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Analytic form for a nonlocal kinetic energy functional with a density-dependent kernel for orbital-free density functional theory under periodic and Dirichlet boundary conditions

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Physical Review B 2008年第4期78卷 045105-045105页

作者： Gregory S. Ho Vincent L. Lignères Emily A. Carter Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang et al., Phys. Rev. B 60, 16350 (1999)] kinetic energy density functional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free density functional theory (OF-DFT) calculations.

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Deep learning inter-atomic potential for thermal and phonon behaviour of silicon carbide with quantum accuracy

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arXiv 2021年

作者： Fu, Baoqin Sun, Yandong Zhang, Linfeng Wang, Han Xu, Ben Key Laboratory of Radiation Physics and Technology of the Ministry of Education Institute of Nuclear Science and Technology Sichuan University Chengdu610064 China Graduate School China Academy of Engineering Physics Beijing100193 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

Silicon carbide (SiC) is an essential material for next generation semiconductors and components for nuclear plants. It’s applications are strongly dependent on its thermal conductivity, which is highly sensitive to microstructures. Molecular dynamics (MD) simulation is the most used methods to address thermal transportation mechanisms in devices or microstructures of nano-meters. However, the implementation of MD is limited in SiC because of lacking accurate inter-atomic potentials. In this work, using the Deep Potential (DP) methodology, we developed two inter-atomic potentials (DP-*Corresponding author. IAPs) for SiC based on two adaptively generated datasets within the density functional approximations at the local density and the generalized gradient levels. These two DP-IAPs manifest their speed with quantum accuracy in lattice dynamics simulations as well as scattering rate analysis of phonon transportation. Combining with molecular dynamics simulations, the thermal transport and mechanical properties were systematically investigated. The presented methodology and the inter-atomic potentials pave the way for a systematic approach to model heat transport in SiC related devices using multiscale modelling. Copyright © 2021, The Authors. All rights reserved.

关键词： Silicon carbide

Existence and Stability of Nonequilibrium Steady States of Nernst-Planck-Navier-Stokes Systems

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arXiv 2022年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Temple University PhiladelphiaPA19122 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

MSC Codes 35Q30, 35Q35, 35Q92We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of Rd, d = 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state solutions and present a sufficient condition in terms of only the boundary data that guarantees that these solutions have nonzero fluid velocity. We show that time evolving solutions are ultimately bounded uniformly, independently of their initial size. In addition, we consider one dimensional steady states with steady nonzero currents and show that they are globally nonlinearly stable as solutions in a three dimensional periodic strip, if the currents are sufficiently weak. © 2022, CC BY.

关键词： Navier Stokes equations

LARGE SCALE DYNAMICS OF PRECIPITATION FRONTS IN THE TROPICAL ATMOSPHERE: A NOVEL RELAXATION LIMIT ¤

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Communications in Mathematical Sciences 2004年第4期2卷 591-626页

作者： Frierson, Dargan M. W. Majda, Andrew J. Pauluis, Olivier M. Program in Applied and Computational Mathematics Princeton University Fine HallWashington Rd Princeton 08544 NJ United States Department of Mathematics and Center for Atmosphere Ocean Science Courant Institute of Mathematical Sciences New York University 251 Mercer St New York 10012 NY United States Center for Atmosphere Ocean Science Courant Institute of Mathematical Sciences New York University 251 Mercer St. New York 10012 NY United States

A simplified set of equations is derived systematically below for the interaction of large scale flow fields and precipitation in the tropical atmosphere. These equations, the Tropical Climate Model, have the form of a shallow water equation and an equation for moisture coupled through a strongly nonlinear source term. This source term, the precipitation, is of relaxation type in one region of state space for the temperature and moisture, and vanishes identically elsewhere in the state space of these variables. In addition, the equations are coupled nonlinearly to the equations for barotropic incompressible flow. Several mathematical features of this system are developed below including energy principles for solutions and their first derivatives independent of relaxation time. With these estimates, the formal infinitely fast relaxation limit converges to a novel hyperbolic free boundary problem for the motion of precipitation fronts from a large scale dynamical perspective. Elementary exact solutions of the limiting dynamics involving precipitation fronts are developed below and include three families of waves: fast drying fronts as well as slow and fast moistening fronts. The last two families of waves violate Lax's Shock Inequalities;nevertheless, numerical experiments presented below confirm their robust realizability with realistic finite relaxation times. From the viewpoint of tropical atmospheric dynamics, the theory developed here provides a new perspective on the fashion in which the prominent large scale regions of moisture in the tropics associated with deep convection can move and interact with large scale dynamics in the quasi-equilibrium approximation. © 2004 International Press

关键词： Equatorial waves Hyperbolic free boundary problems Hyperbolic pde Moisture Nonlinear relaxation equations Tropical atmospheric dynamics Tropical convection

Unbiased Parameter Estimation for Partially Observed Diffusions

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arXiv 2023年

作者： Awadelkarim, Elsiddig Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting log-likelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically out-perform existing unbiased *** Codes 60J22, 62M05, 65C40, 62M20 © 2023, CC BY.

