Exact and approximate Kohn-Sham potentials in ensemble density...
Office of Scientific and Technical Information (OSTI)
Title: Exact and approximate Kohn-Sham potentials in ensemble density-functional theory Authors: Yang, Zeng-hui ; Trail, John R. ; Pribram-Jones, Aurora ; Burke, Kieron ; Needs, ...
The Greatest Mathematical Discovery?
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Quigg, Chris; /Fermilab
2005-02-01
It is a pleasure to be part of the SLAC Summer Institute again, not simply because it is one of the great traditions in our field, but because this is a moment of great promise for particle physics. I look forward to exploring many opportunities with you over the course of our two weeks together. My first task in talking about Nature's Greatest Puzzles, the title of this year's Summer Institute, is to deconstruct the premise a little bit.
Nishikawa, Takeshi
2014-07-15
Most conventional atomic models in a plasma do not treat the effect of the plasma on the free-electron state density. Using a nearest neighbor approximation, the state densities in hydrogenic plasmas for both bound and free electrons were evaluated and the effect of the plasma on the atomic model (especially for the state density of the free electron) was studied. The model evaluates the electron-state densities using the potential distribution formed by the superposition of the Coulomb potentials of two ions. The potential from one ion perturbs the electronic state density on the other. Using this new model, one can evaluate the free-state density without making any ad-hoc assumptions. The resulting contours of the average ionization degree, given as a function of the plasma temperature and density, are shifted slightly to lower temperatures because of the effect of the increasing free-state density.
Double-hybrid density-functional theory with meta-generalized-gradient approximations
Souvi, Sidi M. O. Sharkas, Kamal; Toulouse, Julien; CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris
2014-02-28
We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid approximations using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional and test them on test sets of atomization energies and reaction barrier heights. The most accurate variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard Kohn-Sham TPSS and second-order Møller-Plesset calculations.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
Kühn, Michael; Weigend, Florian
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy){sub 3} (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its “spin-forbidden” triplet-singlet transition.
Kraisler, Eli; Kronik, Leeor
2014-05-14
The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturally from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional – the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.
Relativistic equation of state at subnuclear densities in the Thomas-Fermi approximation
Zhang, Z. W.; Shen, H., E-mail: shennankai@gmail.com [School of Physics, Nankai University, Tianjin 300071 (China)
2014-06-20
We study the non-uniform nuclear matter using the self-consistent Thomas-Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature T, proton fraction Y{sub p} , and baryon mass density ? {sub B}, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner-Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas-Fermi approximation. A detailed comparison is made between the present results and previous calculations in the Thomas-Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen equation of state.
Thermally-assisted-occupation density functional theory with generalized-gradient approximations
Chai, Jeng-Da
2014-05-14
We extend the recently proposed thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] to generalized-gradient approximation (GGA) exchange-correlation density functionals. Relative to our previous TAO-LDA (i.e., the local density approximation to TAO-DFT), the resulting TAO-GGAs are significantly superior for a wide range of applications, such as thermochemistry, kinetics, and reaction energies. For noncovalent interactions, TAO-GGAs with empirical dispersion corrections are shown to yield excellent performance. Due to their computational efficiency for systems with strong static correlation effects, TAO-LDA and TAO-GGAs are applied to study the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy) of acenes with different number of linearly fused benzene rings (up to 100), which is very challenging for conventional electronic structure methods. The ground states of acenes are shown to be singlets for all the chain lengths studied here. With the increase of acene length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy (i.e., a measure of polyradical character) increase monotonically.
Relativistic Coulomb excitation within the time dependent superfluid local density approximation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Stetcu, I.; Bertulani, C. A.; Bulgac, A.; Magierski, P.; Roche, K. J.
2015-01-06
Within the framework of the unrestricted time-dependent density functional theory, we present for the first time an analysis of the relativistic Coulomb excitation of the heavy deformed open shell nucleus 238U. The approach is based on the superfluid local density approximation formulated on a spatial lattice that can take into account coupling to the continuum, enabling self-consistent studies of superfluid dynamics of any nuclear shape. We compute the energy deposited in the target nucleus as a function of the impact parameter, finding it to be significantly larger than the estimate using the Goldhaber-Teller model. The isovector giant dipole resonance, themoreÂ Â» dipole pygmy resonance, and giant quadrupole modes are excited during the process. As a result, the one-body dissipation of collective dipole modes is shown to lead a damping width Î“â†“â‰ˆ0.4 MeV and the number of preequilibrium neutrons emitted has been quantified.Â«Â less
Ribeiro, M.
2015-06-21
Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost.
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Giera, Brian; Lawrence Livermore National Lab.; Henson, Neil; Kober, Edward M.; Shell, M. Scott; Squires, Todd M.
2015-02-27
We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnahanâ€“Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as is the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drivemoreÂ Â» strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.Â«Â less
Mardirossian, Narbe; Head-Gordon, Martin
2015-02-21
A meta-generalized gradient approximation density functional paired with the VV10 nonlocal correlation functional is presented. The functional form is selected from more than 10{sup 10} choices carved out of a functional space of almost 10{sup 40} possibilities. Raw data come from training a vast number of candidate functional forms on a comprehensive training set of 1095 data points and testing the resulting fits on a comprehensive primary test set of 1153 data points. Functional forms are ranked based on their ability to reproduce the data in both the training and primary test sets with minimum empiricism, and filtered based on a set of physical constraints and an often-overlooked condition of satisfactory numerical precision with medium-sized integration grids. The resulting optimal functional form has 4 linear exchange parameters, 4 linear same-spin correlation parameters, and 4 linear opposite-spin correlation parameters, for a total of 12 fitted parameters. The final density functional, B97M-V, is further assessed on a secondary test set of 212 data points, applied to several large systems including the coronene dimer and water clusters, tested for the accurate prediction of intramolecular and intermolecular geometries, verified to have a readily attainable basis set limit, and checked for grid sensitivity. Compared to existing density functionals, B97M-V is remarkably accurate for non-bonded interactions and very satisfactory for thermochemical quantities such as atomization energies, but inherits the demonstrable limitations of existing local density functionals for barrier heights.
Oak Ridge Removes Laboratory's Greatest Source of Groundwater...
Broader source: Energy.gov (indexed) [DOE]
the 4,000-gallon Tank W-1A, which was ORNLs greatest source of groundwater contamination. Workers remove the 4,000-gallon Tank W-1A, which was ORNL's greatest source of ...
Xu, Zhuo Gu, Bo; Mori, Michiyasu; Maekawa, Sadamichi; Ziman, Timothy
2015-05-07
We analyze the spin Hall effect in CuIr alloys in theory by the combined approach of the density functional theory (DFT) and Hartree-Fock (HF) approximation. The spin Hall angle (SHA) is obtained to be negative without the local correlation effects. After including the local correlation effects of the 5d orbitals of Ir impurities, the SHA becomes positive with realistic correlation parameters and consistent with experiment [Niimi et al., Phys. Rev. Lett. 106, 126601 (2011)]. Moreover, our analysis shows that the DFTâ€‰+â€‰HF approach is a convenient and general method to study the influence of local correlation effects on the spin Hall effect.
Aquino, Fredy W.; Govind, Niranjan; Autschbach, Jochen
2011-10-01
Density functional theory (DFT) calculations of NMR chemical shifts and molecular g-tensors with Gaussian-type orbitals are implemented via second-order energy derivatives within the scalar relativistic zeroth order regular approximation (ZORA) framework. Nonhybrid functionals, standard (global) hybrids, and range-separated (Coulomb-attenuated, long-range corrected) hybrid functionals are tested. Origin invariance of the results is ensured by use of gauge-including atomic orbital (GIAO) basis functions. The new implementation in the NWChem quantum chemistry package is verified by calculations of nuclear shielding constants for the heavy atoms in HX (X=F, Cl, Br, I, At) and H2X (X = O, S, Se, Te, Po), and Te chemical shifts in a number of tellurium compounds. The basis set and functional dependence of g-shifts is investigated for 14 radicals with light and heavy atoms. The problem of accurately predicting F NMR shielding in UF6-nCln, n = 1 to 6, is revisited. The results are sensitive to approximations in the density functionals, indicating a delicate balance of DFT self-interaction vs. correlation. For the uranium halides, the results with the range-separated functionals are mixed.
Sato, Shunsuke A.; Taniguchi, Yasutaka; Shinohara, Yasushi; Yabana, Kazuhiro
2015-12-14
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
What the World's Greatest Energy Managers Do Differently
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
concentration of open source materials research Managing the billion-dollar U.S. ITER project I. DO Understand the GAME II. DO Build A Strong Coalition World's Greatest ...
Mizutani, U; Inukai, M; Sato, H; Zijlstra, E S; Lin, Q
2014-05-16
There are three key electronic parameters in elucidating the physics behind the Humeâ€“Rothery electron concentration rule: the square of the Fermi diameter (2kF)2, the square of the critical reciprocal lattice vector and the electron concentration parameter or the number of itinerant electrons per atom e/a. We have reliably determined these three parameters for 10 Rhombic Triacontahedron-type 2/1â€“2/1â€“2/1 (N = 680) and 1/1â€“1/1â€“1/1 (N = 160â€“162) approximants by making full use of the full-potential linearized augmented plane wave-Fourier band calculations based on all-electron density-functional theory. We revealed that the 2/1â€“2/1â€“2/1 approximants Al13Mg27Zn45 and Na27Au27Ga31 belong to two different sub-groups classified in terms of equal to 126 and 109 and could explain why they take different e/a values of 2.13 and 1.76, respectively. Among eight 1/1â€“1/1â€“1/1 approximants Al3Mg4Zn3, Al9Mg8Ag3, Al21Li13Cu6, Ga21Li13Cu6, Na26Au24Ga30, Na26Au37Ge18, Na26Au37Sn18 and Na26Cd40Pb6, the first two, the second two and the last four compounds were classified into three sub-groups with = 50, 46 and 42; and were claimed to obey the e/a = 2.30, 2.10â€“2.15 and 1.70â€“1.80 rules, respectively.
Mardirossian, Narbe; Head-Gordon, Martin
2014-05-14
The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the training and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491Â 508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491Â 508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. The range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements.
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Wang, Jianwei; Zhang, Yong; Wang, Lin-Wang
2015-07-31
We propose a systematic approach that can empirically correct three major errors typically found in a density functional theory (DFT) calculation within the local density approximation (LDA) simultaneously for a set of common cation binary semiconductors, such as III-V compounds, (Ga or In)X with X = N,P,As,Sb, and II-VI compounds, (Zn or Cd)X, with X = O,S,Se,Te. By correcting (1) the binary band gaps at high-symmetry points , L, X, (2) the separation of p-and d-orbital-derived valence bands, and (3) conduction band effective masses to experimental values and doing so simultaneously for common cation binaries, the resulting DFT-LDA-based quasi-first-principles methodmoreÂ Â» can be used to predict the electronic structure of complex materials involving multiple binaries with comparable accuracy but much less computational cost than a GW level theory. This approach provides an efficient way to evaluate the electronic structures and other material properties of complex systems, much needed for material discovery and design.Â«Â less
Particle size for greatest penetration of HEPA filters - and...
Office of Scientific and Technical Information (OSTI)
Subject: 54 ENVIRONMENTAL SCIENCES; AEROSOLS; FILTRATION; FILTERS; EFFICIENCY; RADIOACTIVE AEROSOLS; AIR POLLUTION; AIR POLLUTION CONTROL; COMPARATIVE EVALUATIONS; DENSITY; ...
Question of the Week: What are Your Greatest Energy Concerns as We Approach Winter?
Broader source: Energy.gov [DOE]
We asked, you answered: What are your greatest energy concerns as we approach the winter heating season?
New Lessons Learned: Peer Exchange Call "Greatest Hits" Out Now |
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
Department of Energy Lessons Learned: Peer Exchange Call "Greatest Hits" Out Now New Lessons Learned: Peer Exchange Call "Greatest Hits" Out Now Photo of an outreach event: a woman at a cart with an umbrella, interacting with several people standing nearby, and a sign and car on the curb. The latest in a series of Lessons Learned: Peer Exchange Call "greatest hits" summarizes top marketing and outreach takeaways from Better Buildings Residential Network members
Broader source: Energy.gov [DOE]
Excel file and dataset for Improvements in Fuel Economy for Low-MPG Vehicles Yield the Greatest Savings
Wang, Jianwei; Zhang, Yong; Wang, Lin-Wang
2015-07-31
We propose a systematic approach that can empirically correct three major errors typically found in a density functional theory (DFT) calculation within the local density approximation (LDA) simultaneously for a set of common cation binary semiconductors, such as III-V compounds, (Ga or In)X with X = N,P,As,Sb, and II-VI compounds, (Zn or Cd)X, with X = O,S,Se,Te. By correcting (1) the binary band gaps at high-symmetry points , L, X, (2) the separation of p-and d-orbital-derived valence bands, and (3) conduction band effective masses to experimental values and doing so simultaneously for common cation binaries, the resulting DFT-LDA-based quasi-first-principles method can be used to predict the electronic structure of complex materials involving multiple binaries with comparable accuracy but much less computational cost than a GW level theory. This approach provides an efficient way to evaluate the electronic structures and other material properties of complex systems, much needed for material discovery and design.
What Are Your Greatest Energy Concerns for Summer? | Department of Energy
Broader source: Energy.gov (indexed) [DOE]
Regional Partnership Overview June 2013 Briefing Overview ï‚¨ WRP Background ï‚¨ Importance of Region ï‚¨ WRP Tribal Relations Committee ï‚¨ WRP Energy Committee WRP Region's Uniqueness ï‚¨ 5 states stretching from the Great Plains to the Pacific Ocean ï‚¨ Diverse terrain ranging from desert valleys to forested mountains ï‚¨ Significant State Trust Landholdings ï‚¨ Approximately 188 Federally recognized Tribes ï‚¨ Significant amounts of Federally managed land ï‚¤ According to GSA 2004 study, WRP
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Gedanken densities and exact constraints in density functional theory
Perdew, John P.; Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122 ; Ruzsinszky, Adrienn; Sun, Jianwei; Burke, Kieron
2014-05-14
Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGAâ€™s. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Relativistic Random Phase Approximation At Finite Temperature
Niu, Y. F.; Paar, N.; Vretenar, D.; Meng, J.
2009-08-26
The fully self-consistent finite temperature relativistic random phase approximation (FTRRPA) has been established in the single-nucleon basis of the temperature dependent Dirac-Hartree model (FTDH) based on effective Lagrangian with density dependent meson-nucleon couplings. Illustrative calculations in the FTRRPA framework show the evolution of multipole responses of {sup 132}Sn with temperature. With increased temperature, in both monopole and dipole strength distributions additional transitions appear in the low energy region due to the new opened particle-particle and hole-hole transition channels.
Density-dependent covariant energy density functionals
Lalazissis, G. A.
2012-10-20
Relativistic nuclear energy density functionals are applied to the description of a variety of nuclear structure phenomena at and away fromstability line. Isoscalar monopole, isovector dipole and isoscalar quadrupole giant resonances are calculated using fully self-consistent relativistic quasiparticle randomphase approximation, based on the relativistic Hartree-Bogoliubovmodel. The impact of pairing correlations on the fission barriers in heavy and superheavy nuclei is examined. The role of pion in constructing desnity functionals is also investigated.
Plasma Physics Approximations in Ares
Managan, R. A.
2015-01-08
Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, F_{n}( Î¼/Î¸ ), the chemical potential, Î¼ or Î¶ = ln(1+e^{ Î¼/Î¸} ), and the temperature, Î¸ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either Î¼ or Î¶ . The fits use Î¶ as the independent variable instead of Î¼/Î¸ . New fits are provided for A^{Î±} (Î¶ ),A^{Î²} (Î¶ ), Î¶, f(Î¶ ) = (1 + e^{-Î¼/Î¸})F_{1/2}(Î¼/Î¸), F_{1/2}'/F_{1/2}, F_{c}^{Î±}, and F_{c}^{Î²}. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as Î¶â†’ 0 or âˆž. The original fits due to Lee & More and George Zimmerman are presented for comparison.
QCD in the Hartree approximation
Biro f , T. S.
1989-04-01
For QCD and expansion of the full quantum theory on a variational background forcing vanishing expectation values for colour fields is considered. This approach at low temperature (strong coupling) describes a colourless condensate of gluonic Cooper pairs. Their binding energy cancels exactly their background generated gluon mass, restoring the gauge symmetry. At high temperature (weak coupling) only a perturbative gluon plasma exists. The vacuum energy density and the phase transition temperature are related to the pairing energy. Our results scale according to asymptotic freedom. /copyright/ Academic Press, Inc. 1989
Ions in solution: Density corrected density functional theory (DC-DFT)
Kim, Min-Cheol; Sim, Eunji; Burke, Kieron
2014-05-14
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HOÂ·Cl{sup âˆ’} and HOÂ·H{sub 2}O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.
An approximation technique for jet impingement flow
Najafi, Mahmoud; Fincher, Donald; Rahni, Taeibi; Javadi, KH.; Massah, H.
2015-03-10
The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity.
Phenomenological Relativistic Energy Density Functionals
Lalazissis, G. A.; Kartzikos, S.; Niksic, T.; Paar, N.; Vretenar, D.; Ring, P.
