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Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation

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Physical Review B 2015年第4期91卷 045124-045124页

作者： Junchao Xia Emily A. Carter Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544-5263 USA Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

We present a comprehensive study of single-point kinetic energy density functionals (KEDFs) to be used in orbital-free density functional theory (DFT) calculations. We first propose a form of KEDFs based on a pointwise Kohn-Sham (KS) kinetic energy density (KED) and electron localization function (ELF) analysis. We find that the ELF and modified enhancement factor have a very strong and transferable correlation with the reduced density in various bulk metals. The non-self-consistent kinetic energy errors predicted by our KEDF models are decreased greatly compared to previously reported generalized gradient approximation (GGA) KEDFs. Second, we perform self-consistent calculations with various single-point KEDFs and investigate their numerical convergence behavior. We find striking numerical instabilities for previous GGA KEDFs; most of the GGA KEDFs fail to converge and show unphysical densities during the optimization. In contrast, our KEDFs demonstrate stable convergence, and their self-consistent results of various bulk properties agree reasonably well with KSDFT. A further detailed KED analysis reveals an interesting bifurcation phenomenon in defective metals and alloys, which may shed light on directions for future KEDF development.

关键词： KINETIC energy DENSITY functionals DENSITY functional theory ELECTRON research BIFURCATION theory

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Reply to “Comment on ‘Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation’ ”

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Physical Review B 2015年第11期92卷 117102-117102页

We find that the multivalued character of the G factor as a function of the reduced gradient (s) still exists after accounting for pseudopotential artifacts and the kinetic energy global upper bound. We also find that the VT84F functional indeed exhibits stable convergence and more reasonable results for self-consistent bulk properties compared to other generalized gradient approximation (GGA) kinetic energy density functionals (KEDFs) that we tested earlier. However, VT84F generally yields overestimated equilibrium volumes, which may result from its inability (as with all GGAs) to reproduce the G−s multivalued character. The analogous failure to predict the multivalued character of G as a function of the reduced density (d) is also likely to be responsible for the inaccuracy of our vWGTF functionals reported earlier. Our multivaluedness analysis therefore does not impugn any particular GGA KEDF. Instead, it merely confirms the importance of pointwise analysis for improving KEDFs by emphasizing the need to resolve the multivaluedness of G with respect to various density variables.

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Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection

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Physical Review E 2015年第4期92卷 043012-043012页

作者： Baole Wen Gregory P. Chini Rich R. Kerswell Charles R. Doering Program in Integrated Applied Mathematics University of New Hampshire Durham New Hampshire 03824 USA Center for Fluid Physics University of New Hampshire Durham New Hampshire 03824 USA The Institute for Computational Engineering and Sciences The University of Texas at Austin Austin Texas 78712 USA Department of Mechanical Engineering University of New Hampshire Durham New Hampshire 03824 USA School of Mathematics University of Bristol University Walk Bristol BS8 1TW United Kingdom Department of Physics University of Michigan Ann Arbor Michigan 48109-1040 USA Department of Mathematics University of Michigan Ann Arbor Michigan 48109-1043 USA Center for the Study of Complex Systems University of Michigan Ann Arbor Michigan 48109-1107 USA

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the “background field” variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu∼PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L=22,Nu≤0.106Pr0Ra5/12, which indicates that molecular transport cannot generally be neglected in the “ultimate” high-Ra regime.

关键词： RAYLEIGH-Benard convection RESEARCH BOUNDS (mathematics) CONVECTIVE flow (Fluid dynamics) NATURAL heat convection NUSSELT number

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Hydrodynamic interaction between overlapping domains during recurrence of registration within planar lipid bilayer membranes

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Physical Review E 2014年第3期89卷 032717-032717页

作者： Tao Han Trevor P. Bailey Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Due to a thermodynamic coupling between the two leaflets comprising a lipid bilayer, compositional lipid domains residing within opposing leaflets are often found in registry. If the system is perturbed by displacing one domain relative to the other, diffusive and advective lipid fluxes are established to restore equilibrium and reestablish domain overlap. In this work, we focus on the advective part of the process, and first derive an analytical expression for the hydrodynamic drag coefficient associated with the advective flow for the special case of perfect domain overlap. The resulting expression identifies parameter regions where sliding friction between the leaflets dominates over viscous dissipation within the leaflets or vice versa. It is shown that in all practically relevant cases, sliding friction between the leaflets is the dominant factor. Finally, we investigate the domain separation dependence of the hydrodynamic drag coefficient via direct simulations of a continuum diffuse interface model, and provide useful empirical expressions for its behavior.

关键词： HYDRODYNAMICS BILAYER lipid membranes DRAG coefficient ENERGY dissipation SLIDING friction FLUX (Energy)

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Erratum to: Some Joys and Trials of Mathematical Neuroscience

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Journal of Nonlinear Science 2014年第2期24卷 243-244页

作者： Holmes, Philip Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton USA Princeton Neuroscience Institute Princeton University Princeton USA

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Angular momentum dependent orbital-free density functional theory: Formulation and implementation

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Physical Review B 2014年第15期89卷 155112-155112页

作者： Youqi Ke Florian Libisch Junchao Xia Emily A. Carter []Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

