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Coupled MRT Lattice Boltzmann Study of Electrokinetic Mixing of Power-Law Fluids in Microchannels with Heterogeneous Surface Potential

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Advances in applied mathematics and Mechanics 2018年第6期10卷 1478-1496页

作者： Xuguang Yang Lei Wang Baochang Shi School of Mathematics and Computational Science Hunan First Normal UniversityChangsha 410205HunanChina Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomHong Kong School of Mathematics and Physics China University of GeosciencesWuhan430074HubeiChina School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074HubeiChina

The electrokinetic mixing,as a powerful technique in microfluidic devices,is widely used in many *** this study,a more general dynamic model,which consists of Poisson equation,Nernst-Planck equation and Navier-Stokes equations,is used to describe the electrokinetic mixing of non-Newtonian fluids in ***,a coupled multiple-relaxation-time(MRT)lattice Boltzmann(LB)framework is developed to solve this complicated multi-physics transport *** numerical simulations,we mainly consider the effects of the arrangement of nonuniform surface potentials and the power-law index on the mixing efficiency and the volumetric flow *** results show that the mixing efficiency and the volumetric flow rate of shear-thinning fluids are higher than that of shear-thickening fluids under the same *** is also shown that for both types of fluids,there should be a balance between the mixing and liquid transport in electrokinetic microfluidics.

关键词： Lattice Boltzmann method electrokinetic mixing non-Newtonian fluids

On the cross-validation bias due to unsupervised preprocessing

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arXiv 2019年

作者： Moscovich, Amit Rosset, Saharon Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistics and Operations Research Tel-Aviv University Tel-Aviv Israel

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centering, rescaling, dimensionality reduction, and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or response values) are generally safe to do prior to cross-validation. In this paper, we study three commonly-practiced preprocessing procedures prior to a regression analysis: (i) variance-based feature selection;(ii) grouping of rare categorical features;and (iii) feature rescaling. We demonstrate that unsupervised preprocessing can, in fact, introduce a substantial bias into cross-validation estimates and potentially hurt model selection. This bias may be either positive or negative and its exact magnitude depends on all the parameters of the problem in an intricate manner. Further research is needed to understand the real-world impact of this bias across different application domains, particularly when dealing with small sample sizes and high-dimensional *** Codes 62-07 Copyright © 2019, The Authors. All rights reserved.

关键词： Regression analysis

Direct Monitoring of Li2S2Evolution and Its Influence on the Reversible Capacities of Lithium-Sulfur Batteries

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Angewandte Chemie 2023年第11期135卷

作者： Dr. Yufeng Luo Dr. Zhenhan Fang Dr. Shaorong Duan Hengcai Wu Dr. Haitao Liu Dr. Yuxing Zhao Dr. Ke Wang Prof. Qunqing Li Prof. Shoushan Fan Prof. Zijian Zheng Prof. Wenhui Duan Prof. Yuegang Zhang Prof. Jiaping Wang Tsinghua-Foxconn Nanotechnology Research Center Tsinghua University Beijing 100084 China Laboratory for Advanced Interfacial Materials and Devices School of Fashion and Textiles The Hong Kong Polytechnic University Hong Kong SAR 99077 China Department of Physics Tsinghua University Beijing 100084 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China School of Materials Science and Technology China University of Geosciences Beijing 100083 China Frontier Science Center for Quantum Information Tsinghua University Beijing 100084 China State Key Laboratory of Low-Dimensional Quantum Physics Tsinghua University Beijing 100084 China

The polysulfide (PS) dissolution and low conductivity of lithium sulfides (Li 2 S) are generally considered the main reasons for limiting the reversible capacity of the lithium-sulfur (Li-S) system. However, as the inevitable intermediate between PSs and Li 2 S, lithium disulfide (Li 2 S 2 ) evolutions are always overlooked. Herein, Li 2 S 2 evolutions are monitored from the operando measurements on the pouch cell level. Results indicate that Li 2 S 2 undergoes slow electrochemical reduction and chemical disproportionation simultaneously during the discharging process, leading to further PS dissolution and Li 2 S generation without capacity contribution. Compared with the fully oxidized Li 2 S, Li 2 S 2 still residues at the end of the charging state. Therefore, instead of the considered Li 2 S and PSs, slow electrochemical conversions and side chemical reactions of Li 2 S 2 are the determining factors in limiting the sulfur utilization, corresponding to the poor reversible capacity of Li-S batteries.

关键词： Lithium Disulfides Chemical Reactions Conductive Interlayer Lithium Sulfur Battery Operando Measurement

Exponential convergence of the deep neural network approximation for analytic functions Dedicated to Professor Ta Tsien Li on the Occasion of His 80th Birthday

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Science China mathematics 2018年第10期61卷 1733-1740页

作者： Weinan E Qingcan Wang Department of Mathematics and PACM Princeton University Princeton NJ 08544 USA Center for Big Data Research Peking University Beijing 100871 China Beijing Institute of Big Data Research Beijing 100871 China Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.