2009-08-26
The framework of relativistic nuclear energy density functionals is applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of beta-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure is explored using the fully consistent quasiparticle random-phase approximation based on the relativistic Hartree-Bogoliubov model. Recent applications of energy density functionals with explicit density dependence of the meson-nucleon couplings are presented.
Exploring the Random Phase Approximately for materials chemistry and physics
Ruzsinsky, Adrienn
2015-03-23
This proposal focuses on improved accuracy for the delicate energy differences of interest in materials chemistry with the fully nonlocal random phase approximation (RPA) in a density functional context. Could RPA or RPA-like approaches become standard methods of first-principles electronic-structure calculation for atoms, molecules, solids, surfaces, and nano-structures? Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA also improves upon simple pair-wise interaction potentials or vdW density functional theory. This improvement is essential to capture accurate energy differences in metals and different phases of semiconductors. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current â€œstandard modelâ€ for quantum chemistry and condensed matter physics. Within this project we already applied RPA on different structural phase transitions on semiconductors, metals and molecules. Although RPA predicts accurate structural parameters, RPA has proven not equally accurate in all kinds of structural phase transitions. Therefore a correction to RPA can be necessary in many cases. We are currently implementing and testing a nonempirical, spatially nonlocal, frequency-dependent model for the exchange-correlation kernel in the adiabatic-connection fluctuation-dissipation context. This kernel predicts a nearly-exact correlation energy for the electron gas of uniform density. If RPA or RPA-like approaches prove to be reliably accurate, then expected increases in computer power may make them standard in the electronic-structure calculations of the future.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
A Survey of Techniques for Approximate Computing
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Mittal, Sparsh
2016-03-18
Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is tomoreÂ Â» provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.Â«Â less
Structural physical approximations of unphysical maps and generalized quantum measurements
Fiurasek, Jaromir
2002-11-01
We investigate properties of the structural physical approximation (SPA) of the partial transposition map recently introduced by Horodecki and Ekert [Phys. Rev. Lett. 89, 127902 (2002)]. We focus on the case of two-qubit states and show that in this case the map has the structure of a generalized quantum measurement followed by the preparation of a suitable output state. We also introduce SPA for a map that transforms two copies of density matrix of a single qubit onto a square of that matrix. We prove that also this map is essentially a generalized quantum measurement.
An improved proximity force approximation for electrostatics
Fosco, Cesar D.; Instituto Balseiro, Universidad Nacional de Cuyo, R8402AGP Bariloche ; Lombardo, Fernando C.; IFIBA ; Mazzitelli, Francisco D.
2012-08-15
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces.
Second derivatives for approximate spin projection methods
Thompson, Lee M.; Hratchian, Hrant P.
2015-02-07
The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.
Semiclassical approximation to supersymmetric quantum gravity
Kiefer, Claus; Lueck, Tobias; Moniz, Paulo
2005-08-15
We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schroedinger equation, and quantum gravitational correction terms to this Schroedinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many-fingered) local time parameter has to be present on super Riem {sigma} (the space of all possible tetrad and gravitino fields) (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early Universe. The physical meaning of these equations and results, in particular, the similarities to and differences from the pure bosonic case, are discussed.
Magnetic reconnection under anisotropic magnetohydrodynamic approximation
Hirabayashi, K.; Hoshino, M.
2013-11-15
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observations. Our results showed that once magnetic reconnection takes place, a firehose-sense (p{sub ?}>p{sub ?}) pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with those in an isotropic MHD. In spite of the weakness of the shocks, however, the resultant reconnection rate is 10%–30% higher than that in an isotropic case. This result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.
Approximate Model for Turbulent Stagnation Point Flow.
Dechant, Lawrence
2016-01-01
Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near the stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems.
Bond selective chemistry beyond the adiabatic approximation
Butler, L.J.
1993-12-01
One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
Insight into organic reactions from the direct random phase approximation and its corrections
Ruzsinszky, Adrienn; Zhang, Igor Ying; Scheffler, Matthias
2015-10-14
The performance of the random phase approximation (RPA) and beyond-RPA approximations for the treatment of electron correlation is benchmarked on three different molecular test sets. The test sets are chosen to represent three typical sources of error which can contribute to the failure of most density functional approximations in chemical reactions. The first test set (atomization and n-homodesmotic reactions) offers a gradually increasing balance of error from the chemical environment. The second test set (Diels-Alder reaction cycloaddition = DARC) reflects more the effect of weak dispersion interactions in chemical reactions. Finally, the third test set (self-interaction error 11 = SIE11) represents reactions which are exposed to noticeable self-interaction errors. This work seeks to answer whether any one of the many-body approximations considered here successfully addresses all these challenges.
Weber, J. W.; Bol, A. A. [Department of Applied Physics, Eindhoven University of Technology, Den Dolech 2, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Sanden, M. C. M. van de [Department of Applied Physics, Eindhoven University of Technology, Den Dolech 2, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Dutch Institute for Fundamental Energy Research (DIFFER), Nieuwegein (Netherlands)
2014-07-07
This work presents an improved thin film approximation to extract the optical conductivity from infrared transmittance in a simple yet accurate way. This approximation takes into account the incoherent reflections from the backside of the substrate. These reflections are shown to have a significant effect on the extracted optical conductivity and hence on derived parameters as carrier mobility and density. By excluding the backside reflections, the error for these parameters for typical chemical vapor deposited (CVD) graphene on a silicon substrate can be as high as 17% and 45% for the carrier mobility and density, respectively. For the mid- and near-infrared, the approximation can be simplified such that the real part of the optical conductivity is extracted without the need for a parameterization of the optical conductivity. This direct extraction is shown for Fourier transform infrared (FTIR) transmittance measurements of CVD graphene on silicon in the photon energy range of 370–7000?cm{sup ?1}. From the real part of the optical conductivity, the carrier density, mobility, and number of graphene layers are determined but also residue, originating from the graphene transfer, is detected. FTIR transmittance analyzed with the improved thin film approximation is shown to be a non-invasive, easy, and accurate measurement and analysis method for assessing the quality of graphene and can be used for other 2-D materials.
Visualization of electronic density
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Grosso, Bastien; Cooper, Valentino R.; Pine, Polina; Hashibon, Adham; Yaish, Yuval; Adler, Joan
2015-04-22
An atomâ€™s volume depends on its electronic density. Although this density can only be evaluated exactly for hydrogen-like atoms, there are many excellent numerical algorithms and packages to calculate it for other materials. 3D visualization of charge density is challenging, especially when several molecular/atomic levels are intertwined in space. We explore several approaches to 3D charge density visualization, including the extension of an anaglyphic stereo visualization application based on the AViz package to larger structures such as nanotubes. We will describe motivations and potential applications of these tools for answering interesting questions about nanotube properties.
Visualization of electronic density
Grosso, Bastien; Cooper, Valentino R.; Pine, Polina; Hashibon, Adham; Yaish, Yuval; Adler, Joan
2015-04-22
An atom’s volume depends on its electronic density. Although this density can only be evaluated exactly for hydrogen-like atoms, there are many excellent numerical algorithms and packages to calculate it for other materials. 3D visualization of charge density is challenging, especially when several molecular/atomic levels are intertwined in space. We explore several approaches to 3D charge density visualization, including the extension of an anaglyphic stereo visualization application based on the AViz package to larger structures such as nanotubes. We will describe motivations and potential applications of these tools for answering interesting questions about nanotube properties.
Aggelen, Helen van; Department of Chemistry, Duke University, Durham, North Carolina 27708 ; Yang, Yang; Yang, Weitao
2014-05-14
Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H{sub 2}, and eliminates delocalization errors in H{sub 2}{sup +} and other single-bond systems. It gives surprisingly good non-bonded interaction energies – competitive with the ph-RPA – with the correct R{sup ?6} asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.
An approximate framework for quantum transport calculation with model order reduction
Chen, Quan; Li, Jun; Yam, Chiyung; Zhang, Yu; Wong, Ngai; Chen, Guanhua
2015-04-01
A new approximate computational framework is proposed for computing the non-equilibrium charge density in the context of the non-equilibrium Green's function (NEGF) method for quantum mechanical transport problems. The framework consists of a new formulation, called the X-formulation, for single-energy density calculation based on the solution of sparse linear systems, and a projection-based nonlinear model order reduction (MOR) approach to address the large number of energy points required for large applied biases. The advantages of the new methods are confirmed by numerical experiments.
Litvinova, E.; Ring, P.; Tselyaev, V.; Langanke, K.
2009-05-15
Theoretical studies of low-lying dipole strength in even-even spherical nuclei within the relativistic quasiparticle time blocking approximation (RQTBA) are presented. The RQTBA developed recently as an extension of the self-consistent relativistic quasiparticle random-phase approximation (RQRPA) enables one to investigate the effects of the coupling of two-quasiparticle excitations to collective vibrations within a fully consistent calculation scheme based on covariant energy density functional theory. Dipole spectra of even-even {sup 130}Sn-{sup 140}Sn and {sup 68}Ni-{sup 78}Ni isotopes calculated within both RQRPA and RQTBA show two well-separated collective structures: the higher lying giant dipole resonance and the lower lying pygmy dipole resonance, which can be identified by the different behavior of the transition densities of states in these regions.
The Columbia Americas Greatest Power Stream
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Volume One Film Collection Volume Two 75th Anniversary Hydropower in the Northwest Woody Guthrie Videos Strategic Direction Branding & Logos Power of the River History Book...
The standard modelâ€™s greatest triumph
Gabrielse, Gerald
2013-12-01
The standard model predicts the electron magnetic moment to an astonishing accuracy of one part in a trillion.
The standard modelâ€™s greatest triumph
Gabrielse, Gerald
2013-12-15
The standard model predicts the electron magnetic moment to an astonishing accuracy of one part in a trillion.
Chiral dynamics and peripheral transverse densities
Granados, Carlos G.; Weiss, Christian
2014-01-01
In the partonic (or light-front) description of relativistic systems the electromagnetic form factors are expressed in terms of frame-independent charge and magnetization densities in transverse space. This formulation allows one to identify the chiral components of nucleon structure as the peripheral densities at transverse distances b = O(M{sub {pi}}{sup -1}) and compute them in a parametrically controlled manner. A dispersion relation connects the large-distance behavior of the transverse charge and magnetization densities to the spectral functions of the Dirac and Pauli form factors near the two--pion threshold at timelike t = 4 M{ sub {pi}}{sup 2}, which can be computed in relativistic chiral effective field theory. Using the leading-order approximation we (a) derive the asymptotic behavior (Yukawa tail) of the isovector transverse densities in the "chiral" region b = O(M{sub {pi}}{sup -1}) and the "molecular" region b = O(M{sub N}{sup 2}/M{sub {pi}}{sup 3}); (b) perform the heavy-baryon expansion of the transverse densities; (c) explain the relative magnitude of the peripheral charge and magnetization densities in a simple mechanical picture; (d) include Delta isobar intermediate states and study the peripheral transverse densities in the large-N{ sub c} limit of QCD; (e) quantify the region of transverse distances where the chiral components of the densities are numerically dominant; (f) calculate the chiral divergences of the b{sup 2}-weighted moments of the isovector transverse densities (charge and anomalous magnetic radii) in the limit M{sub {pi}} -> 0 and determine their spatial support. Our approach provides a concise formulation of the spatial structure of the nucleon's chiral component and offers new insights into basic properties of the chiral expansion. It relates the information extracted from low-t elastic form factors to the generalized parton distributions probed in peripheral high-energy scattering processes.
Xianlong, Gao; Polini, Marco; Tosi, M. P.; Campo, Vivaldo L. Jr.; Capelle, Klaus; Rigol, Marcos
2006-04-15
We present an extensive numerical study of the ground-state properties of confined repulsively interacting fermions in one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe ansatz based local-density approximation for the correlation energy that accounts for Luttinger-liquid and Mott-insulator physics. Semianalytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-type local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these provide a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.
Density Equalizing Map Projections
Energy Science and Technology Software Center (OSTI)
1995-07-01
A geographic map is mathematically transformed so that the subareas of the map are proportional to a given quantity such as population. In other words, population density is equalized over the entire map. The transformed map can be used as a display tool, or it can be statistically analyzed. For example, cases of disease plotted on the transformed map should be uniformly distributed at random, if disease rates are everywhere equal. Geographic clusters of diseasemoreÂ Â» can be readily identified, and their statistical significance determined, on a density equalized map.Â«Â less
ANALOG QUANTUM NEURON FOR FUNCTIONS APPROXIMATION A. EZHOV; A...
Office of Scientific and Technical Information (OSTI)
FOR FUNCTIONS APPROXIMATION A. EZHOV; A. KHROMOV; G. BERMAN 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; IMPLEMENTATION; NERVE CELLS; WAVEGUIDES We describe a system able...
Charge-conjugation symmetric complete impulse approximation for...
Office of Scientific and Technical Information (OSTI)
from the spectator quark (referred to as the relativistic impulse approximation). In this study we also include the contributions from the poles of the quark which interacts with ...
How to Solve Schroedinger Problems by Approximating the Potential Function
Ledoux, Veerle; Van Daele, Marnix
2010-09-30
We give a survey over the efforts in the direction of solving the Schroedinger equation by using piecewise approximations of the potential function. Two types of approximating potentials have been considered in the literature, that is piecewise constant and piecewise linear functions. For polynomials of higher degree the approximating problem is not so easy to integrate analytically. This obstacle can be circumvented by using a perturbative approach to construct the solution of the approximating problem, leading to the so-called piecewise perturbation methods (PPM). We discuss the construction of a PPM in its most convenient form for applications and show that different PPM versions (CPM,LPM) are in fact equivalent.
A Multithreaded Algorithm for Network Alignment Via Approximate...
Office of Scientific and Technical Information (OSTI)
The best current approaches are entirely heuristic, and are iterative in nature. They generate real-valued heuristic approximations that must be rounded to find integer solutions. ...
Quasiparticle random-phase approximation with interactions from...
Office of Scientific and Technical Information (OSTI)
Quasiparticle random-phase approximation with interactions from the Similarity Renormalization Group Citation Details In-Document Search Title: Quasiparticle random-phase ...
Multiple density layered insulator
Alger, T.W.
1994-09-06
A multiple density layered insulator for use with a laser is disclosed which provides at least two different insulation materials for a laser discharge tube, where the two insulation materials have different thermoconductivities. The multiple layer insulation materials provide for improved thermoconductivity capability for improved laser operation. 4 figs.
Multiple density layered insulator
Alger, Terry W.
1994-01-01
A multiple density layered insulator for use with a laser is disclosed wh provides at least two different insulation materials for a laser discharge tube, where the two insulation materials have different thermoconductivities. The multiple layer insulation materials provide for improved thermoconductivity capability for improved laser operation.
Vranjes, J.; Kono, M.
2015-01-15
Inhomogeneous plasmas and fluids contain energy stored in inhomogeneity and they naturally tend to relax into lower energy states by developing instabilities or by diffusion. But the actual amount of energy in such inhomogeneities has remained unknown. In the present work, the amount of energy stored in a density gradient is calculated for several specific density profiles in a cylindrical configuration. This is of practical importance for drift wave instability in various plasmas, and, in particular, in its application in models dealing with the heating of solar corona because the instability is accompanied with stochastic heating, so the energy contained in inhomogeneity is effectively transformed into heat. It is shown that even for a rather moderate increase of the density at the axis in magnetic structures in the corona by a factor 1.5 or 3, the amount of excess energy per unit volume stored in such a density gradient becomes several orders of magnitude greater than the amount of total energy losses per unit volume (per second) in quiet regions in the corona. Consequently, within the life-time of a magnetic structure such energy losses can easily be compensated by the stochastic drift wave heating.
The problem of the universal density functional and the density matrix functional theory
Bobrov, V. B. Trigger, S. A.
2013-04-15
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
Density Log | Open Energy Information
Density Log Jump to: navigation, search GEOTHERMAL ENERGYGeothermal Home Exploration Technique: Density Log Details Activities (7) Areas (6) Regions (0) NEPA(0) Exploration...
Rock Density | Open Energy Information
Density Jump to: navigation, search GEOTHERMAL ENERGYGeothermal Home Exploration Technique: Rock Density Details Activities (2) Areas (2) Regions (0) NEPA(0) Exploration Technique...
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, FranÃ§ois; 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 onemoreÂ Â» has also access to the non-approximated result for comparison.Â«Â less
Properties of the Boltzmann equation in the classical approximation
Epelbaum, Thomas; Gelis, FranÃ§ois; 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.
Higher-degree linear approximations of nonlinear systems
Karahan, S.
1989-01-01
In this dissertation, the author develops a new method for obtaining higher degree linear approximations of nonlinear control systems. The standard approach in the analysis and synthesis of nonlinear systems is a first order approximation by a linear model. This is usually performed by obtaining a series expansion of the system at some nominal operating point and retaining only the first degree terms in the series. The accuracy of this approximation depends on how far the system moves away from the normal point, and on the relative magnitudes of the higher degree terms in the series expansion. The approximation is achieved by finding an appropriate nonlinear coordinate transformation-feedback pair to perform the higher degree linearization. With the proposed method, one can improve the accuracy of the approximation up to arbitrarily higher degrees, provided certain solvability conditions are satisfied. The Hunt-Su linearizability theorem makes these conditions precise. This approach is similar to Poincare's Normal Form Theorem in formulation, but different in its solution method. After some mathematical background the author derives a set of equations (called the Homological Equations). A solution to this system of linear equations is equivalent to the solution to the problem of approximate linearization. However, it is generally not possible to solve the system of equations exactly. He outlines a method for systematically finding approximate solutions to these equations using singular value decomposition, while minimizing an error with respect to some defined norm.
