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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

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Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

arXiv

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arXiv 2023年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas 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 Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

arXiv

引用

arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

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Interaction of Ionic Solution with Permeable Membranes:a Variational Approach

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数学研究（英文） 2024年第1期57卷 24-52页

作者： Shixin Xu Zilong Song Robert Eisenberg Huaxiong Huang Zu Chongzhi Center for Mathematics and Computational Sciences(CMCS) Global Health Research Center(GHRC)Duke Kunshan University8 Duke AveKunshan 215316China Mathematics and Statistics Department Utah State UniversityOld Main Hill LoganUT 84322USA Department of Applied Mathematics Illinois Institute of TechnologyChicagoIL 60616USA Department of Physiology and Biophysics Rush UniversityChicagoIL60612USA Research Centre for Mathematics Beijing Normal UniversityZhuhai 519087China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International CollegeZhuhaiGuangdong519088China Department of Mathematics and Statistics York University TorontoONM3J 1P3Canada

The movement of ionic solutions is an essential part of biology and ***,from nano-to microfluidics,is a burgeoning area of technology which is all about the movement of ionic solutions,on various *** cells,tissues,and organs of animals and plants depend on osmosis,as the movement of fluids is called in ***,the movement of fluids through channel proteins(that have a hole down their middle)is fluidics on an atomic *** fluids are complex fluids,with energy stored in many *** fluid flow is driven by gradients of concentration,chemical and electrical potential,and hydrostatic *** this paper,a series of sharp interface models are derived for ionic solution with permeable *** using the energy variation method,the unknown flux and interface conditions are de-rived *** start from the derivation the generic model for the general case that the density of solution varies with ionic solvent concentrations and membrane is *** the constant density and fix membrane cases are derived as special cases of the generic model.

关键词： ionic solution osmotic pressure Permeable membrane transmembrane flux

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High-speed and low-power molecular dynamics processing unit(MDPU)with ab initio accuracy

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npj computational Materials 2024年第1期10卷 559-568页

作者： Pinghui Mo Yujia Zhang Zhuoying Zhao Hanhan Sun Junhua Li Dawei Guan Xi Ding Xin Zhang Bo Chen Mengchao Shi Duo Zhang Denghui Lu Yinan Wang Jianxing Huang Fei Liu Xinyu Li Mohan Chen Jun Cheng Bin Liang Weinan E Jiayu Dai Linfeng Zhang Han Wang Jie Liu College of Integrated Circuits Hunan UniversityChangsha410082P.R.China College of Electrical and Information Engineering Hunan UniversityChangsha410082P.R.China College of Computer National University of Defense TechnologyChangsha410073P.R.China Department of Physics National University of Defense TechnologyChangsha410073P.R.China DP Technology 100080 BeijingP.R.China AI for Science Institute 100080 BeijingP.R.China Academy for Advanced Interdisciplinary Studies Peking University100871 BeijingP.R.China HEDPS CAPTCollege of EngineeringPeking University100871 BeijingP.R.China School of Mathematical Science Peking University100871 BeijingP.R.China State Key Laboratory of Physical Chemistry of Solid Surfaces iChEMCollege of Chemistry and Chemical EngineeringXiamen UniversityXiamen361005P.R.China School of Integrated Circuits Peking University100871 BeijingP.R.China Center for Machine Learning Research Peking University100871 BeijingP.R.China Institute of Applied Physics and Computational Mathematics 100088 BeijingP.R.China Greater Bay Area Institute for Innovation Hunan UniversityGuangzhou511300P.R.China Department of Electrical and Computer Engineering University of WashingtonSeattleWA98195USA

Molecular dynamics(MD)is an indispensable atomistic-scale computational tool widely-used in various *** the past decades,nearly all ab initio MD and machine-learning MD have been based on the general-purpose central/graphics processing units(CPU/GPU),which are well-known to suffer from their intrinsic“memory wall”and“power wall”***,nowadays MD calculations with ab initio accuracy are extremely time-consuming and power-consuming,imposing serious restrictions on the MD simulation size and *** solve this problem,here we propose a special-purpose MD processing unit(MDPU),which could reduce MD time and power consumption by about 103 times(109 times)compared to state-of-the-art machine-learningMD(ab initio MD)based on CPU/GPU,while keeping ab initio *** significantly-enhanced performance,the proposed MDPU may pave a way for the accurate atomistic-scale analysis of large-size and/or longduration problems which were impossible/impractical to compute before.

关键词： consuming power MDP

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Unextendible and Strongly Uncompletable Product Bases

arXiv

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arXiv 2024年

作者： Zhen, Xiao-Fan Zuo, Hui-Juan Shi, Fei Fei, Shao-Ming School of Mathematical Sciences Hebei Normal University Shijiazhuang050024 China State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing100876 China Hebei Key Laboratory of Computational Mathematics and Applications Shijiazhuang050024 China Hebei International Joint Research Center for Mathematics and Interdisciplinary Science Shijiazhuang050024 China Department of Computer Science School of Computing and Data Science University of Hong Kong Hong Kong999077 Hong Kong School of Mathematical Sciences Capital Normal University Beijing10048 China

In 2003, DiVincenzo et al. put forward the question that whether there exists an unextendible product basis (UPB) which is an uncompletable product basis (UCPB) in every bipartition [DiVincenzo et al. Commun. Math. Phys. 238, 379-410(2003)]. Recently, Shi et al. presented a UPB in tripartite systems that is also a strongly uncompletable product basis (SUCPB) in every bipartition [Shi et al. New J. Phys. 24, 113-025 (2022)]. However, whether there exist UPBs that are SUCPBs in only one or two bipartitions remains unknown. We provide a sufficient condition for the existence of SUCPBs based on a quasi U-tile structure. We analyze all possible cases about the relationship between UPBs and SUCPBs in tripartite systems. In particular, we construct a UPB with smaller size d3 − 3d2 + 1 in Cd Cd Cd, which is an SUCPB in every bipartition and has a smaller cardinality than the existing one. Copyright © 2024, The Authors. All rights reserved.

