Model
Juarez W, S. Rebeca; Solis R, H. Gabriel; Kielanowski, P.
2006-01-06
In the context of the Standard Model (SM), we compare the analytical and the numerical solutions of the Renormalization Group Equations (RGE) for the relevant couplings to one and two loops. This information will be an important ingredient for the precise evaluation of boundary values on the physical Higgs Mass.
Derivation of quantum mechanics from the Boltzmann equation for the Planch aether
Winterberg, F.
1995-10-01
The Planck aether hypothesis assumes that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck masses can be described by a quantum mechanical two-component nonrelativistic operator field equation having the form of a two-component nonlinear Schroedinger equation, with a spectrum of quasiparticles obeying Lorentz invariance as a dynamic symmetry for energies small compared to the Planck energy. We show that quantum mechanics itself can be derived from the Newtonian mechanics of the Planck aether as an approximate solution of Boltzmann`s equation for the locally interacting positive and negative Planck masses, and that the validity of the nonrelativistic Schroedinger equation depends on Lorentz invariance as a dynamic symmetry. We also show how the many-body Schroedinger wave function can be factorized into a product of quasiparticles of the Planck aether with separable quantum potentials. Finally, we present a possible explanation of wave function collapse as a kind of enhanced gravitational collapse in the presence of the negative Planck masses.
Neutron skin thickness and neutron star equations of state: a strong relationship
Menezes, D. P.; Avancini, S. S.; Marinelli, J. R.; Watanabe de Moraes, M. M.; Providencia, C.
2007-10-26
A density dependent hadronic model and a common parametrization of the non-linear Walecka model are used to obtain the lead neutron skin thickness through its proton and neutron density profiles. The neutron skin thickness is known to reflect the equation of state properties. A direct correlation between the neutron skin thickness and the slope of the symmetry energy is found.
FWAVE V1.0 a framework for finite difference wave equation modeling
Energy Science and Technology Software Center (OSTI)
2002-07-01
FWAVE provides a computation framework for the rapid prototyping and efficient use of finite difference wave equation solutions. The user provides single grid Fortran solver components that are integrated using opaque handles to C++ distributed data structures. Permits the scientific researcher to make of clusters and parallel computers by concentrating only on the numerical schemes.
Zhang, Zhongqiang; Yang, Xiu; Lin, Guang; Karniadakis, George Em
2013-03-01
We consider a piston with a velocity perturbed by Brownian motion moving into a straight tube filled with a perfect gas at rest. The shock generated ahead of the piston can be located by solving the one-dimensional Euler equations driven by white noise using the Stratonovich or Ito formulations. We approximate the Brownian motion with its spectral truncation and subsequently apply stochastic collocation using either sparse grid or the quasi-Monte Carlo (QMC) method. In particular, we first transform the Euler equations with an unsteady stochastic boundary into stochastic Euler equations over a fixed domain with a time-dependent stochastic source term. We then solve the transformed equations by splitting them up into two parts, i.e., a deterministic part and a stochastic part. Numerical results verify the StratonovichEuler and ItoEuler models against stochastic perturbation results, and demonstrate the efficiency of sparse grid and QMC for small and large random piston motions, respectively. The variance of shock location of the piston grows cubically in the case of white noise in contrast to colored noise reported in [1], where the variance of shock location grows quadratically with time for short times and linearly for longer times.
Kadanoff-Baym equations with non-Gaussian initial conditions: The equilibrium limit
Garny, Mathias; Mueller, Markus Michael
2009-10-15
The nonequilibrium dynamics of quantum fields is an initial-value problem, which can be described by Kadanoff-Baym equations. Typically, and, in particular, when numerical solutions are demanded, these Kadanoff-Baym equations are restricted to Gaussian initial states. However, physical initial states are non-Gaussian correlated initial states. In particular, renormalizability requires the initial state to feature n-point correlations that asymptotically agree with the vacuum correlations at short distances. In order to identify physical nonequilibrium initial states, it is therefore a precondition to describe the vacuum correlations of the interacting theory within the nonequilibrium framework. In this paper, Kadanoff-Baym equations for non-Gaussian correlated initial states describing vacuum and thermal equilibrium are derived from the 2PI effective action. A diagrammatic method for the explicit construction of vacuum and thermal initial correlations from the 2PI effective action is provided. We present numerical solutions of Kadanoff-Baym equations for a real scalar {phi}{sup 4} quantum field theory, which take the thermal initial four-point correlation as the leading non-Gaussian correction into account. We find that this minimal non-Gaussian initial condition yields an approximation to the complete equilibrium initial state that is quantitatively and qualitatively significantly improved as compared to Gaussian initial states.