Smith, Kyle K. G.; Poulsen, Jens Aage Nyman, Gunnar; Rossky, Peter J.
2015-06-28
We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.
Communication: Improved pair approximations in local coupled-cluster methods
Schwilk, Max; Werner, Hans-Joachim; Usvyat, Denis
2015-03-28
In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order MÃ¸ller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger.
Improved approximate formulas for flux from cylindrical and rectangular sources
Wallace, O.J.; Bokharee, S.A.
1993-03-01
This report provides two new approximate formulas for the flux at detector points outside the radial and axial extensions of a homogeneous cylindrical source and improved approximate formulas for the flux at points opposite rectangular surface sources. These formulas extend the range of geometries for which analytic approximations may be used by shield design engineers to make rapid scoping studies and check more extensive calculations for reasonableness. These formulas can be used to support skeptical, independent evaluations and are also valuable teaching tools for introducing shield designers to complex shield analyses.
Study of multiband disordered systems using the typical medium dynamical cluster approximation
Zhang, Yi; Terletska, Hanna; Moore, C.; Ekuma, Chinedu; Tam, Ka-Ming; Berlijn, Tom; Ku, Wei; Moreno, Juana; Jarrell, Mark
2015-11-06
We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to K_{x}Fe_{2-y}Se_{2} with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Moreover our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.
Study of multiband disordered systems using the typical medium dynamical cluster approximation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Zhang, Yi; Terletska, Hanna; Moore, C.; Ekuma, Chinedu; Tam, Ka-Ming; Berlijn, Tom; Ku, Wei; Moreno, Juana; Jarrell, Mark
2015-11-06
We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to KxFe2-ySe2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Moreover our resultsmoreÂ Â» demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.Â«Â less
Integral approximations to classical diffusion and smoothed particle hydrodynamics
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.
2014-12-31
The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.moreÂ Â» The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.Â«Â less
Second post-Newtonian approximation of Einstein-aether theory
Xie Yi; Huang Tianyi
2008-06-15
In this paper, second post-Newtonian approximation of Einstein-aether theory is obtained by Chandrasekhar's approach. Five parametrized post-Newtonian parameters in first post-Newtonian approximation are presented after a time transformation and they are identical with previous works, in which {gamma}=1, {beta}=1, and two preferred-frame parameters remain. Meanwhile, in second post-Newtonian approximation, a parameter, which represents third order nonlinearity for gravity, is zero--the same as in general relativity. For an application for future deep space laser ranging missions, we reduce the metric coefficients for light propagation in a case of N point masses as a simplified model of the Solar System. The resulting light deflection angle in second post-Newtonian approximation poses another constraint on the Einstein-aether theory.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Menikoff, Ralph
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gr Ìˆuneisen EOS developed for an atomic solid, the specific heat and Gr Ìˆuneisen coefficient depend on both density and temperature.
High Energy Density Capacitors
2010-07-01
BEEST Project: Recapping is developing a capacitor that could rival the energy storage potential and price of today’s best EV batteries. When power is needed, the capacitor rapidly releases its stored energy, similar to lightning being discharged from a cloud. Capacitors are an ideal substitute for batteries if their energy storage capacity can be improved. Recapping is addressing storage capacity by experimenting with the material that separates the positive and negative electrodes of its capacitors. These separators could significantly improve the energy density of electrochemical devices.
Berkel, M. van; Hogeweij, G. M. D.; Tamura, N.; Ida, K.; Zwart, H. J.; Inagaki, S.; Baar, M. R. de
2014-11-15
In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (Ï‡), convectivity (V), and damping (Ï„) in a cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based upon the heat equation in a semi-infinite cylindrical domain. The approximations are based upon continued fractions, asymptotic expansions, and multiple harmonics. The relative error for the different derived approximations is presented for different values of frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can yield good approximations over a wide parameter space for different cases, such as no convection and damping, only damping, and both convection and damping. This paper is the second part (Part II) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part III, cylindrical approximations are treated for heat waves traveling towards the center of the plasma.
Ou, Qi; Fatehi, Shervin; Alguire, Ethan; Subotnik, Joseph E.; Shao, Yihan
2014-07-14
Working within the Tamm-Dancoff approximation, we calculate the derivative couplings between time-dependent density-functional theory excited states by assuming that the Kohn-Sham superposition of singly excited determinants represents a true electronic wavefunction. All Pulay terms are included in our derivative coupling expression. The reasonability of our approach can be established by noting that, for closely separated electronic states in the infinite basis limit, our final expression agrees exactly with the Chernyak-Mukamel expression (with transition densities from response theory). Finally, we also validate our approach empirically by analyzing the behavior of the derivative couplings around the T{sub 1}/T{sub 2} conical intersection of benzaldehyde.
Berkel, M. van; Zwart, H. J.; Tamura, N.; Ida, K.; Hogeweij, G. M. D.; Inagaki, S.; Baar, M. R. de
2014-11-15
In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (Ï‡), convectivity (V), and damping (Ï„) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of Ï‡ under the influence of V and Ï„ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate Ï‡ well in cylindrical geometry, the relationships between heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate Ï‡, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which Ï‡, V, and Ï„ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and Ï„ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and Ï„ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.
Low density microcellular foams
LeMay, J.D.
1991-11-19
Disclosed is a process of producing microcellular foam which comprises the steps of: (a) selecting a multifunctional epoxy oligomer resin; (b) mixing said epoxy resin with a non-reactive diluent to form a resin-diluent mixture; (c) forming a diluent containing cross-linked epoxy gel from said resin-diluent mixture; (d) replacing said diluent with a solvent therefore; (e) replacing said solvent with liquid carbon dioxide; and (f) vaporizing off said liquid carbon dioxide under supercritical conditions, whereby a foam having a density in the range of 35-150 mg/cc and cell diameters less than about 1 [mu]m is produced. Also disclosed are the foams produced by the process. 8 figures.
Low density microcellular foams
LeMay, James D.
1992-01-01
Disclosed is a process of producing microcellular from which comprises the steps of: (a) selecting a multifunctional epoxy oligomer resin; (b) mixing said epoxy resin with a non-reactive diluent to form a resin-diluent mixture; (c) forming a diluent containing cross-linked epoxy gel from said resin-diluent mixture; (d) replacing said diluent with a solvent therefore; (e) replacing said solvent with liquid carbon dioxide; and (f) vaporizing off said liquid carbon dioxide under supercritical conditions, whereby a foam having a density in the range of 35-150 mg/cc and cell diameters less than about 1 .mu.m is produced. Also disclosed are the foams produced by the process.
Low density microcellular foams
LeMay, James D.
1991-01-01
Disclosed is a process of producing microcellular foam which comprises the steps of: (a) selecting a multifunctional epoxy oligomer resin; (b) mixing said epoxy resin with a non-reactive diluent to form a resin-diluent mixture; (c) forming a diluent containing cross-linked epoxy gel from said resin-diluent mixture; (d) replacing said diluent with a solvent therefore; (e) replacing said solvent with liquid carbon dioxide; and (f) vaporizing off said liquid carbon dioxide under supercritical conditions, whereby a foam having a density in the range of 35-150 mg/cc and cell diameters less than about 1 .mu.m is produced. Also disclosed are the foams produced by the process.
Low density microcellular foams
Aubert, James H.; Clough, Roger L.; Curro, John G.; Quintana, Carlos A.; Russick, Edward M.; Shaw, Montgomery T.
1987-01-01
Low density, microporous polymer foams are provided by a process which comprises forming a solution of polymer and a suitable solvent followed by rapid cooling of the solution to form a phase-separated system and freeze the phase-separated system. The phase-separated system comprises a polymer phase and a solvent phase, each of which is substantially continuous within the other. The morphology of the polymer phase prior to and subsequent to freezing determine the morphology of the resultant foam. Both isotropic and anisotropic foams can be produced. If isotropic foams are produced, the polymer and solvent are tailored such that the solution spontaneously phase-separates prior to the point at which any component freezes. The morphology of the resultant polymer phase determines the morphology of the resultant foam and the morphology of the polymer phase is retained by cooling the system at a rate sufficient to freeze one or both components of the system before a change in morphology can occur. Anisotropic foams are produced by forming a solution of polymer and solvent that will not phase separate prior to freezing of one or both components of the solution. In such a process, the solvent typically freezes before phase separation occurs. The morphology of the resultant frozen two-phase system determines the morphology of the resultant foam. The process involves subjecting the solution to essentially one-dimensional cooling. Means for subjecting such a solvent to one-dimensional cooling are also provided. Foams having a density of less than 0.1 g/cc and a uniform cell size of less than 10 .mu.m and a volume such that the foams have a length greater than 1 cm are provided.
Low density microcellular foams
Aubert, J.H.; Clough, R.L.; Curro, J.G.; Quintana, C.A.; Russick, E.M.; Shaw, M.T.
1985-10-02
Low density, microporous polymer foams are provided by a process which comprises forming a solution of polymer and a suitable solvent followed by rapid cooling of the solution to form a phase-separated system and freeze the phase-separated system. The phase-separated system comprises a polymer phase and a solvent phase, each of which is substantially continuous within the other. The morphology of the polymer phase prior to and subsequent to freezing determine the morphology of the resultant foam. Both isotropic and anisotropic foams can be produced. If isotropic foams are produced, the polymer and solvent are tailored such that the solution spontaneously phase-separates prior to the point at which any component freezes. The morphology of the resultant polymer phase determines the morphology of the reusltant foam and the morphology of the polymer phase is retained by cooling the system at a rate sufficient to freeze one or both components of the system before a change in morphology can occur. Anisotropic foams are produced by forming a solution of polymer and solvent that will not phase separate prior to freezing of one or both components of the solution. In such a process, the solvent typically freezes before phase separation occurs. The morphology of the resultant frozen two-phase system determines the morphology of the resultant foam. The process involves subjecting the solution to essentially one-dimensional cooling. Foams having a density of less than 0.1 g/cc and a uniform cell size of less than 10 ..mu..m and a volume such that the foams have a length greater than 1 cm are provided.
Variational principles with Padé approximants for tearing mode analysis
Cole, Andrew J.; Finn, John M.
2014-03-15
Tearing modes occur in several distinct physical regimes, and it is often important to compute the inner layer response for these modes with various effects. There is a need for an approximate and efficient method of solving the inner layer equations in all these regimes. In this paper, we introduce a method of solving the inner layer equations based on using a variational principle with Padé approximants. For all the regimes considered, the main layer equations to be solved are inhomogeneous, and Padé approximants give a convenient and efficient method of satisfying the correct asymptotic behavior at the edge of the layer. Results using this variational principle—Padé approximant method in three of these regimes is presented. These regimes are the constant-? resistive-inertial (RI) regime, the constant-? viscoresistive regime, and the non-constant-? inviscid tearing regime. The last regime includes the constant-? RI regime and the inertial regime. The results show that reasonable accuracy can be obtained very efficiently with Padé approximants having a small number of parameters.
SHOCK EMERGENCE IN SUPERNOVAE: LIMITING CASES AND ACCURATE APPROXIMATIONS
Ro, Stephen; Matzner, Christopher D.
2013-08-10
We examine the dynamics of accelerating normal shocks in stratified planar atmospheres, providing accurate fitting formulae for the scaling index relating shock velocity to the initial density and for the post-shock acceleration factor as functions of the polytropic and adiabatic indices which parameterize the problem. In the limit of a uniform initial atmosphere, there are analytical formulae for these quantities. In the opposite limit of a very steep density gradient, the solutions match the outcome of shock acceleration in exponential atmospheres.
Fokker-Planck approximation of monoenergetic transport processes
Boergers, C.; Larsen, E.W.
1994-12-31
For transport problems with highly forward-peaked scattering, the transport equation is often approximated by the Fokker-Planck equation or, if large-angle scattering is deemed sufficiently important, by the Boltzmann-Fokker-Planck equation. In this paper, we state a simple, necessary, and sufficient condition for the validity of the simpler Fokker-Planck approximation for monoenergetic particle transport. We also show that for screened Rutherford scattering, the Fokker-Planck approximation is only marginally valid and is inaccurate unless the scattering is extremely forward peaked. (The same is true for more sophisticated models of elastic scattering of charged particles. In this paper, we restrict ourselves to screened Rutherford scattering for simplicity). More details on the results presented here will be given in forthcoming publications.
Approximate Bisimulation-Based Reduction of Power System Dynamic Models
Stankovic, AM; Dukic, SD; Saric, AT
2015-05-01
In this paper we propose approximate bisimulation relations and functions for reduction of power system dynamic models in differential- algebraic (descriptor) form. The full-size dynamic model is obtained by linearization of the nonlinear transient stability model. We generalize theoretical results on approximate bisimulation relations and bisimulation functions, originally derived for a class of constrained linear systems, to linear systems in descriptor form. An algorithm for transient stability assessment is proposed and used to determine whether the power system is able to maintain the synchronism after a large disturbance. Two benchmark power systems are used to illustrate the proposed algorithm and to evaluate the applicability of approximate bisimulation relations and bisimulation functions for reduction of the power system dynamic models.
On the approximation of crack shapes found during inservice inspection
Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S.
1997-04-01
This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component.
Trigonometric Pade approximants for functions with regularly decreasing Fourier coefficients
Labych, Yuliya A; Starovoitov, Alexander P [Gomel State University, Gomel (Belarus)
2009-08-31
Sufficient conditions describing the regular decrease of the coefficients of a Fourier series f(x)=a{sub 0}/2 + {sigma} a{sub n} cos kx are found which ensure that the trigonometric Pade approximants {pi}{sup t}{sub n,m}(x;f) converge to the function f in the uniform norm at a rate which coincides asymptotically with the highest possible one. The results obtained are applied to problems dealing with finding sharp constants for rational approximations. Bibliography: 31 titles.
Harsij, Zeynab Mirza, Behrouz
2014-12-15
A helicity entangled tripartite state is considered in which the degree of entanglement is preserved in non-inertial frames. It is shown that Quantum Entanglement remains observer independent. As another measure of quantum correlation, Quantum Discord has been investigated. It is explicitly shown that acceleration has no effect on the degree of quantum correlation for the bipartite and tripartite helicity entangled states. Geometric Quantum Discord as a Hilbert–Schmidt distance is computed for helicity entangled states. It is shown that living in non-inertial frames does not make any influence on this distance, either. In addition, the analysis has been extended beyond single mode approximation to show that acceleration does not have any impact on the quantum features in the limit beyond the single mode. As an interesting result, while the density matrix depends on the right and left Unruh modes, the Negativity as a measure of Quantum Entanglement remains constant. Also, Quantum Discord does not change beyond single mode approximation. - Highlights: • The helicity entangled states here are observer independent in non-inertial frames. • It is explicitly shown that Quantum Discord for these states is observer independent. • Geometric Quantum Discord is also not affected by acceleration increase. • Extending to beyond single mode does not change the degree of entanglement. • Beyond single mode approximation the degree of Quantum Discord is also preserved.
High Energy Density Microwaves
Phillips, R.M. [Stanford Linear Accelerator Center, Stanford, CA 94309 (United States)
1999-04-01
These proceedings represent papers presented at the RF98 Workshop entitled `High Energy Density Microwaves` held in California in October, 1998. The topics discussed were predominantly accelerator{minus}related. The Workshop dealt, for the most part, with the generation and control of electron beams, the amplification of RF signals, the design of mode converters, and the effect of very high RF field gradients. This Workshop was designed to address the concerns of the microwave tube industry worldwide, the plasma physicists who deal with very high beam currents and gigawatts of RF power, and researchers in accelerator centers around the world. Papers were presented on multibeam klystrons, gyrotron development, plasmas in microwave tubes, RF breakdown, and alternatives to conventional linear coliders at 1 TeV and above. The Workshop was partially sponsored by the US Department of Energy. There were 46 papers presented at the conference,out of which 19 have been abstracted for the Energy,Science and Technology database.(AIP)
Approximations of very weak solutions to boundary-value problems.
Berggren, Martin Olof
2003-03-01
Standard weak solutions to the Poisson problem on a bounded domain have square-integrable derivatives, which limits the admissible regularity of inhomogeneous data. The concept of solution may be further weakened in order to define solutions when data is rough, such as for inhomogeneous Dirichlet data that is only square-integrable over the boundary. Such very weak solutions satisfy a nonstandard variational form (u, v) = G(v). A Galerkin approximation combined with an approximation of the right-hand side G defines a finite-element approximation of the very weak solution. Applying conforming linear elements leads to a discrete solution equivalent to the text-book finite-element solution to the Poisson problem in which the boundary data is approximated by L{sub 2}-projections. The L{sub 2} convergence rate of the discrete solution is O(h{sub s}) for some s {element_of} (0,1/2) that depends on the shape of the domain, asserting a polygonal (two-dimensional) or polyhedral (three-dimensional) domain without slits and (only) square-integrable boundary data.
Doorway states in the random-phase approximation
De Pace, A.; Molinari, A.; WeidenmÃ¼ller, H.A.