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Head-on collision of compressional shocks in two-dimensional Yukawa systems

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Physical Review E 2021年第1期103卷 013202-013202页

作者： Xia Ding Shaoyu Lu Tianyue Sun M. S. Murillo Yan Feng Center for Soft Condensed Matter Physics and Interdisciplinary Research School of Physical Science and Technology Soochow University Suzhou 215006 China Department of Computational Mathematics Science and Engineering Michigan State University East Lansing Michigan 48824 USA

The head-on collision of compressional shocks in two-dimensional dusty plasmas is investigated using both molecular dynamical and Langevin simulations. Two compressional shocks are generated from the inward compressional boundaries in simulations. It is found that, during the collision of shocks, there is a generally existing time delay of shocks τ, which diminishes monotonically with the increasing compressional speed of boundaries, corresponding to the time resolution of the studied system. Dispersive shock waves (DSWs) are generated around the shock front for some conditions. It is also found that the period of the DSW decreases monotonically with the inward compressional speed of boundaries, more substantially than the time delay of shocks τ. When the inward compressional speed of boundaries increases further, the DSWs gradually vanish. We speculate that, for these high compressional speeds of boundaries, the period of the DSW might be reduced to a comparable timescale of the time delay of shocks τ, i.e., the time resolution of our studied system, or even shorter, thus the DSW reasonably vanishes.

关键词： Dusty or complex plasma Plasma crystals Strongly-coupled plasmas

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Beyond a binary theorizing of prosociality

arXiv

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arXiv 2024年

作者： Shen, Chen He, Zhixue Guo, Hao Hu, Shuyue Tanimoto, Jun Shi, Lei Holme, Petter Faculty of Engineering Sciences Kyushu University Fukuoka816-8580 Japan School of Statistics and Mathematics Yunnan University of Finance and Economics Kunming650221 China Department of Computer Science and Technology Tsinghua University Beijing100084 China Shanghai Artificial Intelligence Laboratory Shanghai China Interdisciplinary Graduate School of Engineering Sciences Kyushu University Fukuoka816-8580 Japan Department of Computer Science Aalto University Espoo02150 Finland Center for Computational Social Science Kobe University Kobe650-0017 Japan

A stylized experiment, the public goods game, has taught us the peculiar reproducible fact that humans tend to contribute more to shared resources than expected from economically rational assumptions. There have been two competing explanations for this phenomenon: either contributing to the public good is an innate human trait (the prosocial preference hypothesis) or a transitory effect while learning the game (the confused learner hypothesis). We use large-scale experimental data from a novel experimental design to distinguish between these two hypotheses. By monitoring the effects of zealots (persistently cooperating bots) and varying the participants’ awareness of them, we find a considerably more complex scenario than previously reported. People indeed have a prosocial bias, but not to the degree that they always forego taking action to increase their profit. While our findings end the simplistic theorizing of prosociality in the public goods game, an observed positive, cooperative response to zealots has actionable policy implications. © 2024, CC BY-NC-SA.

关键词： Public policy

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Deep Potentials for Materials science

arXiv

引用

arXiv 2022年

作者： Wen, Tongqi Zhang, Linfeng Wang, Han Weinan, E. Srolovitz, David J. Department of Mechanical Engineering The University of Hong Kong Hong Kong DP Technology Beijing China AI for Science Institute Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China HEDPS CAPT College of Engineering Peking University Beijing China School of Mathematical Sciences Peking University Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton United States Shenzhen China

To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied;i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials. Copyright © 2022, The Authors. All rights reserved.

关键词： Calculations

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Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

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Physical Review Materials 2022年第2期6卷 025603-025603页

作者： Charles Emmett Maher Frank H. Stillinger Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by |x1|2p+|x2|2p+|x3|2p≤1, where p∈(0,∞) is a deformation parameter indicating to what extent the shape deviates from a sphere. As p increases from the sphere point (p=1), the superball tends to a cuboidal shape and approaches a cube in the p→∞ limit. As p→0.5, it approaches an octahedron, becomes a concave body with octahedral symmetry for p<0.5, and approaches a three-dimensional cross in the limit p→0. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction ϕ, average contact number Z¯) vary nonanalytically as p diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with 0.85≤p≤1.50. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors S(Q) and spectral densities χ̃V(Q), as the wave number Q tends to zero, and find that these packings are effectively hyperuniform for all values of p examined. We show that the mean width w¯ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution F(δ) and find that the pore sizes tend to decrease as |1−p| increases. From F(δ), we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of p. Additionally, we compute the diffusion “spreadability” S(t) [Torquato, Phys. Rev. E 104, 054102 (2021)] of

关键词： Granular packing

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