A new three-equation model for the CO{sub 2} laser
Stanghini, M.; Basso, M.; Genesio, R.; Tesi, A.; Meucci, R.; Ciofini, M.
1996-07-01
Three rate equations describing the single-mode CO{sub 2} laser dynamics are derived by applying the theory of linear filters to an improved four-level model. The model is studied in the case of periodic modulations of the losses and compared with the outcome of an experiment, revealing a good agreement.
SciCADE 95: International conference on scientific computation and differential equations
1995-12-31
This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included.
Dynamic behavior of the quantum Zakharov-Kuznetsov equations in dense quantum magnetoplasmas
Zhen, Hui-Ling; Tian, Bo Wang, Yu-Feng; Zhong, Hui; Sun, Wen-Rong
2014-01-15
Quantum Zakharov-Kuznetsov (qZK) equation is found in a dense quantum magnetoplasma. Via the spectral analysis, we investigate the Hamiltonian and periodicity of the qZK equation. Using the Hirota method, we obtain the bilinear forms and N-soliton solutions. Asymptotic analysis on the two-soliton solutions shows that the soliton interaction is elastic. Figures are plotted to reveal the propagation characteristics and interaction between the two solitons. We find that the one soliton has a single peak and its amplitude is positively related to H{sub e}, while the two solitons are parallel when H{sub e} < 2, otherwise, the one soliton has two peaks and the two solitons interact with each other. Hereby, H{sub e} is proportional to the ratio of the strength of magnetic field to the electronic Fermi temperature. External periodic force on the qZK equation yields the chaotic motions. Through some phase projections, the process from a sequence of the quasi-period doubling to chaos can be observed. The chaotic behavior is observed since the power spectra are calculated, and the quasi-period doubling states of perturbed qZK equation are given. The final chaotic state of the perturbed qZK is obtained.
Dynamics of a nonautonomous soliton in a generalized nonlinear Schroedinger equation
Yang Zhanying; Zhang Tao; Zhao Lichen; Feng Xiaoqiang; Yue Ruihong
2011-06-15
We solve a generalized nonautonomous nonlinear Schroedinger equation analytically by performing the Darboux transformation. The precise expressions of the soliton's width, peak, and the trajectory of its wave center are investigated analytically, which symbolize the dynamic behavior of a nonautonomous soliton. These expressions can be conveniently and effectively applied to the management of soliton in many fields.
Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation
Mani Rajan, M.S.; Mahalingam, A.; Uthayakumar, A.
2014-07-15
We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.
Soliton Theory of Two-Dimensional Lattices: The Discrete Nonlinear Schroedinger Equation
Arevalo, Edward
2009-06-05
We theoretically investigate the motion of collective excitations in the two-dimensional nonlinear Schroedinger equation with cubic nonlinearity. The form of these excitations for a broad range of parameters is derived. Their evolution and interaction is numerically studied and the modulation instability is discussed. The case of saturable nonlinearity is revisited.
Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1 + 2) dimensions
Zarmi, Yair
2014-10-15
Despite the fact that it is not integrable, the (1 + 2)-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N ≥ 1. Based on these solutions, a quantum-mechanical system is constructed over a Fock space of particles. The coordinate of each particle is an angle around the unit circle. U, a nonlinear functional of the particle number-operators, which obeys the Sine-Gordon equation in (1 + 2) dimensions, is constructed. Its eigenvalues on N-particle states in the Fock space are the slower-than-light, N-soliton solutions of the equation. A projection operator (a nonlinear functional of U), which vanishes on the single-particle subspace, is a mass-density generator. Its eigenvalues on multi-particle states play the role of the mass density of structures that emulate free, spatially extended, relativistic particles. The simplicity of the quantum-mechanical system allows for the incorporation of perturbations with particle interactions, which have the capacity to “annihilate” and “create” solitons – an effect that does not have an analog in perturbed classical nonlinear evolution equations.
The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion
Guo, Ran; Du, Jiulin
2015-08-15
We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.
Cross, J. E.; Gregori, G.; Reville, B.
2014-11-01
We introduce the equations of magneto-quantum-radiative hydrodynamics. By rewriting them in a dimensionless form, we obtain a set of parameters that describe scale-dependent ratios of characteristic hydrodynamic quantities. We discuss how these dimensionless parameters relate to the scaling between astrophysical observations and laboratory experiments.
On the solution of the continuity equation for precipitating electrons in solar flares
Emslie, A. Gordon; Holman, Gordon D.; Litvinenko, Yuri E. E-mail: gordon.d.holman@nasa.gov
2014-09-01
Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis and Zharkova claim to have found an 'updated exact analytical solution' to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii and Shmeleva, and many others is invalid. We show that the solution of Dobranskis and Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the 'new' analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result. We conclude that Dobranskis and Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii and Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.