关键词： Parameter estimation

Nernst-Planck-Navier-stokes systems far from equilibrium

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arXiv 2020年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Temple University PhiladelphiaPA19122 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data: aribitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. The result holds for any positive diffusivities of ions, in bounded domains with smooth boundary in three space dimensions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier-Stokes coupling, if the velocity is regular. The global smoothness of solutions is also true for arbitrarily many ionic species, if all their diffusivities are the *** Codes 35Q30, 35Q35, 35Q92 Copyright © 2020, The Authors. All rights reserved.

关键词： Navier Stokes equations

Benchmark problems for phase retrieval

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arXiv 2017年

作者： Elser, Veit Lan, Ti-Yen Bendory, Tamir Department of Physics Cornell University IthacaNY14853-2501 United States Program in Applied and Computational Mathematics Princeton University Princeton08544-1000 United States

In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be recovered is periodic and comprised of atomic distributions arranged homogeneously in the unit cell of the crystal. The crystallographic problem is both the leading application and one of the hardest forms of phase retrieval. We have constructed a graded set of benchmark problems for evaluating algorithms that perform this type of phase retrieval. The data, publicly available online1, is provided in an easily interpretable format. We also propose a simple and unambiguous success/failure criterion based on the actual needs in crystallography. Baseline runtimes were obtained with an iterative algorithm that is similar but more transparent than those used in crystallography. Empirically,the runtimes grow exponentially with respect to a new hardness parameter: the sparsity of the signal autocorrelation. We also review the algorithms used by the leading software packages. This set of benchmark problems, we hope, will encourage the development of new algorithms for the phase retrieval problem in general, and crystallography in particular. Copyright © 2017, The Authors. All rights reserved.

关键词： Benchmarking

ON THE GLOBAL WELL-POSEDNESS AND GEVREY REGULARITY OF SOME ELECTRODIFFUSION MODELS

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arXiv 2022年

作者： Abdo, Elie Lee, Fizay-Noah Wang, Weinan Department of Mathematics Temple University PhiladelphiaPA19122 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics University of Arizona TucsonAZ85712 United States

We consider the Nernst-Planck equations describing the nonlinear time evolution of multiple ionic concentrations in a two-dimensional incompressible fluid. The velocity of the fluid evolves according to either the Euler or Darcy’s equations, both forced nonlinearly by the electric forces generated by the presence of charged ions. We address the global well-posedness and Gevrey regularity of the resulting electrodiffusion models in the periodic setting. © 2022, CC BY.

关键词： Nonlinear equations

USING REED-MULLER SEQUENCES AS DETERMINISTIC COMPRESSED SENSING MATRICES FOR IMAGE RECONSTRUCTION

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USING REED-MULLER SEQUENCES AS DETERMINISTIC COMPRESSED SENS...

IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Kangyu Ni Somantika Datta Prasun Mahanti Svetlana Roudenko Douglas Cochran School of Mathematical and Statistical Sciences Arizona State University Program in Applied and Computational Mathematics Princeton University School of Electrical Computer and Energy Engineering Arizona State University

ISBN: (纸本)9781424442959;9781424442966

An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of second-order Reed-Muller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers significant loss in speed and accuracy when the degree of sparsity is not high, making it inviable for 2D signals. This paper describes an efficient 2D CS algorithm using RM sequences, provides medical image reconstruction examples, and compares it with the original 2D CS using noiselets. This algorithm entails several innovations that enhance its suitability for images: initial best approximation, a greedy algorithm for the nonzero locations, and a new approach in the least-squares step. These enhancements improve fidelity, execution time, and stability in the context of image reconstruction.

关键词： Compressed Sensing Reed-Muller Sequences Image Reconstruction image reconstruction Compressed sensing deterministic CONTAINMENT SPRAY carbon monosulfide Cesium matrices Redmouth disease greedy algorithm COMPRESSED conditioned stimulus