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System Approach to mathematical Description of Transport Processes with Chemical Reaction in Multiphase Multicomponent Body 2

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System Approach to Mathematical Description of Transport Pro...

2nd IEEE International Conference on System Analysis and Intelligent Computing, SAIC 2020

作者： Chernukha, Olha Bilushchak, Yurii Pakholok, Bohdan Ctr. of Math. Modelling of Y. S. Pidstryhach Inst. of Appl. Prob. of Mechanics and Math. of the Natl. Acad. of Sci. of Ukraine Department of Mathematical Modeling of Nonequilibrium Processes Lviv Ukraine Lviv Polytechnic National University Institute of Applied Mathematics and Fundamental Sciences Department of Computational Mathematics and Programming Lviv Ukraine

ISBN: (纸本)9781728190822

In the work the system approach to the description of complex and compound systems is proposed. It is based on the synthesis of the classical mathematical modeling approach of coupled processes of different physical nature in nonhomogeneous media for a well-structured part of the system and the non-classical statistical approach to modeling an unknown boundary condition based on experimental data. © 2020 IEEE.

关键词： Chemical reactions

Fast acoustic source imaging using multi-frequency sparse data

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arXiv 2017年

作者： Alzaalig, Ala Hu, Guanghui Liu, Xiaodong Sun, Jiguang Department of Mathematical Sciences Michigan Technological University Beijing Computational Science Research Center Beijing100193 China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Mathematical Sciences Michigan Technological University College of Mathematical Sciences University of Electronic Science and Technology of China

We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some information (size and location) of the source support can be recovered. A non-iterative method is then proposed to image the source for the Helmholtz equation using multiple frequency far field data of one or several observation directions. The method is simple to implement and extremely fast since it only computes an indicator function on the interested domain using only matrix vector multiplications. Numerical examples are presented to validate the effectiveness of the *** Codes 35P25, 35Q30, 45Q05, 78A46 Copyright © 2017, The Authors. All rights reserved.

关键词： Iterative methods

Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics

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Physical Review Letters 2018年第14期120卷 143001-143001页

作者： Linfeng Zhang Jiequn Han Han Wang Roberto Car Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing 100871 People’s Republic of China

We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is first-principles based in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DPMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.

关键词： Classical statistical mechanics Density functional theory First-principles calculations Interatomic & molecular potentials Learning Neuronal networks Potential energy surfaces Solid-state chemistry Thermal properties Van der Waals interaction Molecular dynamics

A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach

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Communications in computational Physics 2012年第7期12卷 544-576页

作者： Satoshi Ii Xiaobo Gong Kazuyasu Sugiyama Jinbiao Wu Huaxiong Huang Shu Takagi Department of Mechanical Engineering The University of Tokyo7-3-1 Hongo Bunkyo-kuTokyo113-8656Japan Department of Engineering Mechanics NAOCEShanghai Jiaotong UniversityShanghai 200240China LMAM&School of Mathematical Sciences Peking UniversityBeijing 100871China Department of Mathematics and Statistics York University4700 Keele StreetTorontoOntarioCanada Computational Science Research Program RIKEN2-1 Hirosawa WakoSaitama351-0198Japan.

A novel full Eulerian fluid-elastic membrane coupling method on the fixed Cartesian coordinate mesh is proposed within the framework of the volume-of-fluid *** present method is based on a full Eulerian fluid-(bulk)structure coupling solver(Sugiyama et al.,***.,230(2011)596–627),with the bulk structure replaced by elastic *** this study,a closed membrane is considered,and it is described by a volume-of-fluid or volume-fraction information generally called VOF function.A smoothed indicator(or characteristic)function is introduced as a phase indicator which results in a smoothed VOF *** smoothed VOF function uses a smoothed delta function,and it enables a membrane singular force to be incorporated into a mixture momentum *** order to deal with a membrane deformation on the Eulerian mesh,a deformation tensor is introduced and updated within a compactly supported region near the *** the neo-Hookean and the Skalak models are employed in the numerical simulations.A smoothed(and less dissipative)interface capturing method is employed for the advection of the VOF function and the quantities defined on the *** stability restriction due to membrane stiffness is relaxed by using a quasi-implicit *** present method is validated by using the spherical membrane deformation problems,and is applied to a pressure-driven flow with the biconcave membrane capsules(red blood cells).

关键词： Fluid-membrane interaction Eulerian formulation Cartesian mesh volume-of-fluid quasi-implicit approach red blood cell

A discrete entropy power inequality for uniform distributions

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A discrete entropy power inequality for uniform distribution...