2014-12-15
By coupling a doorway state to a sea of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically different from the standard description of doorway states in the shell model. We derive the Pastur equation in the limit of large matrix dimension and show that the results agree with those of matrix diagonalization in large spaces. The complexity of the Pastur equation does not allow for an analytical approach that would approximately describe the doorway state. Our numerical results display unexpected features: The coupling of the doorway state with states of opposite energy leads to strong mutual attraction.
Thermal effects and sudden decay approximation in the curvaton scenario
Kitajima, Naoya; Takesako, Tomohiro; Yokoyama, Shuichiro; Langlois, David; Takahashi, Tomo E-mail: langlois@apc.univ-paris7.fr E-mail: takesako@icrr.u-tokyo.ac.jp
2014-10-01
We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the total entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.
Data approximation using a blending type spline construction
Dalmo, Rune; Bratlie, Jostein
2014-11-18
Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C{sup k}-smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features. We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which are necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences.
The Monte Carlo Independent Column Approximation Model Intercomparison
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Project (McMIP) The Monte Carlo Independent Column Approximation Model Intercomparison Project (McMIP) Barker, Howard Meteorological Service of Canada Cole, Jason Meteorological Service of Canada Raisanen, Petri Finnish Meteorological Institute Pincus, Robert NOAA-CIRES Climate Diagnostics Center Morcrette, Jean-Jacques European Centre for Medium-Range Weather Forecasts Li, Jiangnan Canadian Center for Climate Modelling Stephens, Graeme Colorado State University Vaillancourt, Paul
COMPLEXITY & APPROXIMABILITY OF QUANTIFIED & STOCHASTIC CONSTRAINT SATISFACTION PROBLEMS
H. B. HUNT; M. V. MARATHE; R. E. STEARNS
2001-06-01
Let D be an arbitrary (not necessarily finite) nonempty set, let C be a finite set of constant symbols denoting arbitrary elements of D, and let S and T be an arbitrary finite set of finite-arity relations on D. We denote the problem of determining the satisfiability of finite conjunctions of relations in S applied to variables (to variables and symbols in C) by SAT(S) (by SATc(S).) Here, we study simultaneously the complexity of decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. We present simple yet general techniques to characterize simultaneously, the complexity or efficient approximability of a number of versions/variants of the problems SAT(S), Q-SAT(S), S-SAT(S),MAX-Q-SAT(S) etc., for many different such D,C,S,T. These versions/variants include decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. Our unified approach is based on the following two basic concepts: (i) strongly-local replacements/reductions and (ii) relational/algebraic representability. Some of the results extend the earlier results in [Pa85,LMP99,CF+93,CF+94] Our techniques and results reported here also provide significant steps towards obtaining dichotomy theorems, for a number of the problems above, including the problems MAX-Q-SAT(S), and MAX-S-SAT(S). The discovery of such dichotomy theorems, for unquantified formulas, has received significant recent attention in the literature [CF+93, CF+94, Cr95, KSW97]. Keywords: NP-hardness; Approximation Algorithms; PSPACE-hardness; Quantified and Stochastic Constraint Satisfaction Problems.
Crossing contours in the interacting boson approximation (IBA) symmetry triangle
McCutchan, E. A.; Casten, R. F.
2006-11-15
Constant contours of basic observables are discussed in the context of the interacting boson approximation (IBA) symmetry triangle. Contours that exhibit orthogonal crossing within the triangle are presented as a method for determining a set of parameter values for a particular nucleus and trajectories for isotopic chains. A set of contours that highlights a class of nuclei that are outside the two-parameter IBA-1 Hamitonian space is also presented.
Erba, A. Dovesi, R.; Shahrokhi, M.; Moradian, R.
2015-01-28
Harmonic and quasi-harmonic thermal properties of two isostructural simple oxides (periclase, MgO, and lime, CaO) are computed with ab initio periodic simulations based on the density-functional-theory (DFT). The more polarizable character of calcium with respect to magnesium cations is found to dramatically affect the validity domain of the quasi-harmonic approximation that, for thermal structural properties (such as temperature dependence of volume, V(T), bulk modulus, K(T), and thermal expansion coefficient, Î±(T)), reduces from [0 K-1000 K] for MgO to just [0 K-100 K] for CaO. On the contrary, thermodynamic properties (such as entropy, S(T), and constant-volume specific heat, C{sub V}(T)) are described reliably at least up to 2000 K and quasi-harmonic constant-pressure specific heat, C{sub P}(T), up to about 1000 K in both cases. The effect of the adopted approximation to the exchange-correlation functional of the DFT is here explicitly investigated by considering five different expressions of three different classes (local-density approximation, generalized-gradient approximation, and hybrids). Computed harmonic thermodynamic properties are found to be almost independent of the adopted functional, whereas quasi-harmonic structural properties are more affected by the choice of the functional, with differences that increase as the system becomes softer.
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COMPLEXITY&APPROXIMABILITY OF QUANTIFIED&STOCHASTIC CONSTRAINT SATISFACTION PROBLEMS
Hunt, H. B.; Marathe, M. V.; Stearns, R. E.
2001-01-01
Let D be an arbitrary (not necessarily finite) nonempty set, let C be a finite set of constant symbols denoting arbitrary elements of D, and let S and T be an arbitrary finite set of finite-arity relations on D. We denote the problem of determining the satisfiability of finite conjunctions of relations in S applied to variables (to variables and symbols in C) by SAT(S) (by SATc(S).) Here, we study simultaneously the complexity of decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. We present simple yet general techniques to characterize simultaneously, the complexity or efficient approximability of a number of versions/variants of the problems SAT(S), Q-SAT(S), S-SAT(S),MAX-Q-SAT(S) etc., for many different such D,C ,S, T. These versions/variants include decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. Our unified approach is based on the following two basic concepts: (i) strongly-local replacements/reductions and (ii) relational/algebraic represent ability. Some of the results extend the earlier results in [Pa85,LMP99,CF+93,CF+94O]u r techniques and results reported here also provide significant steps towards obtaining dichotomy theorems, for a number of the problems above, including the problems MAX-&-SAT( S), and MAX-S-SAT(S). The discovery of such dichotomy theorems, for unquantified formulas, has received significant recent attention in the literature [CF+93,CF+94,Cr95,KSW97
Compton scattering from positronium and validity of the impulse approximation
Kaliman, Z.; Pisk, K.; Pratt, R. H.
2011-05-15
The cross sections for Compton scattering from positronium are calculated in the range from 1 to 100 keV incident photon energy. The calculations are based on the A{sup 2} term of the photon-electron or photon-positron interaction. Unlike in hydrogen, the scattering occurs from two centers and the interference effect plays an important role for energies below 8 keV. Because of the interference, the criterion for validity of the impulse approximation for positronium is more restrictive compared to that for hydrogen.
Multigroup Free-atom Doppler-broadening Approximation. Experiment
Gray, Mark Girard
2015-11-06
The multigroup energy Doppler-broadening approximation agrees with continuous energy Dopplerbroadening generally to within ten percent for the total cross sections of ^{1}H,^{ 56}Fe, and ^{235}U at 250 lanl. Although this is probably not good enough for broadening from room temperature through the entire temperature range in production use, it is better than any interpolation scheme between temperatures proposed to date, and may be good enough for extrapolation from high temperatures. The method deserves further study since additional improvements are possible.
EMERGENCE OF THE KENNICUTT-SCHMIDT RELATION FROM THE SMALL-SCALE SFR-DENSITY RELATION
Gnedin, Nickolay Y.; Tasker, Elizabeth J.; Fujimoto, Yusuke
2014-05-20
We use simulations of isolated galaxies with a few parsec resolution to explore the connection between the small-scale star formation rate (SFR)-gas density relation and the induced large-scale correlation between the SFR surface density and the surface density of the molecular gas (the Kennicutt-Schmidt relation). We find that, in the simulations, a power-law small-scale ''star formation law'' directly translates into an identical power-law Kennicutt-Schmidt relation. If this conclusion holds in the reality as well, it implies that the observed approximately linear Kennicutt-Schmidt relation must reflect the approximately linear small-scale ''star formation law''.
Improved association in a classical density functional theory for water
Krebs, Eric J.; Schulte, Jeff B.; Roundy, David
2014-03-28
We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment.
Neutrinoless double-beta decay in covariant density functional theory
Ring, P.; Yao, J. M.; Song, L. S.; Hagino, K.; Meng, J.
2015-10-15
We use covariant density functional theory beyond mean field in order to describe neutrinoless double-beta decay in a fully relativistic way. The dynamic effects of particle-number and angular-momentum conservations as well as shape fluctuations of quadrupole character are taken into account within the generator coordinate method for both initial and final nuclei. The calculations are based on the full relativistic transition operator. The nuclear matrix elements (NMEâ€™s) for a large number of possible transitions are investigated. The results are compared with various non-relativistic calculations, in particular also with the density functional theory based on the Gogny force. We find that the non-relativistic approximation is justified and that the total NMEâ€™s can be well approximated by the pure axial-vector coupling term. This corresponds to a considerable reduction of the computational effort.
Nikiforov, Alexander; Gamez, Jose A.; Thiel, Walter; Huix-Rotllant, Miquel; Filatov, Michael
2014-09-28
Quantum-chemical computational methods are benchmarked for their ability to describe conical intersections in a series of organic molecules and models of biological chromophores. Reference results for the geometries, relative energies, and branching planes of conical intersections are obtained using ab initio multireference configuration interaction with single and double excitations (MRCISD). They are compared with the results from more approximate methods, namely, the state-interaction state-averaged restricted ensemble-referenced Kohn-Sham method, spin-flip time-dependent density functional theory, and a semiempirical MRCISD approach using an orthogonalization-corrected model. It is demonstrated that these approximate methods reproduce the ab initio reference data very well, with root-mean-square deviations in the optimized geometries of the order of 0.1 Å or less and with reasonable agreement in the computed relative energies. A detailed analysis of the branching plane vectors shows that all currently applied methods yield similar nuclear displacements for escaping the strong non-adiabatic coupling region near the conical intersections. Our comparisons support the use of the tested quantum-chemical methods for modeling the photochemistry of large organic and biological systems.
A multiscale two-point flux-approximation method
Møyner, Olav Lie, Knut-Andreas
2014-10-15
A large number of multiscale finite-volume methods have been developed over the past decade to compute conservative approximations to multiphase flow problems in heterogeneous porous media. In particular, several iterative and algebraic multiscale frameworks that seek to reduce the fine-scale residual towards machine precision have been presented. Common for all such methods is that they rely on a compatible primal–dual coarse partition, which makes it challenging to extend them to stratigraphic and unstructured grids. Herein, we propose a general idea for how one can formulate multiscale finite-volume methods using only a primal coarse partition. To this end, we use two key ingredients that are computed numerically: (i) elementary functions that correspond to flow solutions used in transmissibility upscaling, and (ii) partition-of-unity functions used to combine elementary functions into basis functions. We exemplify the idea by deriving a multiscale two-point flux-approximation (MsTPFA) method, which is robust with regards to strong heterogeneities in the permeability field and can easily handle general grids with unstructured fine- and coarse-scale connections. The method can easily be adapted to arbitrary levels of coarsening, and can be used both as a standalone solver and as a preconditioner. Several numerical experiments are presented to demonstrate that the MsTPFA method can be used to solve elliptic pressure problems on a wide variety of geological models in a robust and efficient manner.
Attractor comparisons based on density
Carroll, T. L.
2015-01-15
Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling.
Approximate Weighted Matching On Emerging Manycore and Multithreaded Architectures
Halappanavar, Mahantesh; Feo, John T.; Villa, Oreste; Tumeo, Antonino; Pothen, Alex
2012-11-30
Graph matching is a prototypical combinatorial problem with many applications in computer science and scientific computing, but algorithms for computing optimal matchings are challenging to parallelize. Approximate matching algorithms provide an alternate route for parallelization, and in many contexts compute near-optimal matchings for large-scale graphs. We present sharedmemory parallel implementations for computing half-approximate weighted matching on state-of-the-art multicore (Intel Nehalem and AMD Magny-Cours), manycore (Nvidia Tesla and Nvidia Fermi) and massively multithreaded (Cray XMT) platforms. We provide two implementations: the first implementation uses shared work queues, and is suited to all these platforms; the second implementation is based on dataflow principles, and exploits the architectural features of the Cray XMT. Using a carefully chosen dataset that exhibits characteristics from a wide range of real-world applications, we show scalable performance across different platforms. In particular, for one instance of the input, an R-MAT graph (RMAT-G), we show speedups of: about 32 on 48 cores of an AMD Magny-Cours; 7 on 8 cores of Intel Nehalem; 3 on Nvidia Tesla and 10 on Nvidia Fermi relative to one core of Intel Nehalem; and 60 on 128 processors of Cray XMT. We demonstrate good weak and strong scaling for graphs with up to a billion edges using up to 12, 800 threads. Given the breadth of this work, we focus on simplicity and portability of software rather than excessive fine-tuning for each platform. To the best of our knowledge, this is the first such large-scale study of the half-approximate weighted matching problem on shared-memory platforms. Driven by the critical enabling role of combinatorial algorithms such as matching in scientific computing and the emergence of informatics applications, there is a growing demand to support irregular computations on current and future computing platforms. In this context, we evaluate the capability
Low density carbonized composite foams
Kong, Fung-Ming
1993-01-01
A carbonized composite foam having a density less than about 50 mg/cm.sup.3 and individual cell sizes no greater than about 1 .mu.m in diameter is described, and the process of making it.
Low density carbonized composite foams
Kong, Fung-Ming
1991-01-01
A carbonized composite foam having a density less than about 50 mg/cm.sup.3 and individual cell sizes no greater than about 1 .mu.m in diameter is described, and the process of making it.
Bonatsos, Dennis; Karampagia, S.; Casten, R. F.
2011-05-15
Using a contraction of the SU(3) algebra to the algebra of the rigid rotator in the large-boson-number limit of the interacting boson approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first-order shape/phase transition separating the spherical and prolate deformed phases, and it lies within the Alhassid-Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices in the midst of chaotic regions. In addition to providing an explanation for the existence of the arc of regularity, the present line represents an example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state and its rotational band become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.
Above-threshold ionization beyond the dipole approximation
Klaiber, Michael; Hatsagortsyan, Karen Z.; Keitel, Christoph H.
2005-03-01
A generalization of the analytical theory of above-threshold ionization in the single active electron approximation is developed while taking into account leading non-dipole and relativistic corrections in the starting Hamiltonian. Special interest is placed on the high energy part of the photoelectron spectrum which consists of a plateau and a characteristic cutoff. It is shown that the correction due to the magnetic component of the laser field gives rise to a decrease of the plateau height, an increase of the maximal cutoff energy, and a drift of the emitted electrons in propagation direction of the laser field. Furthermore, the influence of the relativistic mass shift may become non-neglible by reducing the cutoff energy significantly. Spin effects or the Zitterbewegung play a comparably minor role in the investigated parameter regime of suboptical frequencies and high but not ultra-high laser intensities.
Surface wake in the random-phase approximation
Garcia de Abajo, F.J. ); Echenique, P.M. )
1993-11-01
The scalar-electric-potential distribution set up by an ion traveling in the vicinity of a plane solid-vacuum interface, that is, the surface-wake potential, is investigated with the specular-reflection model to describe the response of the surface and with the random-phase approximation for the dielectric function of the bulk material. This permits us to address the study of the low-velocity surface wake: the static potential is found to have a dip at the position of the ion; that dip is shifted towards the direction opposite to the velocity vector for velocities smaller than the threshold of creation of plasmons ([approx]1.3[ital v][sub [ital F
Mixed series in ultraspherical polynomials and their approximation properties
Sharapudinov, I I
2003-04-30
New (mixed) series in ultraspherical polynomials P{sub n}{sup {alpha}}{sup ,{alpha}}(x) are introduced. The basic difference between a mixed series in the polynomials P{sub n}{sup {alpha}}{sup ,{alpha}}(x) and a Fourier series in the same polynomials is as follows: a mixed series contains terms of the form (2{sup r}f{sub r,k}{sup {alpha}})/(k+2{alpha}){sup [r]}) P{sub k+r}{sup {alpha}}{sup -r,{alpha}}{sup -r}(x), where 1{<=}r is an integer and f{sub r,k}{sup {alpha}} is the kth Fourier coefficient of the derivative f{sup (r)}(x) with respect to the ultraspherical polynomials P{sub k}{sup {alpha}}{sup ,{alpha}}(x). It is shown that the partial sums Y{sub n+2r}{sup {alpha}}(f,x) of a mixed series in the polynomial P{sub k}{sup {alpha}}{sup ,{alpha}}(x) contrast favourably with Fourier sums S{sub n}{sup {alpha}}(f,x) in the same polynomials as regards their approximation properties in classes of differentiable and analytic functions, and also in classes of functions of variable smoothness. In particular, the Y{sub n+2r}{sup {alpha}}(f,x) can be used for the simultaneous approximation of a function f(x) and its derivatives of orders up to (r- 1), whereas the S{sub n}{sup {alpha}}(f,x) are not suitable for this purpose.
Low density metal hydride foams
Maienschein, Jon L.; Barry, Patrick E.