Orbital-free density functional theory (OFDFT) directly solves for the ground-state electron density. It scales linearly with respect to system size, providing a promising tool for large-scale material simulations. Removal of the orbitals requires use of approximate noninteracting kinetic energy density functionals. If replacing ionic cores with pseudopotentials, removal of the orbitals also requires these pseudopotentials to be local. These are two severe challenges to the capabilities of conventional OFDFT. While main group elements are often well described within conventional OFDFT, transition metals remain intractable due to their localized d electrons. To advance the accuracy and general applicability of OFDFT, we have recently reported a general angular momentum dependent formulation as a next-generation OFDFT. In this formalism, we incorporate the angular momenta of electrons by devising a hybrid scheme based on a muffin tin geometry: inside spheres centered at the ionic cores, the electron density is expanded in a set of atom-centered basis functions combined with an onsite density matrix. The explicit treatment of the angular momenta of electrons provides an important basis for accurately describing the important ionic core region, which is not possible in conventional OFDFT. In addition to the conventional OFDFT total energy functional, we introduce a nonlocal energy term containing a set of angular momentum dependent energies to correct the errors due to the approximate kinetic energy density functional and local pseudopotentials. Our approach greatly increases the accuracy of OFDFT while largely preserving its numerical simplicity. Here, we provide details of the theoretical formulation and practical implementation, including the hybrid scheme, the derivation of the nonlocal energy term, the choice of basis functions, the direct minimization of the total energy, the procedure to determine the angular momentum dependent energies, the force formula with Pu

关键词： ANGULAR momentum (Nuclear physics) DENSITY functional theory GROUND state (Quantum mechanics) ELECTRON density SIMULATION methods & models DENSITY functionals

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Near optimal feedback guidance design and the planar restricted three-body problem 24

Near optimal feedback guidance design and the planar restric...

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24th AAS/AIAA Space Flight Mechanics Meeting, 2014

作者： Dinius, Joseph Furfaro, Roberto Topputo, Francesco Selnick, Scott Program in Applied Mathematics University of Arizona 617 N Santa Rita Ave TucsonAZ85721 United States Department of Systems and Industrial Engineering University of Arizona 1127 E James E. Rogers Way TucsonAZ85721 United States Department of Aerospace and Mechanical Engineering University of Arizona 1130 N Mountain Ave TucsonAZ85721 United States Department of Aerospace Science and Technology Politecnico di Milano Via La Masa 34 Milan20156 Italy

ISBN: (纸本)9780877036111

In this paper, we present the application of the ZEM/ZEV guidance algorithm to the planar restricted three-body problem (PR3BP). The ZEM/ZEV guidance law as a feedback guidance strategy is presented and applied to the PR3BP. The fuel optimal solution to the PR3BP for a transfer from GTO to L1 in the Earth-Moon system is presented as a point for comparison, showing the near optimality of the closed-loop guidance approach. Challenges of the approach and strategies for implementation in spacecraft mission design are discussed.

关键词： Feedback

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Calibrated Langevin-dynamics simulations of intrinsically disordered proteins

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Physical Review E 2014年第4期90卷 042709-042709页

作者： W. Wendell Smith Po-Yi Ho Corey S. O'Hern Department of Physics Yale University New Haven Connecticut 06520-8120 USA Integrated Graduate Program in Physical and Engineering Biology Yale University New Haven Connecticut 06520-8114 USA Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut 06520-8286 USA Department of Applied Physics Yale University New Haven Connecticut 06520-8267 USA Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: α−, β−, and γ-synuclein, the microtubule-associated protein τ, and prothymosin α. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein.

关键词： LANGEVIN equations SIMULATION methods & models CONFORMATIONAL analysis MICROTUBULE-associated proteins HYDROPHOBIC compounds

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A New Extrapolation Treatment for Boundary Conditions in Lattice Boltzmann Method

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Chinese Physics Letters 2013年第9期30卷 89-93页

作者： WANG Zheng-Dao YANG Jian-Fei WEI Yi-Kun QIAN Yue-Hong Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072 Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai 200072 Shanghai Program for Innovative Research Team in Universities Shanghai 200072 Faculty of Mechanical Engineering and Automatic Zhejiang Sci-Tech UniversityHangzhou 310018 Department of Mechanical and Aerospace Enigineering UC IrvineCA 92617USA

The lattice Boltzmann method is widely used in solving hydrodynamics for various *** accuracy of the extrapolation method for boundary conditions and Mei’s method for curved boundary is not high *** propose a modified extrapolation method for boundary *** simulations conform the higher accuracy and stability compared with the other methods.

关键词： conditions methods boundary

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Synchronization of a class of second order distributed parameter systems

Synchronization of a class of second order distributed param...

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1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2013

作者： Demetriou, Michael A. Fahroo, Fariba Aerospace Engineering Program Mechanical Engineering Department Worcester Polytechnic Institute Worcester MA 01609 United States Department of Applied Mathematics Naval Postgraduate School Monterey CA 93943 United States

ISBN: (纸本)9783902823540

In this work, we examine the synchronization control for a class of second order distributed parameter systems. The objective is to design controllers that guarantee agreement between the position and velocity states of N identical second order systems. The controller structure involves coupling terms consisting of the pairwise difference of both position and velocity states of the second order systems in order to enforce consensus. Possible improvements of the agreement amongst the states of each of the systems are considered and compared to the case of noninteracting controllers. Extensions to synchronizing controllers for the case of partial connectivity are discussed. Extensive numerical studies are included to provide a further insight on the effects of synchronization control of second order distributed parameter systems. © IFAC.

关键词： Synchronization

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