IEEE International Symposium on Information Theory

作者： Jae Oh Woo Mokshay Madiman Applied Mathematics Program Yale University New Haven CT USA Department of Mathematical Sciences Uiversity of Delaware Newark DE USA

ISBN: (纸本)9781467377058

We explore various tempting conjectures for discrete entropy power inequalities on the integers, proving both positive results for interesting subclasses of distributions and negative results that falsify some of the conjectures in general. In particular, we show that an inequality very similar to the usual entropy power inequality holds for uniform distributions over finite subsets of the integers.

关键词： Entropy Random variables Volume measurement Electronic mail Cognition Convolution

Ab Initio Generalized Langevin Equation

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arXiv 2022年

作者： Xie, Pinchen Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing China

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multi-scale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of collective variables by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude, and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency. © 2022, CC BY.

关键词： Molecular dynamics

Uniform Anisotropic Regularity and Low Mach Number Limit of Non-isentropic Ideal MHD Equations with a Perfectly Conducting Boundary

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arXiv 2024年

作者： Ju, Qiangchang Wang, Jiawei Zhang, Junyan Institute of Applied Physics and Computational Mathematics Beijing China Hua Loo-Keng Center for Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics National University of Singapore Singapore

We prove the low Mach number limit of non-isentropic ideal magnetohydrodynamic (MHD) equations with general initial data in the half-space whose boundary satisfies the perfectly conducting wall condition. By observing a special structure contributed by Lorentz force in vorticity analysis, we establish uniform estimates in suitable anisotropic Sobolev spaces with weights of Mach number determined by the number of material derivatives. We also observe that the entropy has the enhanced regularity in the direction of the magnetic field. These two observations help us get rid of the loss of derivatives and weights of Mach number in vorticity analysis caused by the simultaneous appearance of entropy, general initial data and the magnetic field, which is one of the major difficulties that do not appear in Euler equations or the isentropic problems. By utilizing the technique of Alinhac good unknowns, the anti-symmetric structure is preserved in the tangential estimates for the system differenetiated by high-order material derivatives. © 2024, CC BY.

关键词： Euler equations

CONVERGENCE RATES FOR BACKWARD SDEs DRIVEN BY LÉVY PROCESSES

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arXiv 2024年

作者： Liu, Chenguang Papapantoleon, Antonis Saplaouras, Alexandros DELFT INSTITUTE OF APPLIED MATHEMATICS EEMCS TU DELFT Delft2628 Netherlands DEPARTMENT OF MATHEMATICS SCHOOL OF APPLIED MATHEMATICAL AND PHYSICAL SCIENCES NATIONAL TECHNICAL UNIVERSITY OF ATHENS Zografou15780 Greece INSTITUTE OF APPLIED AND COMPUTATIONAL MATHEMATICS FORTH Heraklion70013 Greece

We consider Lévy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by Lévy processes that are approximated by BSDEs driven by their compound Poisson approximations. We are interested in the rate of convergence of the approximate BSDEs to the ones driven by the Lévy processes. The rate of convergence of the Lévy processes depends on the Blumenthal–Getoor index of the process. We derive the rate of convergence for the BSDEs in the L2-norm and in the Wasserstein distance, and show that, in both cases, this equals the rate of convergence of the corresponding Lévy process, and thus is *** Codes 60G51, 91G60, 60G44, 60G42 Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Efficient sampling of high-dimensional free energy landscapes using adaptive reinforced dynamics

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arXiv 2021年

作者： Wang, Dongdong Zhang, Linfeng Wang, Yanze Chang, Junhan Wang, Han Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States DP Technology Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China School of Mathematical Sciences Peking University Beijing China Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

Enhanced sampling methods such as metadynamics and umbrella sampling have become essential tools for exploring the configuration space of molecules and materials. At the same time, they have long faced a number of issues such as the inefficiency when dealing with a large number of collective variables (CVs) or systems with high free energy barriers. In this work, we show that with the clustering and adaptive tuning techniques, the reinforced dynamics (RiD) scheme can be used to efficiently explore the configuration space and free energy landscapes with a large number of CVs or systems with high free energy barriers. We illustrate this by studying various representative and challenging examples. Firstly we demonstrate the efficiency of adaptive RiD compared with other methods, and construct the 9-dimensional free energy landscape of peptoid trimer which has energy barriers of more than 8 kcal/mol. We then study the folding of the protein chignolin using 18 CVs. In this case, both the folding and unfolding rates are observed to be equal to 4.30 µs−1. Finally, we propose a protein structure refinement protocol based on RiD. This protocol allows us to efficiently employ more than 100 CVs for exploring the landscape of protein structures and it gives rise to an overall improvement of 14.6 units over the initial Global Distance Test-High Accuracy (GDT-HA) score. © 2021, CC BY.

关键词： Wave functions