1991-01-01
Disclosed is a low density foam having a porosity of from 0 to 98% and a density less than about 0.67 gm/cc, prepared by heating a mixture of powered lithium hydride and beryllium hydride in an inert atmosphere at a temperature ranging from about 455 to about 490 K for a period of time sufficient to cause foaming of said mixture, and cooling the foam thus produced. Also disclosed is the process of making the foam.
Characterization of the homogeneous tissue mixture approximation in breast imaging dosimetry
Sechopoulos, Ioannis; Bliznakova, Kristina; Qin Xulei; Fei Baowei; Feng, Steve Si Jia
2012-08-15
Purpose: To compare the estimate of normalized glandular dose in mammography and breast CT imaging obtained using the actual glandular tissue distribution in the breast to that obtained using the homogeneous tissue mixture approximation. Methods: Twenty volumetric images of patient breasts were acquired with a dedicated breast CT prototype system and the voxels in the breast CT images were automatically classified into skin, adipose, and glandular tissue. The breasts in the classified images underwent simulated mechanical compression to mimic the conditions present during mammographic acquisition. The compressed thickness for each breast was set to that achieved during each patient's last screening cranio-caudal (CC) acquisition. The volumetric glandular density of each breast was computed using both the compressed and uncompressed classified images, and additional images were created in which all voxels representing adipose and glandular tissue were replaced by a homogeneous mixture of these two tissues in a proportion corresponding to each breast's volumetric glandular density. All four breast images (compressed and uncompressed; heterogeneous and homogeneous tissue) were input into Monte Carlo simulations to estimate the normalized glandular dose during mammography (compressed breasts) and dedicated breast CT (uncompressed breasts). For the mammography simulations the x-ray spectra used was that used during each patient's last screening CC acquisition. For the breast CT simulations, two x-ray spectra were used, corresponding to the x-ray spectra with the lowest and highest energies currently being used in dedicated breast CT prototype systems under clinical investigation. The resulting normalized glandular dose for the heterogeneous and homogeneous versions of each breast for each modality was compared. Results: For mammography, the normalized glandular dose based on the homogeneous tissue approximation was, on average, 27% higher than that estimated using the
High Density Sensor Network Development | The Ames Laboratory
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High Density Sensor Network Development
Communication: Self-interaction correction with unitary invariance in density functional theory
Pederson, Mark R.; Ruzsinszky, Adrienn; Perdew, John P.; Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122
2014-03-28
Standard spin-density functionals for the exchange-correlation energy of a many-electron ground state make serious self-interaction errors which can be corrected by the Perdew-Zunger self-interaction correction (SIC). We propose a size-extensive construction of SIC orbitals which, unlike earlier constructions, makes SIC computationally efficient, and a true spin-density functional. The SIC orbitals are constructed from a unitary transformation that is explicitly dependent on the non-interacting one-particle density matrix. When this SIC is applied to the local spin-density approximation, improvements are found for the atomization energies of molecules.
High-density fluid compositions
Sanders, D.C.
1981-09-29
Clear, high-density fluids suitable for use as well completion, packing, and perforation media comprise aqueous solutions of zinc bromide and calcium bromide having densities lying in the range of about 14.5 up to about 18.0 pounds per gallon and measured PH's lying in the range of about 3.5 up to about 6.0. Optionally, such fluids may also comprise calcium chloride and/or a soluble film-forming amine-based corrosion inhibitor. Such fluids under conditions of ordinary use exhibit low corrosion rates and have crystallization points lying well below the range of temperatures under which they are used.
Markov Jump Processes Approximating a Non-Symmetric Generalized Diffusion
Limic, Nedzad
2011-08-15
Consider a non-symmetric generalized diffusion X( Dot-Operator ) in Double-Struck-Capital-R {sup d} determined by the differential operator A(x) = -{Sigma}{sub ij} {partial_derivative}{sub i}a{sub ij}(x){partial_derivative}{sub j} + {Sigma}{sub i} b{sub i}(x){partial_derivative}{sub i}. In this paper the diffusion process is approximated by Markov jump processes X{sub n}( Dot-Operator ), in homogeneous and isotropic grids G{sub n} Subset-Of Double-Struck-Capital-R {sup d}, which converge in distribution in the Skorokhod space D([0,{infinity}), Double-Struck-Capital-R {sup d}) to the diffusion X( Dot-Operator ). The generators of X{sub n}( Dot-Operator ) are constructed explicitly. Due to the homogeneity and isotropy of grids, the proposed method for d{>=}3 can be applied to processes for which the diffusion tensor {l_brace}a{sub ij}(x){r_brace}{sub 11}{sup dd} fulfills an additional condition. The proposed construction offers a simple method for simulation of sample paths of non-symmetric generalized diffusion. Simulations are carried out in terms of jump processes X{sub n}( Dot-Operator ). For piece-wise constant functions a{sub ij} on Double-Struck-Capital-R {sup d} and piece-wise continuous functions a{sub ij} on Double-Struck-Capital-R {sup 2} the construction and principal algorithm are described enabling an easy implementation into a computer code.
Plasma digital density determining device
Sprott, Julien C.; Lovell, Thomas W.; Holly, Donald J.
1976-01-01
The density of a decaying plasma in an electrically conducting enclosure is determined by applying an excitation to the cavity formed by the enclosure and counting digitally the number of resonant frequencies traversed by the combination of the cavity and the decaying plasma.
High energy density thermal cell
Fletcher, A.N.
1980-04-29
A thermal battery is described that uses a calcium anode and a catholyte consisting of a mixture of lithium, potassium, nitrate and chloride ions. The device is operable over a temperature range of about 150 to 600/sup 0/C and produces a long lasting, high energy density output.
Statistical density modification using local pattern matching
Terwilliger, Thomas C.
2007-01-23
A computer implemented method modifies an experimental electron density map. A set of selected known experimental and model electron density maps is provided and standard templates of electron density are created from the selected experimental and model electron density maps by clustering and averaging values of electron density in a spherical region about each point in a grid that defines each selected known experimental and model electron density maps. Histograms are also created from the selected experimental and model electron density maps that relate the value of electron density at the center of each of the spherical regions to a correlation coefficient of a density surrounding each corresponding grid point in each one of the standard templates. The standard templates and the histograms are applied to grid points on the experimental electron density map to form new estimates of electron density at each grid point in the experimental electron density map.
ARM - Lesson Plans: Air Density and Temperature
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Teachers' Toolbox Lesson Plans Lesson Plans: Air Density and Temperature Objective The objective of this activity is to investigate the effect of temperature on the density of air. ...
Building a Universal Nuclear Energy Density Functional
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Building a Universal Nuclear Energy Density Functional Building a Universal Nuclear Energy Density Functional VaryMatrix.png Collaboration with mathematicians and computational...
Hollman, David S.; Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061 ; Schaefer, Henry F.; Valeev, Edward F.
2014-02-14
A local density fitting scheme is considered in which atomic orbital (AO) products are approximated using only auxiliary AOs located on one of the nuclei in that product. The possibility of variational collapse to an unphysical â€œattractive electronâ€ state that can affect such density fitting [P. Merlot, T. KjÃ¦rgaard, T. Helgaker, R. Lindh, F. Aquilante, S. Reine, and T. B. Pedersen, J. Comput. Chem. 34, 1486 (2013)] is alleviated by including atom-wise semidiagonal integrals exactly. Our approach leads to a significant decrease in the computational cost of density fitting for Hartreeâ€“Fock theory while still producing results with errors 2â€“5 times smaller than standard, nonlocal density fitting. Our method allows for large Hartreeâ€“Fock and density functional theory computations with exact exchange to be carried out efficiently on large molecules, which we demonstrate by benchmarking our method on 200 of the most widely used prescription drug molecules. Our new fitting scheme leads to smooth and artifact-free potential energy surfaces and the possibility of relatively simple analytic gradients.
Upgrading of biorenewables to high energy density fuels
Gordon, John C; Batista, Enrique R; Chen, Weizhong; Currier, Robert P; Dirmyer, Matthew R; John, Kevin D; Kim, Jin K; Keith, Jason; Martin, Richard L; Pierpont, Aaron W; Silks Ill, L. A. "" Pete; Smythe, Mathan C; Sutton, Andrew D; Taw, Felicia L; Trovitch, Ryan J; Vasudevan, Kalyan V; Waidmann, Christopher R; Wu, Ruilian; Baker, R. Thomas; Schlaf, Marcel
2010-12-07
According to a recent report, lignocellulose is the most abundant renewable biological resource on earth, with an annual production of {approx} 200 x 10{sup 9} tons. Conversion of lignocellulosics derived from wood, agricultural wastes, and woody grasses into liquid fuels and value-added chemical feedstocks is an active area of research that has seen an explosion of effort due to the need to replace petroleum based sources. The carbohydrates D-glucose (C{sub 6}), L-arabinose (C{sub 5}), and D-xylose (C{sub 5}) are readily obtained from the hydrolysis of lignocellulose and constitute the most abundant renewable organic carbon source on the planet. Because they are naturally produced on such a large scale, these sugars have the greatest potential to displace petrochemical derived transportation fuel. Recent efforts in our laboratories aimed towards the production of high energy density transportation fuels from carbohydrates have been structured around the parameters of selective carbohydrate carbon chain extension chemistries, low reaction temperatures, and the desired use of water or neat substrate as the solvent. Some of our efforts in this regard will be presented.
Density variations and anomalies in palladium compacts
Back, D.; Jones, T.; Ransick, M.; Walburg, T.; Werkmeister, D.
1992-05-14
Low-density compacts of palladium powder have relative densities of about 30{plus minus}10% TD. The variations in density are of concern for operations such as chemical/hydrogen pump systems because heat, mass, and momentum transport properties can be affected. Variations in density result from the inherent nature and interacting forces of UASA compaction of powder in cylinders. In addition to these expected variations, discontinuous density anomalies, such as cracks or high density ridges, are also found. An anomaly of particular concern was found to resemble a steer's head.'' it is a symmetrical region of low density located at or near the center of a compact. Typically, this region is surrounded by a band of high density, compacted palladium that sometimes exceeds the density of the surrounding compact matrix by a factor of three. This report examines these density variations and anomalies both theoretically and empirically.
Density variations and anomalies in palladium compacts
Back, D.; Jones, T.; Ransick, M.; Walburg, T.; Werkmeister, D.
1992-05-14
Low-density compacts of palladium powder have relative densities of about 30{plus_minus}10% TD. The variations in density are of concern for operations such as chemical/hydrogen pump systems because heat, mass, and momentum transport properties can be affected. Variations in density result from the inherent nature and interacting forces of UASA compaction of powder in cylinders. In addition to these expected variations, discontinuous density anomalies, such as cracks or high density ridges, are also found. An anomaly of particular concern was found to resemble a ``steer`s head.`` it is a symmetrical region of low density located at or near the center of a compact. Typically, this region is surrounded by a band of high density, compacted palladium that sometimes exceeds the density of the surrounding compact matrix by a factor of three. This report examines these density variations and anomalies both theoretically and empirically.
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (â‰ˆ16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
Probability distribution of the vacuum energy density
Duplancic, Goran; Stefancic, Hrvoje; Glavan, Drazen
2010-12-15
As the vacuum state of a quantum field is not an eigenstate of the Hamiltonian density, the vacuum energy density can be represented as a random variable. We present an analytical calculation of the probability distribution of the vacuum energy density for real and complex massless scalar fields in Minkowski space. The obtained probability distributions are broad and the vacuum expectation value of the Hamiltonian density is not fully representative of the vacuum energy density.
Marshall, J. Jr.
1961-10-24
A reactor is described in which natural-uranium bodies are located in parallel channels which extend through the graphite mass in a regular lattice. The graphite mass has additional channels that are out of the lattice and contain no uranium. These additional channels decrease in number per unit volume of graphite from the center of the reactor to the exterior and have the effect of reducing the density of the graphite more at the center than at the exterior, thereby spreading neutron activity throughout the reactor. (AEC)
Lykissa, Iliana; Li, Shu-Yi; Granqvist, Claes G.; Niklasson, Gunnar A.; Ramzan, Muhammad; Chakraborty, Sudip; Ahuja, Rajeev
2014-05-14
Thin films of V{sub 2}O{sub 5} were prepared by sputter deposition onto transparent and electrically conducting substrates and were found to be X-ray amorphous. Their electrochemical density of states was determined by chronopotentiometry and displayed a pronounced low-energy peak followed by an almost featureless contribution at higher energies. These results were compared with density functional theory calculations for amorphous V{sub 2}O{sub 5}. Significant similarities were found between measured data and computations; specifically, the experimental low-energy peak corresponds to a split-off part of the conduction band apparent in the computations. Furthermore, the calculations approximately reproduce the experimental band gap observed in optical measurements.
Investigation of physical processes limiting plasma density in H-mode on DIII-D
Maingi, R.; Mahdavi, M.A.; Jernigan, T.C.
1996-12-01
A series of experiments was conducted on the DIII-D tokamak to investigate the physical processes which limit density in high confinement mode (H-mode) discharges. The typical H-mode to low confinement mode (L-mode) transition limit at high density near the empirical Greenwald density limit was avoided by divertor pumping, which reduced divertor neutral pressure and prevented formation of a high density, intense radiation zone (MARFE) near the X-point. It was determined that the density decay time after pellet injection was independent of density relative to the Greenwald limit and increased non-linearly with the plasma current. Magnetohydrodynamic (MHD) activity in pellet-fueled plasmas was observed at all power levels, and often caused unacceptable confinement degradation, except when the neutral beam injected (NBI) power was {le} 3 MW. Formation of MARFEs on closed field lines was avoided with low safety factor (q) operation but was observed at high q, qualitatively consistent with theory. By using pellet fueling and optimizing discharge parameters to avoid each of these limits, an operational space was accessed in which density {approximately} 1.5 {times} Greenwald limit was achieved for 600 ms, and good H-mode confinement was maintained for 300 ms of the density flattop. More significantly, the density was successfully increased to the limit where a central radiative collapse was observed, the most fundamental density limit in tokamaks.
Progress at the interface of wave-function and density-functional theories
Gidopoulos, Nikitas I.
2011-04-15
The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schroedinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly - thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.
Xi Yanbin; Liu Yue [MOE Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams, School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)
2012-07-15
Considering different typical electron density profiles, a multi slab approximation model is built up to study the power absorption of broadband (0.75-30 GHz) electromagnetic waves in a partially ionized nonuniform magnetized plasma layer. Based on the model, the power absorption spectra for six cases are numerically calculated and analyzed. It is shown that the absorption strongly depends on the electron density fluctuant profile, the background electron number density, and the collision frequency. A potential optimum profile is also analyzed and studied with some particular parameters.
Weck, Philippe F.; Kim, Eunja
2015-06-11
The structure, lattice dynamics and thermodynamic properties of bulk technetium were investigated within the framework of density functional theory. The phonon density of states spectrum computed with density functional perturbation theory closely matches inelastic coherent neutron scattering measurements. The thermal properties of technetium were derived from phonon frequencies calculated within the quasi-harmonic approximation (QHA), which introduces a volume dependence of phonon frequencies as a part of the anharmonic effect. As a result, the predicted thermal expansion and isobaric heat capacity of technetium are in excellent agreement with available experimental data for temperatures up to ~1600 K.
Gambacurta, D.; Catara, F.
2011-09-15
Low-energy dipole excitations are analyzed for the stable isotopes {sup 40}Ca and {sup 48}Ca in the framework of the Skyrme-second random-phase approximation. The corresponding random-phase approximation calculations provide a negligible strength distribution for both nuclei in the energy region from 5 to 10 MeV. The inclusion and the coupling of 2 particle-2 hole configurations in the second random-phase approximation lead to an appreciable dipole response at low energies for the neutron-rich nucleus {sup 48}Ca. The presence of a neutron skin in the nucleus {sup 48}Ca would suggest the interpretation of the low-lying response in terms of a pygmy excitation. The composition of the excitation modes (content of 1 particle-1 hole and 2 particle-2 hole configurations), their transition densities and their collectivity (number and coherence of the different contributions) are analyzed. This analysis indicates that, in general, these excitations cannot be clearly interpreted in terms of oscillations of the neutron skin against the core with the exception of the peak with the largest B(E1) value, which is located at 9.09 MeV. For this peak the neutron transition density dominates and the neutron and proton transition densities oscillate out of phase in the internal part of the nucleus leading to a strong mixing of isoscalar and isovector components. Therefore, this state shows some features usually associated to pygmy resonances.
New Lessons Learned: Peer Exchange Call "Greatest Hits" Out Now...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
Effective marketing of multifamily upgrades depends on whether the decision maker is a tenant or building owner. Tenants are more concerned with issues, such as reduced noise, ...
Peer Exchange Calls Inspire New Lessons Learned Greatest Hits
Broader source: Energy.gov [DOE]
A new â€œLessons Learned: Peer Exchange Callsâ€ resource summarizes top takeaways shared by Better Buildings Residential Network members, from tips to collaborating with utilities to cost-effective...
Question of the Week: What are Your Greatest Energy Concerns...
Broader source: Energy.gov (indexed) [DOE]
... As an alternative to defrey the cost we purchased a pellet stove now we are watching the price of pellets. Our old farm house gets plastic on the windos every winter and a major ...
Peer Exchange Calls Inspire New Lessons Learned Greatest Hits...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
To make collaboration with a utility easier, show how energy efficiency can solve a financial, public relations, or customer service problem for the utility. Point-based systems ...
What the World's GREATEST Energy Managers Do Differently | Department...
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
10, 2012) (2.36 MB) More Documents & Publications Energy Management and Financing Unveiling the Implementation Guide Communicating Success, Measuring Improvements, Sharing Results
Oxides having high energy densities
Ceder, Gerbrand; Kang, Kisuk
2013-09-10
Certain disclosed embodiments generally relate to oxide materials having relatively high energy and/or power densities. Various aspects of the embodiments are directed to oxide materials having a structure B.sub.i(M.sub.jY.sub.k)O.sub.2, for example, a structure Li.sub.j(Ni.sub.jY.sub.k)O.sub.2 such as Li(Ni.sub.0.5Mn.sub.0.5)O.sub.2. In this structure, Y represents one or more atoms, each independently selected from the group consisting of alkaline earth metals, transition metals, Group 14 elements, Group 15, or Group 16 elements. In some embodiments, such an oxide material may have an O3 crystal structure, and/or a layered structure such that the oxide comprises a plurality of first, repeating atomic planes comprising Li, and a plurality of second, repeating atomic planes comprising Ni and/or Y.
Marushka, Viktor; Zabeida, Oleg Martinu, Ludvik
2014-11-01
The uniformity of ion density is critical for applications relying on the ion assisted deposition technique for the fabrication of the high quality thin films. The authors propose and describe here a method allowing one to calculate the ion density distribution on spherical substrate holders under stationary and rotating conditions for different positions of the ion source. The ion beam shape was approximated by a cos{sup n} function, and the ion current density was represented by a function inversely proportional to the distance from the ion source in accordance with our experimental results. As an example, a calculation of the current density distribution on the spherical cap substrate was performed for a broad beam ion source operated with an anode current of 3?A. The authors propose an approach for process optimization with respect to the ion source position and its inclination, in terms of uniformity and absolute value of the ion current density.
Vazquez-Mayagoitia, Alvaro; Sherrill, David; Apra, Edoardo; Sumpter, Bobby G
2010-01-01
A recently proposed double-hybrid functional called XYG3 and a semilocal GGA functional (B97-D) with a semiempirical correction for van der Waals interactions have been applied to study the potential energy curves along the dissociation coordinates of weakly bound pairs of molecules governed by London dispersion and induced dipole forces. Molecules treated in this work were the parallel sandwich, T-shaped, and parallel-displaced benzene dimer, (C6H6)2; hydrogen sulfide and benzene, H2S C6H6; methane and benzene, CH4 C6H6; the methane dimer, (CH4)2; and the pyridine dimer, (C5H5N)2. We compared the potential energy curves of these functionals with previously published benchmarks at the coupled cluster singles, doubles, and perturbative triplets [CCSD(T)] complete-basis-set limit. Both functionals, XYG3 and B97-D, exhibited very good performance, reproducing accurate energies for equilibrium distances and a smooth behavior along the dissociation coordinate. Overall, we found an agreement within a few tenths of one kcal mol-1 with the CCSD(T) results across the potential energy curves.
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space, get 33%-50% power savings Implemented These Ideas in Crayon System Crayon Software Architecture Cairo is a standard, widely-used graphics API Firefox, Graphviz, Poppler, ......
Ensemble density variational methods with self- and ghost-interaction-corrected functionals
Pastorczak, Ewa; Pernal, Katarzyna
2014-05-14
Ensemble density functional theory (DFT) offers a way of predicting excited-states energies of atomic and molecular systems without referring to a density response function. Despite a significant theoretical work, practical applications of the proposed approximations have been scarce and they do not allow for a fair judgement of the potential usefulness of ensemble DFT with available functionals. In the paper, we investigate two forms of ensemble density functionals formulated within ensemble DFT framework: the Gross, Oliveira, and Kohn (GOK) functional proposed by Gross et al. [Phys. Rev. A 37, 2809 (1988)] alongside the orbital-dependent eDFT form of the functional introduced by Nagy [J. Phys. B 34, 2363 (2001)] (the acronym eDFT proposed in analogy to eHF – ensemble Hartree-Fock method). Local and semi-local ground-state density functionals are employed in both approaches. Approximate ensemble density functionals contain not only spurious self-interaction but also the so-called ghost-interaction which has no counterpart in the ground-state DFT. We propose how to correct the GOK functional for both kinds of interactions in approximations that go beyond the exact-exchange functional. Numerical applications lead to a conclusion that functionals free of the ghost-interaction by construction, i.e., eDFT, yield much more reliable results than approximate self- and ghost-interaction-corrected GOK functional. Additionally, local density functional corrected for self-interaction employed in the eDFT framework yields excitations energies of the accuracy comparable to that of the uncorrected semi-local eDFT functional.
Snow Depth and Density at End-of-Winter for NGEE Areas A, B, C and D, Barrow, Alaska, 2012-2014
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Anna Liljedahl; Cathy Wilson
2016-02-02
End-of-winter snow depth and average snow density from area A, B, C and D, which include 1000's of point depth measurement located between approximately 20 and 50 cm apart.
Aerodynamic Focusing Of High-Density Aerosols
Ruiz, D. E.; Fisch, Nathaniel
2014-02-24
High-density micron-sized particle aerosols might form the basis for a number of applications in which a material target with a particular shape might be quickly ionized to form a cylindrical or sheet shaped plasma. A simple experimental device was built in order to study the properties of high-density aerosol focusing for 1#22; m silica spheres. Preliminary results recover previous findings on aerodynamic focusing at low densities. At higher densities, it is demonstrated that the focusing properties change in a way which is consistent with a density dependent Stokes number.
The transition to the metallic state in low density hydrogen
McMinis, Jeremy; Morales, Miguel A.; Ceperley, David M.; Kim, Jeongnim
2015-11-18
Solid atomic hydrogen is one of the simplest systems to undergo a metal-insulator transition. Near the transition, the electronic degrees of freedom become strongly correlated and their description provides a difficult challenge for theoretical methods. As a result, the order and density of the phase transition are still subject to debate. In this work we use diffusion quantum Monte Carlo to benchmark the transition between the paramagnetic and anti-ferromagnetic phases of ground state body centered cubic atomic hydrogen. We locate the density of the transition by computing the equation of state for these two phases and identify the phase transition order by computing the band gap near the phase transition. These benchmark results show that the phase transition is continuous and occurs at a Wigner-Seitz radius of r_{s} = 2.27(3)a_{0}. As a result, we compare our results to previously reported density functional theory, Hedin s GW approximation, and dynamical mean field theory results.
The transition to the metallic state in low density hydrogen
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
McMinis, Jeremy; Morales, Miguel A.; Ceperley, David M.; Kim, Jeongnim
2015-11-18
Solid atomic hydrogen is one of the simplest systems to undergo a metal-insulator transition. Near the transition, the electronic degrees of freedom become strongly correlated and their description provides a difficult challenge for theoretical methods. As a result, the order and density of the phase transition are still subject to debate. In this work we use diffusion quantum Monte Carlo to benchmark the transition between the paramagnetic and anti-ferromagnetic phases of ground state body centered cubic atomic hydrogen. We locate the density of the transition by computing the equation of state for these two phases and identify the phase transitionmoreÂ Â» order by computing the band gap near the phase transition. These benchmark results show that the phase transition is continuous and occurs at a Wigner-Seitz radius of rs = 2.27(3)a0. As a result, we compare our results to previously reported density functional theory, Hedin s GW approximation, and dynamical mean field theory results.Â«Â less
Calibration models for density borehole logging - construction report
Engelmann, R.E.; Lewis, R.E.; Stromswold, D.C.
1995-10-01
Two machined blocks of magnesium and aluminum alloys form the basis for Hanford`s density models. The blocks provide known densities of 1.780 {plus_minus} 0.002 g/cm{sup 3} and 2.804 {plus_minus} 0.002 g/cm{sup 3} for calibrating borehole logging tools that measure density based on gamma-ray scattering from a source in the tool. Each block is approximately 33 x 58 x 91 cm (13 x 23 x 36 in.) with cylindrical grooves cut into the sides of the blocks to hold steel casings of inner diameter 15 cm (6 in.) and 20 cm (8 in.). Spacers that can be inserted between the blocks and casings can create air gaps of thickness 0.64, 1.3, 1.9, and 2.5 cm (0.25, 0.5, 0.75 and 1.0 in.), simulating air gaps that can occur in actual wells from hole enlargements behind the casing.
A simple approximation for the current-voltage characteristics of high-power, relativistic diodes
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Ekdahl, Carl
2016-06-10
A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. Lastly, the approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.
Wu, H.; Wang, R.; Liu, Y.; Zhao, E. , P.O. Box 8730, Beijing Physics Department, Suzhou University, Suzhou Institute of High Energy Physics, Academia Sinica, Beijing Institute of Theoretical Physics, Academia Sinica, Beijing )
1992-04-01
The double-charge-exchange (DCX) reaction with Ca isotopes as targets is studied by employing the interacting-boson approximation (IBA). A comparison between the IBA and the shell-model results shows that IBA is a good approximation of the shell model in describing the DCX reactions.
Quartz resonator fluid density and viscosity monitor
Martin, Stephen J.; Wiczer, James J.; Cernosek, Richard W.; Frye, Gregory C.; Gebert, Charles T.; Casaus, Leonard; Mitchell, Mary A.
1998-01-01
A pair of thickness-shear mode resonators, one smooth and one with a textured surface, allows fluid density and viscosity to be independently resolved. A textured surface, either randomly rough or regularly patterned, leads to trapping of liquid at the device surface. The synchronous motion of this trapped liquid with the oscillating device surface allows the device to weigh the liquid; this leads to an additional response that depends on liquid density. This additional response enables a pair of devices, one smooth and one textured, to independently resolve liquid density and viscosity; the difference in responses determines the density while the smooth device determines the density-viscosity product, and thus, the pair determines both density and viscosity.
The Quantum Energy Density: Improved E
Krogel, Jaron; Yu, Min; Kim, Jeongnim; Ceperley, David M.
2013-01-01
We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, dened in terms of Hamiltonian components and density operators, returns the correct Hamiltonian when integrated over a volume containing a cluster of particles. This property is demonstrated for a helium-neon \\gas," showing that atomic energies obtained from the energy density correspond to eigenvalues of isolated systems. The formation energies of defects or interfaces are typically calculated as total energy dierences. Using a model of delta-doped silicon (where dopant atoms form a thin plane) we show how interfacial energies can be calculated more eciently with the energy density, since the region of interest is small. We also demonstrate how the energy density correctly transitions to the bulk limit away from the interface where the correct energy is obtainable from a separate total energy calculation.
High Density Fuel Development for Research Reactors
Daniel Wachs; Dennis Keiser; Mitchell Meyer; Douglas Burkes; Curtis Clark; Glenn Moore; Jan-Fong Jue; Totju Totev; Gerard Hofman; Tom Wiencek; Yeon So Kim; Jim Snelgrove
2007-09-01
An international effort to develop, qualify, and license high and very high density fuels has been underway for several years within the framework of multi-national RERTR programs. The current development status is the result of significant contributions from many laboratories, specifically CNEA in Argentina, AECL in Canada, CEA in France, TUM in Germany, KAERI in Korea, VNIIM, RDIPE, IPPE, NCCP and RIARR in Russia, INL, ANL and Y-12 in USA. These programs are mainly engaged with UMo dispersion fuels with densities from 6 to 8 gU/cm3 (high density fuel) and UMo monolithic fuel with density as high as 16 gU/cm3 (very high density fuel). This paper, mainly focused on the French & US programs, gives the status of high density UMo fuel development and perspectives on their qualification.
Normal and abnormal evolution of argon metastable density in high-density plasmas
Seo, B. H.; Kim, J. H.; You, S. J.
2015-05-15
A controversial problem on the evolution of Ar metastable density as a function of electron density (increasing trend versus decreasing trend) was resolved by discovering the anomalous evolution of the argon metastable density with increasing electron density (discharge power), including both trends of the metastable density [Daltrini et al., Appl. Phys. Lett. 92, 061504 (2008)]. Later, by virtue of an adequate physical explanation based on a simple global model, both evolutions of the metastable density were comprehensively understood as part of the abnormal evolution occurring at low- and high-density regimes, respectively, and thus the physics behind the metastable evolution has seemed to be clearly disclosed. In this study, however, a remarkable result for the metastable density behavior with increasing electron density was observed: even in the same electron density regime, there are both normal and abnormal evolutions of metastable-state density with electron density depending on the measurement position: The metastable density increases with increasing electron density at a position far from the inductively coupled plasma antenna but decreases at a position close to the antenna. The effect of electron temperature, which is spatially nonuniform in the plasma, on the electron population and depopulation processes of Argon metastable atoms with increasing electron density is a clue to understanding the results. The calculated results of the global model, including multistep ionization for the argon metastable state and measured electron temperature, are in a good agreement with the experimental results.
Momentum and energy approximations for elementary squeeze-film damper flows
Crandall, S.H.; El-shafei, A.
1993-09-01
To provide understanding of the effects of inertia on squeeze-film damper performance, two elementary flow patterns are studied. These elementary flows each depend on a single generalized motion coordinate whereas general planar motions of a damper are described by two independent generalized coordinates. Momentum and energy approximations for the elementary flows are compared with exact solutions. It is shown that the energy approximation, not previously applied to squeeze films, is superior to the momentum approximation in that at low Reynolds number the energy approximations agree with the exact solutions to first order in the Reynolds number whereas there are 20 percent errors in the first-order terms of the momentum approximations. 17 refs.
Method of synthesizing a low density material
Lorensen, L.E.; Monaco, S.B.
1987-02-27
A novel method of synthesizing a polymeric material of low density of the order of 50mg/cc or less. Such a low density material has applications in many areas including laser target fabrication. The method comprises preparing a polymer blend of two incompatible polymers as a major and a minor phase by mixing them and extruding the mixture, and then selectively extracting the major component, to yield a fine, low density structure.
Power balance in a high-density field reversed configuration plasma
Renneke, R. M.; Intrator, T. P.; Hsu, S. C.; Wurden, G. A.; Waganaar, W. J.; Ruden, E. L.; Grabowski, T. C.
2008-06-15
A global power balance analysis has been performed for the Field Reversed Experiment with Liner high density (>5x10{sup 22} m{sup -3}) field reversed configuration (FRC) plasma. The analysis was based on a zero-dimensional power balance model [D. J. Rey and M. Tuszewski, Phys. Fluids 27, 1514 (1984)]. The key findings are as follows. First, the percentage of radiative losses relative to total loss is an order of magnitude lower than previous lower density FRC experiments. Second, Ohmic heating was found to correlate with the poloidal flux trapping at FRC formation, suggesting that poloidal flux dissipation is primarily responsible for plasma heating. Third, high density FRCs analyzed in this work reinforce the low-density adiabatic scaling, which shows that particle confinement time and flux confinement time are approximately equal.
Mini-review of Electron Density Visualization
Adler, Joan; Adler, Omri; Kreif, Meytal; Cohen, Or; Grosso, Bastien; Hashibon, Adham; Cooper, Valentino R
2015-01-01
We describe both educational and research oriented examples of electronic density visualization with AViz. Several detailed cases are presented and the procedures for their preparation are described.
Screening potential in high density plasmas
Amari, M.; Arranz, J. P.; Butaux, J.; Nguyen, H.
1997-01-05
On the basis of a two-ion center model, an accurate closed form of the screening potential is suggested for intermediate and high density plasmas.
Building a Universal Nuclear Energy Density Functional
Bertulani, Carlos A.
2014-09-10
This grant had two components: Density functional theory and pairing and Nuclear reactions. This final report summarizes the activities for this SciDAC-2 project.
3-D capacitance density imaging system
Fasching, G.E.
1988-03-18
A three-dimensional capacitance density imaging of a gasified bed or the like in a containment vessel is achieved using a plurality of electrodes provided circumferentially about the bed in levels and along the bed in channels. The electrodes are individually and selectively excited electrically at each level to produce a plurality of current flux field patterns generated in the bed at each level. The current flux field patterns are suitably sensed and a density pattern of the bed at each level determined. By combining the determined density patterns at each level, a three-dimensional density image of the bed is achieved. 7 figs.
Calculating Atomic Number Densities for Uranium
Energy Science and Technology Software Center (OSTI)
1993-01-01
Provides method to calculate atomic number densities of selected uranium compounds and hydrogenous moderators for use in nuclear criticality safety analyses at gaseous diffusion uranium enrichment facilities.
Chiral dynamics and peripheral transverse densities Granados...
Office of Scientific and Technical Information (OSTI)
dynamics and peripheral transverse densities Granados, Carlos G. Uppsala University (Sweden); Weiss, Christian JLAB, Newport News, VA (United States) 72 PHYSICS OF ELEMENTARY...
Uncertainty Quantification for Nuclear Density Functional Theory...
Office of Scientific and Technical Information (OSTI)
Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements Citation Details In-Document Search This content will become publicly...
Universal Nuclear Energy Density Functional (Technical Report...
Office of Scientific and Technical Information (OSTI)
Country of Publication: United States Language: English Subject: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS Nuclear structure; nuclear energy density functional Word Cloud ...
High Energy Density Ultracapacitors | Department of Energy
Broader source: Energy.gov (indexed) [DOE]
and Vehicle Technologies Program Annual Merit Review and Peer Evaluation es038smith2011p.pdf (1.95 MB) More Documents & Publications High Energy Density Ultracapacitors ...
Density gradient free electron collisionally excited x-ray laser
Campbell, E.M.; Rosen, M.D.
1984-11-29
An operational x-ray laser is provided that amplifies 3p-3s transition x-ray radiation along an approximately linear path. The x-ray laser is driven by a high power optical laser. The driving line focused optical laser beam illuminates a free-standing thin foil that may be associated with a substrate for improved structural integrity. This illumination produces a generally cylindrically shaped plasma having an essentially uniform electron density and temperature, that exists over a long period of time, and provides the x-ray laser gain medium. The x-ray laser may be driven by more than one optical laser beam. The x-ray laser has been successfully demonstrated to function in a series of experimental tests.
Density gradient free electron collisionally excited X-ray laser
Campbell, Edward M.; Rosen, Mordecai D.
1989-01-01
An operational X-ray laser (30) is provided that amplifies 3p-3s transition X-ray radiation along an approximately linear path. The X-ray laser (30) is driven by a high power optical laser. The driving line focused optical laser beam (32) illuminates a free-standing thin foil (34) that may be associated with a substrate (36) for improved structural integrity. This illumination produces a generally cylindrically shaped plasma having an essentially uniform electron density and temperature, that exists over a long period of time, and provides the X-ray laser gain medium. The X-ray laser (30) may be driven by more than one optical laser beam (32, 44). The X-ray laser (30) has been successfully demonstrated to function in a series of experimental tests.
Towards time-dependent current-density-functional theory in the non-linear regime
Escartín, J. M.; Vincendon, M.; Dinh, P. M.; Suraud, E.; Romaniello, P.; Reinhard, P.-G.
2015-02-28
Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na{sub 2}. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.
Convergence properties of polynomial chaos approximations for L2 random variables.
Field, Richard V., Jr. (.,; .); Grigoriu, Mircea (Cornell University, Ithaca, NY)
2007-03-01
Polynomial chaos (PC) representations for non-Gaussian random variables are infinite series of Hermite polynomials of standard Gaussian random variables with deterministic coefficients. For calculations, the PC representations are truncated, creating what are herein referred to as PC approximations. We study some convergence properties of PC approximations for L{sub 2} random variables. The well-known property of mean-square convergence is reviewed. Mathematical proof is then provided to show that higher-order moments (i.e., greater than two) of PC approximations may or may not converge as the number of terms retained in the series, denoted by n, grows large. In particular, it is shown that the third absolute moment of the PC approximation for a lognormal random variable does converge, while moments of order four and higher of PC approximations for uniform random variables do not converge. It has been previously demonstrated through numerical study that this lack of convergence in the higher-order moments can have a profound effect on the rate of convergence of the tails of the distribution of the PC approximation. As a result, reliability estimates based on PC approximations can exhibit large errors, even when n is large. The purpose of this report is not to criticize the use of polynomial chaos for probabilistic analysis but, rather, to motivate the need for further study of the efficacy of the method.
Tao, Jianmin; Perdew, John P; Staroverov, Viktor N; Scuseria, Gustavo E
2008-01-01
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent density functional with full exact exchange. It satisfies other known exact constraints
Eich, F. G.; Hellgren, Maria
2014-12-14
We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative.
High bandwidth vapor density diagnostic system
Globig, Michael A.; Story, Thomas W.
1992-01-01
A high bandwidth vapor density diagnostic system for measuring the density of an atomic vapor during one or more photoionization events. The system translates the measurements from a low frequency region to a high frequency, relatively noise-free region in the spectrum to provide improved signal to noise ratio.
High density laser-driven target
Lindl, John D.
1981-01-01
A high density target for implosion by laser energy composed of a central quantity of fuel surrounded by a high-Z pusher shell with a low-Z ablator-pusher shell spaced therefrom forming a region filled with low-density material.
Enhancing critical current density of cuprate superconductors
Chaudhari, Praveen
2015-06-16
The present invention concerns the enhancement of critical current densities in cuprate superconductors. Such enhancement of critical current densities include using wave function symmetry and restricting movement of Abrikosov (A) vortices, Josephson (J) vortices, or Abrikosov-Josephson (A-J) vortices by using the half integer vortices associated with d-wave symmetry present in the grain boundary.
First and second order approximations to stage numbers in multicomponent enrichment cascades
Scopatz, A.
2013-07-01
This paper describes closed form, Taylor series approximations to the number product stages in a multicomponent enrichment cascade. Such closed form approximations are required when a symbolic, rather than a numeric, algorithm is used to compute the optimal cascade state. Both first and second order approximations were implemented. The first order solution was found to be grossly incorrect, having the wrong functional form over the entire domain. On the other hand, the second order solution shows excellent agreement with the 'true' solution over the domain of interest. An implementation of the symbolic, second order solver is available in the free and open source PyNE library. (authors)
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo Zhong, Chongli
2014-05-28
We present a density functional approach to describe the solid?liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.
Neutral depletion and the helicon density limit
Magee, R. M.; Galante, M. E.; Carr, J. Jr.; Lusk, G.; McCarren, D. W.; Scime, E. E.
2013-12-15
It is straightforward to create fully ionized plasmas with modest rf power in a helicon. It is difficult, however, to create plasmas with density >10{sup 20} m{sup ?3}, because neutral depletion leads to a lack of fuel. In order to address this density limit, we present fast (1 MHz), time-resolved measurements of the neutral density at and downstream from the rf antenna in krypton helicon plasmas. At the start of the discharge, the neutral density underneath the antenna is reduced to 1% of its initial value in 15 ?s. The ionization rate inferred from these data implies that the electron temperature near the antenna is much higher than the electron temperature measured downstream. Neutral density measurements made downstream from the antenna show much slower depletion, requiring 14 ms to decrease by a factor of 1/e. Furthermore, the downstream depletion appears to be due to neutral pumping rather than ionization.
Core density turbulence in the HSX Stellarator
Deng, C. B.; Brower, D. L.; Anderson, D. T.; Anderson, F. S. B.; Briesemeister, Alexis R.; Likin, K. M.
2015-10-23
Broadband turbulent density fluctuations are explored in the helically symmetric stellarator experiment (HSX) by investigating changes related to plasma heating power and location. No fluctuation response is observed to occur with large changes in electron temperature and its gradient, thereby eliminating temperature gradient as a driving mechanism. Instead, measurements reveal that density turbulence varies inversely with electron density scale length. This response is consistent with density gradient drive as one might expect for trapped electron mode (TEM) turbulence. In general, the plasma stored energy and particle confinement are higher for discharges with reduced fluctuations in the plasma core. When the density fluctuation amplitude is reduced, increased plasma rotation is also evident suggesting a role is being played by intrinsic plasma flow.
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.
Far-Field Approximation in the Generalized Geometry Holdup (GGH) Model
Oberer, R. B.; Gunn, C. A.; Chiang, L.G.
2006-09-07
Quantitative gamma spectrometry measurements of uranium frequently require corrections for attenuation by an equipment or container layer and by the uranium bearing material itself. It is common to correct for attenuation using the ''far-field approximation''. Under this approximation, the minimum thickness of equipment or material is used for the correction rather than an average thickness over the detector field-of-view. In reality this aspect of the far-field approximation is really a narrow field-of-view approximation. The price of this simplification is the introduction of a bias. This bias will be investigated in this paper. In addition, there is a distance dependence of the radial response of a detector. This dependence will also be investigated.
Gambacurta, D.; Grasso, M.; Catara, F.
2012-10-20
The low-lying dipole strength distributions of {sup 40}CaCa and {sup 48}Ca, in the energy region between 5 and 10 MeV, are studied within the second random phase approximation (RPA) with Skyrme interaction. Standard RPA models do not usually predict any presence of strength in this energy region, while experimentally a significant amount of strength is found. The inclusion of the 2 particle -2 hole configurations allows to obtain a description in a rather good agreement with the experimental data. The properties of the most collective state are analyzed in terms of its 1 particle -1 hole nature and its transition densities.
Density functional theory for d- and f-electron materials and compounds
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Mattson, Ann E.; Wills, John M.
2016-02-12
Here, the fundamental requirements for a computationally tractable Density Functional Theory-based method for relativistic f- and (nonrelativistic) d-electron materials and compounds are presented. The need for basing the Kohnâ€“Sham equations on the Dirac equation is discussed. The full Dirac scheme needs exchange-correlation functionals in terms of four-currents, but ordinary functionals, using charge density and spin-magnetization, can be used in an approximate Dirac treatment. The construction of a functional that includes the additional confinement physics needed for these materials is illustrated using the subsystem-functional scheme. If future studies show that a full Dirac, four-current based, exchange-correlation functional is needed, the subsystemmoreÂ Â» functional scheme is one of the few schemes that can still be used for constructing functional approximations.Â«Â less
Phonon and magnetic structure in Î´-plutonium from density-functional theory
SÃ¶derlind, Per; Zhou, F.; Landa, A.; Klepeis, J. E.
2015-10-30
We present phonon properties of plutonium metal obtained from a combination of density-functional-theory (DFT) electronic structure and the recently developed compressive sensing lattice dynamics (CSLD). The CSLD model is here trained on DFT total energies of several hundreds of quasi-random atomic configurations for best possible accuracy of the phonon properties. The calculated phonon dispersions compare better with experiment than earlier results obtained from dynamical mean-field theory. The density-functional model of the electronic structure consists of disordered magnetic moments with all relativistic effects and explicit orbital-orbital correlations. The magnetic disorder is approximated in two ways: (i) a special quasi-random structure and (ii) the disordered-local-moment (DLM) method within the coherent potential approximation. Magnetism in plutonium has been debated intensely, However, the present magnetic approach for plutonium is validated by the close agreement between the predicted magnetic form factor and that of recent neutron-scattering experiments.
Time-dependent density functional theory quantum transport simulation in non-orthogonal basis
Kwok, Yan Ho; Xie, Hang; Yam, Chi Yung; Chen, Guan Hua; Zheng, Xiao
2013-12-14
Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed.
Orbital relaxation effects on Kohnâ€“Sham frontier orbital energies in density functional theory
Zhang, DaDi; Zheng, Xiao; Li, Chen; Yang, Weitao
2015-04-21
We explore effects of orbital relaxation on Kohnâ€“Sham frontier orbital energies in density functional theory by using a nonempirical scaling correction approach developed in Zheng et al. [J. Chem. Phys. 138, 174105 (2013)]. Relaxation of Kohnâ€“Sham orbitals upon addition/removal of a fractional number of electrons to/from a finite system is determined by a systematic perturbative treatment. The information of orbital relaxation is then used to improve the accuracy of predicted Kohnâ€“Sham frontier orbital energies by Hartreeâ€“Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scaling correction approach provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent-field calculations for (N Â± 1)-electron systems.
DOE Seeks to Invest Approximately $1.3 Billion to Commercialize CCS
Office of Energy Efficiency and Renewable Energy (EERE) Indexed Site
Technology | Department of Energy Approximately $1.3 Billion to Commercialize CCS Technology DOE Seeks to Invest Approximately $1.3 Billion to Commercialize CCS Technology June 24, 2008 - 2:15pm Addthis Funding Opportunity Announcement Solicits Applications for Restructured FutureGen Program WASHINGTON, DC - The U.S. Department of Energy (DOE) today issued a Funding Opportunity Announcement (FOA) to invest in multiple commercial-scale Integrated Gasification Combined Cycle (IGCC) or other
Pusa, M.; Leppaenen, J.
2012-07-01
The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides. (authors)
Periodic subsystem density-functional theory
Genova, Alessandro; Pavanello, Michele; Ceresoli, Davide
2014-11-07
By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohnâ€“Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohnâ€“Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.
Vignolo, Patrizia; Minguzzi, Anna
2003-05-01
We develop a Green's function method to evaluate the exact equilibrium particle-density profiles of noninteracting Fermi gases in external harmonic confinement in any spatial dimension and for arbitrary trap anisotropy. While in a spherically symmetric configuration the shell effects are negligible in the case of a large number of particles, we find that for very anisotropic traps the quantum effects due to single-level occupancy and the deviations from the Thomas-Fermi approximation are also visible for mesoscopic clouds.
Low density, resorcinol-formaldehyde aerogels
Pekala, Richard W.
1991-01-01
The polycondensation of resorcinol with formaldehyde under alkaline conditions results in the formation of surface functionalized polymer "Clusters". The covalent crosslinking of these "clusters" produces gels which when processed under supercritical conditions, produce low density, organic aerogels (density.ltoreq.100 mg/cc; cell size .ltoreq.0.1 microns). The aerogels are transparent, dark red in color and consist of interconnected colloidal-like particles with diameters of about 100.circle.. These aerogels may be further carbonized to form low density carbon foams with cell size of about 0.1 micron.
Low density, resorcinol-formaldehyde aerogels
Pekala, Richard W.
1989-01-01
The polycondensation of resorcinol with formaldehyde under alkaline conditions results in the formation of surface functionalized polymer "clusters". The covalent crosslinking of these "clusters" produces gels which when processed under supercritical conditions, produce low density, organic aerogels (density .ltoreq.100 mg/cc; cell size .ltoreq.0.1 microns). The aerogels are transparent, dark red in color and consist of interconnected colloidal-like particles with diameters of about 100 .ANG.. These aerogels may be further carbonized to form low density carbon foams with cell size of about 0.1 micron.
Low density, resorcinol-formaldehyde aerogels
Pekala, R.W.
1989-10-10
The polycondensation of resorcinol with formaldehyde under alkaline conditions results in the formation of surface functionalized polymer clusters. The covalent crosslinking of these clusters produces gels which when processed under supercritical conditions, produce low density, organic aerogels (density [<=]100 mg/cc; cell size [<=]0.1 microns). The aerogels are transparent, dark red in color and consist of interconnected colloidal-like particles with diameters of about 100 [angstrom]. These aerogels may be further carbonized to form low density carbon foams with cell size of about 0.1 micron.
Low density, resorcinol-formaldehyde aerogels
Pekala, R.W.
1988-05-26
The polycondensation of resorcinol with formaldehyde under alkaline conditions results in the formation of surface functionalized polymer ''clusters''. The covalent crosslinking of these ''clusters'' produces gels which when processed under supercritical conditions, produce low density, organic aerogels (density less than or equal to100 mg/cc; cell size less than or equal to0.1 microns). The aerogels are transparent,dark red in color and consist of interconnected colloidal-like particles with diameters of about 100 A/degree/. These aerogels may be further carbonized to form low density carbon foams with cell size of about 0.1 micron. 1 fig., 1 tab.
Breast Density and Cancer | GE Global Research
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Breast Cancer Awareness Series: Understanding Breast Density Click to email this to a friend (Opens in new window) Share on Facebook (Opens in new window) Click to share (Opens in ...
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Density controlled carbon nanotube array electrodes
Ren, Zhifeng F.; Tu, Yi
2008-12-16
CNT materials comprising aligned carbon nanotubes (CNTs) with pre-determined site densities, catalyst substrate materials for obtaining them and methods for forming aligned CNTs with controllable densities on such catalyst substrate materials are described. The fabrication of films comprising site-density controlled vertically aligned CNT arrays of the invention with variable field emission characteristics, whereby the field emission properties of the films are controlled by independently varying the length of CNTs in the aligned array within the film or by independently varying inter-tubule spacing of the CNTs within the array (site density) are disclosed. The fabrication of microelectrode arrays (MEAs) formed utilizing the carbon nanotube material of the invention is also described.
Separation of carbon nanotubes in density gradients
Hersam, Mark C.; Stupp, Samuel I.; Arnold, Michael S.
2012-02-07
The separation of single-walled carbon nanotubes (SWNTs), by chirality and/or diameter, using centrifugation of compositions of SWNTs in and surface active components in density gradient media.
Separation of carbon nanotubes in density gradients
Hersam, Mark C.; Stupp, Samuel I.; Arnold, Michael S.
2010-02-16
The separation of single-walled carbon nanotubes (SWNTs), by chirality and/or diameter, using centrifugation of compositions of SWNTs in and surface active components in density gradient media.
High density load bearing insulation peg
Nowobilski, Jeffert J.; Owens, William J.
1985-01-01
A high density peg which can support a large load and exhibits excellent thermal resistance produced by a method wherein the peg is made in compliance with specified conditions of time, temperature and pressure.
High density load bearing insulation peg
Nowobilski, J.J.; Owens, W.J.
1985-01-29
A high density peg is disclosed which can support a large load and exhibits excellent thermal resistance produced by a method wherein the peg is made in compliance with specified conditions of time, temperature and pressure. 4 figs.
Spacetime Average Density (SAD) cosmological measures
Page, Don N.
2014-11-01
The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also the danger of domination by Boltzmann Brains. Here two new Spacetime Average Density (SAD) measures are proposed, Maximal Average Density (MAD) and Biased Average Density (BAD), for getting a finite number of observation occurrences by using properties of the Spacetime Average Density (SAD) of observation occurrences to restrict to finite regions of spacetimes that have a preferred beginning or bounce hypersurface. These measures avoid Boltzmann brain domination and appear to give results consistent with other observations that are problematic for other widely used measures, such as the observation of a positive cosmological constant.
Chiral dynamics and peripheral transverse densities (Journal...
Office of Scientific and Technical Information (OSTI)
Journal Article: Chiral dynamics and peripheral transverse densities Citation Details ... Report Number(s): JLAB-THY--13-1763; DOEOR--23177-2641 Journal ID: ISSN 1029-8479; TRN: ...
Shock compression of low-density foams
Holmes, N.C.
1993-07-01
Shock compression of very low density micro-cellular materials allows entirely new regimes of hot fluid states to be investigated experimentally. Using a two-stage light-gas gun to generate strong shocks, temperatures of several eV are readily achieved at densities of roughly 0.5--1 g/cm{sup 3} in large, uniform volumes. The conditions in these hot, expanded fluids are readily found using the Hugoniot jump conditions. We will briefly describe the basic methodology for sample preparation and experimental measurement of shock velocities. We present data for several materials over a range of initial densities. This paper will explore the applications of these methods for investigations of equations of state and phase diagrams, spectroscopy, and plasma physics. Finally, we discus the need for future work on these and related low-density materials.
High Energy Density Ultracapacitors | Department of Energy
Broader source: Energy.gov (indexed) [DOE]
Merit Review and Peer Evaluation Meeting, May 18-22, 2009 -- Washington D.C. esp22smith.pdf (1.09 MB) More Documents & Publications High Energy Density Ultracapacitors High ...
High-Energy-Density Plasmas, Fluids
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
High-Energy-Density Plasmas, Fluids High-Energy-Density Plasmas, Fluids National security depends on science and technology. The United States relies on Los Alamos National Laboratory for the best of both. No place on Earth pursues a broader array of world-class scientific endeavors. TRIDENT target chamber Sasi Palaniyappan, right, and Rahul Shah left inside a target chamber where the TRIDENT short pulse laser is aimed at a very thin diamond- foil target, a fraction of a micrometer thick. The
de Stadler, M; Chand, K
2007-11-12
Gas centrifuges exhibit very complex flows. Within the centrifuge there is a rarefied region, a transition region, and a region with an extreme density gradient. The flow moves at hypersonic speeds and shock waves are present. However, the flow is subsonic in the axisymmetric plane. The analysis may be simplified by treating the flow as a perturbation of wheel flow. Wheel flow implies that the fluid is moving as a solid body. With the very large pressure gradient, the majority of the fluid is located very close to the rotor wall and moves at an azimuthal velocity proportional to its distance from the rotor wall; there is no slipping in the azimuthal plane. The fluid can be modeled as incompressible and subsonic in the axisymmetric plane. By treating the centrifuge as long, end effects can be appropriately modeled without performing a detailed boundary layer analysis. Onsager's pancake approximation is used to construct a simulation to model fluid flow in a gas centrifuge. The governing 6th order partial differential equation is broken down into an equivalent coupled system of three equations and then solved numerically. In addition to a discussion on the baseline solution, known problems and future work possibilities are presented.
L. Whinnery; S. Goods; B. Even
2000-08-01
This study was initiated to produce a low-density centering medium for use in experiments investigating the response of materials to shock-loading. While the main drivers for material selection were homogeneity, dimensional stability, performance and cost, other secondary requirements included fine cell size, the ability to manufacture 5--10 cm-sized parts and an extremely compressed development time. The authors chose a non-traditional methodology using a hollow, expandable, polymeric microballoon material system called Expancel{reg_sign}. These microballoons are made from a copolymer of polyacrylonitrile (PAN) and polymethacrylonitrile (PMAN) and use iso-pentane as the blowing agent. The average diameter (by volume) of the unexpanded powder is approximately 13 {micro}m, while the average of the expanded powder is 35--55 {micro}m, with a few large microballoons approaching 150--200 p.m. A processing method was developed that established a pre-mixed combination of unexpanded and expanded Expancel at a ratio such that the tap (or vibration) density of the mixed powders was the same as that desired of the final part. Upon heating above the tack temperature of the polymer, this zero-rise approach allowed only expansion of the unexpanded powder to fill the interstices between the pre-expanded balloons. The mechanical action of the expanding powder combined with the elevated processing temperature yielded flee-standing and mechanically robust parts. Although mechanical properties of these foams were not a key performance requirement, the data allowed for the determination of the best temperature to heat the samples. Processing the foam at higher temperatures enhanced both modulus and strength. The maximum allowable temperature was limited by dimensional stability and shrinkback considerations. Tomographic analysis of foam billets revealed very flat density profiles. Parts of any density between the low density expanded powder (approximately 0.013 g/cm{sup 3}) and the
Hierarchy of beam plasma instabilities up to high beam densities for fast ignition scenario
Bret, A.; Deutsch, C.
2005-08-15
The hierarchy of electromagnetic instabilities suffered by a relativistic electron beam passing through a plasma is investigated. The fluid approximation is used and beam densities up to the plasma one are considered. The hierarchy between instabilities is established in terms of two parameters only: the beam relativistic factor and the ratio n{sub b}/n{sub p} of the beam density to the plasma one. It is found that for n{sub b}/n{sub p} < or approx. 0.53, the most unstable modes are a mix between filamentation and two-stream instabilities. Beyond this limit, filamentation instability may dominate, depending on the beam relativistic factor. The largest growth rates are found for a beam density slightly smaller than the plasma one.
Bret, A.; Deutsch, C.
2005-10-01
The integrated growth rate of various relativistic beam/plasma instabilities in a weakly varying plasma density gradient is calculated using a WKB-like approximation. It is proven that such an assumption can be made in fast ignition scenario conditions. The formalism is applied to the two-stream, the filamentation, and the two-stream/filamentation instabilities, the latter instability being a mixture of the former two, and is the fastest growing one. The results are restricted to collisionless plasmas and nonrelativistic beam and plasma temperatures. Filamentation instability is reduced by the density gradient and eventually does not develop in the core, whereas two-stream and two-stream/filamentation instabilities should saturate even before they feel the gradient. Various effects connected to the density gradient are discussed. It is found they should be negligible as long as these later instabilities remain in their respective linear regime.
Density fitting for three-electron integrals in explicitly correlated electronic structure theory
Womack, James C.; Manby, Frederick R.
2014-01-28
The principal challenge in using explicitly correlated wavefunctions for molecules is the evaluation of nonfactorizable integrals over the coordinates of three or more electrons. Immense progress was made in tackling this problem through the introduction of a single-particle resolution of the identity. Decompositions of sufficient accuracy can be achieved, but only with large auxiliary basis sets. Density fitting is an alternative integral approximation scheme, which has proven to be very reliable for two-electron integrals. Here, we extend density fitting to the treatment of all three-electron integrals that appear at the MP2-F12/3*A level of theory. We demonstrate that the convergence of energies with respect to auxiliary basis size is much more rapid with density fitting than with the traditional resolution-of-the-identity approach.
Alekseev, A E; Potapov, V T
2013-10-31
Spectral characteristics of the noise intensity fluctuations at the output of a scattered-light interferometer, caused by phase fluctuations of semiconductor laser radiation are considered. This kind of noise is one of the main factors limiting sensitivity of interferometric sensors. For the first time, to our knowledge, the expression is obtained for the average noise power spectral density at the interferometer output versus the degree of a light source coherence and length of the scattering segment. Also, the approximate expressions are considered which determine the power spectral density in the low-frequency range (up to 200 kHz) and in the limiting case of extended scattering segments. The expression obtained for the noise power spectral density agrees with experimental normalised power spectra with a high accuracy. (interferometry of radiation)
Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Simulating higher-dimensional geometries in GADRAS using approximate one-dimensional solutions.
Thoreson, Gregory G.; Mitchell, Dean James; Harding, Lee T.
2013-02-01
The Gamma Detector Response and Analysis Software (GADRAS) software package is capable of simulating the radiation transport physics for one-dimensional models. Spherical shells are naturally one-dimensional, and have been the focus of development and benchmarking. However, some objects are not spherical in shape, such as cylinders and boxes. These are not one-dimensional. Simulating the radiation transport in two or three dimensions is unattractive because of the extra computation time required. To maintain computational efficiency, higher-dimensional geometries require approximations to simulate them in one-dimension. This report summarizes the theory behind these approximations, tests the theory against other simulations, and compares the results to experimental data. Based on the results, it is recommended that GADRAS users always attempt to approximate reality using spherical shells. However, if fissile material is present, it is imperative that the shape of the one-dimensional model matches the fissile material, including the use of slab and cylinder geometry.
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.
On the approximations of the distribution function of fusion alpha particles
Bilato, R. Brambilla, M.; Poli, E.
2014-10-15
The solution of the drift-kinetic equation for fusion-born alpha particles is derived in the limit of dominant parallel streaming, and it is related to the usual slowing-down distribution function. The typical approximations of the fast tail of fusion-born alpha particles are briefly compared and discussed. In particular, approximating the distribution function of fast-alpha particles with an “equivalent” Maxwellian is inaccurate to describe absorption of radio-frequency waves in the ion-cyclotron range of frequencies.
Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations
El Bouajaji, M.
2014-12-15
The aim of this paper is to propose new local and accurate approximate magnetic-to-electric surface boundary operators for the three-dimensional time-harmonic Maxwell's equations. After their construction where their accuracy is improved through a regularization process, a localization of these operators and a full finite element approximation is introduced. Next, their numerical efficiency and accuracy is investigated in detail for different scatterers when these operators are used in the extreme situation of On-Surface Radiation Conditions methods.
Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; Jornada, Felipe H. da; Deslippe, Jack; Yang, Chao; and others
2015-04-01
We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.
Orbital-optimized density cumulant functional theory
Sokolov, Alexander Yu. Schaefer, Henry F.
2013-11-28
In density cumulant functional theory (DCFT) the electronic energy is evaluated from the one-particle density matrix and two-particle density cumulant, circumventing the computation of the wavefunction. To achieve this, the one-particle density matrix is decomposed exactly into the mean-field (idempotent) and correlation components. While the latter can be entirely derived from the density cumulant, the former must be obtained by choosing a specific set of orbitals. In the original DCFT formulation [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] the orbitals were determined by diagonalizing the effective Fock operator, which introduces partial orbital relaxation. Here we present a new orbital-optimized formulation of DCFT where the energy is variationally minimized with respect to orbital rotations. This introduces important energy contributions and significantly improves the description of the dynamic correlation. In addition, it greatly simplifies the computation of analytic gradients, for which expressions are also presented. We offer a perturbative analysis of the new orbital stationarity conditions and benchmark their performance for a variety of chemical systems.
Gorham, Caroline S.; Gaskins, John T.; Hopkins, Patrick E.; Parsons, Gregory N.; Losego, Mark D.
2014-06-23
We report on the thermal conductivity of atomic layer deposition-grown amorphous alumina thin films as a function of atomic density. Using time domain thermoreflectance, we measure the thermal conductivity of the thin alumina films at room temperature. The thermal conductivities vary ?35% for a nearly 15% change in atomic density and are substrate independent. No density dependence of the longitudinal sound speeds is observed with picosecond acoustics. The density dependence of the thermal conductivity agrees well with a minimum limit to thermal conductivity model that is modified with a differential effective-medium approximation.
Fabrication of low density ceramic material
Meek, T.T.; Blake, R.D.; Sheinberg, H.
1985-01-01
A precursor mixture and a method of making a low-density ceramic structural material are disclosed. The precursor mixture includes hollow microballoons, typically made of glass, together with a cementing agent capable of being cured by microwave irradiation. A preferred cementing agent is liquid hydrated potassium silicate, which is mixed with the glass microballoons to form a slurry. Upon irradiation the potassium silicate is dehydrated to form a solid porous matrix in which the microballoons are evenly distributed. Ground glass or other filling agents may be included in the slurry to enhance the properties of the final product. Low-density structural ceramics having densities on the order of 0.1 to 0.3 are obtained.
Statistical approach to nuclear level density
Sen'kov, R. A.; Horoi, M.; Zelevinsky, V. G.
2014-10-15
We discuss the level density in a finite many-body system with strong interaction between the constituents. Our primary object of applications is the atomic nucleus but the same techniques can be applied to other mesoscopic systems. We calculate and compare nuclear level densities for given quantum numbers obtained by different methods, such as nuclear shell model (the most successful microscopic approach), our main instrument - moments method (statistical approach), and Fermi-gas model; the calculation with the moments method can use any shell-model Hamiltonian excluding the spurious states of the center-of-mass motion. Our goal is to investigate statistical properties of nuclear level density, define its phenomenological parameters, and offer an affordable and reliable way of calculation.
High power density solid oxide fuel cells
Pham, Ai Quoc; Glass, Robert S.
2004-10-12
A method for producing ultra-high power density solid oxide fuel cells (SOFCs). The method involves the formation of a multilayer structure cells wherein a buffer layer of doped-ceria is deposited intermediate a zirconia electrolyte and a cobalt iron based electrode using a colloidal spray deposition (CSD) technique. For example, a cobalt iron based cathode composed of (La,Sr)(Co,Fe)O (LSCF) may be deposited on a zirconia electrolyte via a buffer layer of doped-ceria deposited by the CSD technique. The thus formed SOFC have a power density of 1400 mW/cm.sup.2 at 600.degree. C. and 900 mW/cm.sup.2 at 700.degree. C. which constitutes a 2-3 times increased in power density over conventionally produced SOFCs.
Hydrogen atom excitation in intense attosecond laser field: Gauge dependence of dipole approximation
Aldarmaa, Ch. E-mail: l-xemee@yahoo.com; Khenmedekh, L. E-mail: l-xemee@yahoo.com; Lkhagva, O.
2014-03-24
It is assumed that, the atomic excitations probability can be calculated using first order perturbation theory and dipole approximations. The validity of the dipole approximations had been examined by comparing the results with the results obtained by exact calculations within the first order perturbation theory[2]. Figure 1 shows the time dependence of the transition probability in the dipole approximation. From these plots it is obvious that, the probabilities obtained in the length gauge are higher than that in the velocity gauge, in the interaction period (??/2
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 â€œ2D/1Dâ€ 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.
Zhou, Zhennan
2014-09-01
In this paper, we approximate the semi-classical Schrödinger equation in the presence of electromagnetic field by the Hagedorn wave packets approach. By operator splitting, the Hamiltonian is divided into the modified part and the residual part. The modified Hamiltonian, which is the main new idea of this paper, is chosen by the fact that Hagedorn wave packets are localized both in space and momentum so that a crucial correction term is added to the truncated Hamiltonian, and is treated by evolving the parameters associated with the Hagedorn wave packets. The residual part is treated by a Galerkin approximation. We prove that, with the modified Hamiltonian only, the Hagedorn wave packets dynamics give the asymptotic solution with error O(?{sup 1/2}), where ? is the scaled Planck constant. We also prove that, the Galerkin approximation for the residual Hamiltonian can reduce the approximation error to O(?{sup k/2}), where k depends on the number of Hagedorn wave packets added to the dynamics. This approach is easy to implement, and can be naturally extended to the multidimensional cases. Unlike the high order Gaussian beam method, in which the non-constant cut-off function is necessary and some extra error is introduced, the Hagedorn wave packets approach gives a practical way to improve accuracy even when ? is not very small.
Low density, microcellular foams, preparation, and articles
Young, Ainslie T.; Marsters, Robert G.; Moreno, Dawn K.
1984-01-01
A microcellular low density foam of poly(4-methyl-1-pentene) which is particularly useful for forming targets for inertial confinement fusion has been developed. Articles made from the foam have been machined to tolerances of 0.0001 inch, although the densities of the fragile foam are low (about 10 to about 100 mg/cc) and the cell sizes are small (about 10 to about 30 .mu.m). Methods for forming the foam and articles are given; and the yield strength of the foam of the invention is higher than was obtained in other structures of this same material.
Low density, microcellular foams, preparation, and articles
Young, A.T.
1982-03-03
A microcellular low-density foam of poly(4-methyl-1-pentene) particularly useful for forming targets for inertial confinement fusion has been developed. Articles made from the foam have been machined to tolerances of 0.0001 inch, although the densities of the fragile foam are low (about 10 to about 100 mg/cc) and the cell sizes are small (about 10 to about 30 ..mu..m). Methods for forming the foam and articles are given. The yield strength of the foam of the invention is higher than was obtained in other structures of this same material.
NEUTRON DENSITY CONTROL IN A NEUTRONIC REACTOR
Young, G.J.
1959-06-30
The method and means for controlling the neutron density in a nuclear reactor is described. It describes the method and means for flattening the neutron density distribution curve across the reactor by spacing the absorbing control members to varying depths in the central region closer to the center than to the periphery of the active portion of the reactor to provide a smaller neutron reproduction ratio in the region wherein the members are inserted, than in the remainder of the reactor thereby increasing the over-all potential power output.
Size-dependent error of the density functional theory ionization potential in vacuum and solution
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Sosa Vazquez, Xochitl A.; Isborn, Christine M.
2015-12-22
Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potentialmoreÂ Â» for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. As a result, in vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.Â«Â less
Size-dependent error of the density functional theory ionization potential in vacuum and solution
Sosa Vazquez, Xochitl A.; Isborn, Christine M.
2015-12-28
Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.
Size-dependent error of the density functional theory ionization potential in vacuum and solution
Sosa Vazquez, Xochitl A.; Isborn, Christine M.
2015-12-22
Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. As a result, in vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.