关键词： neural networks approximation theory analytic functions

DeePMD-kit v3: A Multiple-Backend Framework for Machine Learning Potentials

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arXiv 2025年

作者： Zeng, Jinzhe Zhang, Duo Peng, Anyang Zhang, Xiangyu He, Sensen Wang, Yan Liu, Xinzijian Bi, Hangrui Li, Yifan Cai, Chun Zhang, Chengqian Du, Yiming Zhu, Jia-Xin Mo, Pinghui Huang, Zhengtao Zeng, Qiyu Shi, Shaochen Qin, Xuejian Yu, Zhaoxi Luo, Chenxing Ding, Ye Liu, Yun-Pei Shi, Ruosong Wang, Zhenyu Bore, Sigbjørn Løland Chang, Junhan Deng, Zhe Ding, Zhaohan Han, Siyuan Jiang, Wanrun Ke, Guolin Liu, Zhaoqing Lu, Denghui Muraoka, Koki Oliaei, Hananeh Singh, Anurag Kumar Que, Haohui Xu, Weihong Xu, Zhangmancang Zhuang, Yong-Bin Dai, Jiayu Giese, Timothy J. Jia, Weile Xu, Ben York, Darrin M. Zhang, Linfeng Wang, Han School of Artificial Intelligence and Data Science Unversity of Science and Technology of China Hefei China AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100871 China University of Chinese Academy of Sciences Beijing China Baidu Inc. Beijing China Department of Computer Science University of Toronto TorontoON Canada Department of Chemistry Princeton University PrincetonNJ08540 United States University of Chinese Academy of Sciences Beijing100871 China State Key Laboratory of Physical Chemistry of Solid Surfaces iChEM College of Chemistry and Chemical Engineering Xiamen University Xiamen361005 China College of Integrated Circuits Hunan University Changsha410082 China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing Center for Smart Materials and Device Integration School of Material Science and Engineering Wuhan University of Technology Wuhan430070 China College of Science National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Extreme Matter and Applications National University of Defense Technology Changsha410073 China ByteDance Research Beijing100098 China Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Ningbo315201 China College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Sciences Beijing100049 China Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education College of Chemistry Beijing Normal University Beijing100875 China Department of Geosciences Princeton University PrincetonNJ08544 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States IKKEM Fujian Xiamen361005 China Graduate

In recent years, machine learning potentials (MLPs) have become indispensable tools in physics, chemistry, and materials science, driving the development of software packages for molecular dynamics (MD) simulations and related applications. These packages, typically built on specific machine learning frameworks such as TensorFlow, PyTorch, or JAX, face integration challenges when advanced applications demand communication across different frameworks. The previous TensorFlow-based implementation of DeePMD-kit exemplified these limitations. In this work, we introduce DeePMD-kit version 3, a significant update featuring a multi-backend framework that supports TensorFlow, PyTorch, JAX, and PaddlePaddle backends, and demonstrate the versatility of this architecture through the integration of other MLPs packages and of Differentiable Molecular Force Field. This architecture allows seamless backend switching with minimal modifications, enabling users and developers to integrate DeePMD-kit with other packages using different machine learning frameworks. This innovation facilitates the development of more complex and interoperable workflows, paving the way for broader applications of MLPs in scientific research. Copyright © 2025, The Authors. All rights reserved.

关键词： Molecular dynamics

Reed-Muller codes polarize

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arXiv 2019年

作者： Abbe, Emmanuel Ye, Min Mathematics Institute School of Computer and Communication Sciences Epfl Switzerland Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University United States Department of Electrical Engineering Princeton University PrincetonNJ United States

Reed-Muller (RM) codes and polar codes are generated by the same matrix Gm= [1 0/1 1]⊗mbut using different subset of rows. RM codes select simply rows having largest weights. Polar codes select instead rows having the largest conditional mutual information proceeding top to down in Gm;while this is a more elaborate and channel-dependent rule, the top-to-down ordering has the advantage of making the conditional mutual information polarize, giving directly a capacity-achieving code on any binary memoryless symmetric channel (BMSC). RM codes are yet to be proved to have such property. In this paper, we reconnect RM codes to polarization theory. It is shown that proceeding in the RM code ordering, i.e., not top-to-down but from the lightest to the heaviest rows in Gm, the conditional mutual information again polarizes. We further demonstrate that it does so faster than for polar codes. This implies that Gmcontains another code, different than the polar code and called here the twin code, that is provably capacity-achieving on any BMSC. This proves a necessary condition for RM codes to achieve capacity on BMSCs. It further gives a sufficient condition if the rows with largest conditional mutual information correspond to the heaviest rows, i.e., if the twin code is the RM code. We show here that the two codes bare similarity with each other and give further evidence that they are likely the same. Copyright © 2019, The Authors. All rights reserved.

关键词： Forward error correction

ON THE MOTION OF CURVED DISLOCATIONS IN THREE DIMENSIONS: SIMPLIFIED LINEARIZED ELASTICITY

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arXiv 2020年

作者： Fonseca, Irene Ginster, Janusz Wojtowytsch, Stephan Department of Mathematical Sciences Carnegie-Mellon University 5000 Forbes Avenue PittsburghPA15213 United States Institut für Mathematik Humboldt-Universität zu Berlin Rudower Chaussee 25 Berlin12489 Germany Program in Applied and Computational Mathematics Princeton University 205 Fine Hall PrincetonNJ08544 United States

It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the negative gradient of the elastic energy asymptotically approaches the mean curvature of the curve as the cutoff radius converges to zero. Rigorous error bounds in Hölder spaces are provided. As an application, convergence of dislocations moving by the gradient flow of the elastic energy to dislocations moving by the gradient flow of the arclength functional, when the motion law is given by an H1-type dissipation, and convergence to curve shortening flow in co-dimension 2 for the usual L2-dissipation is established. In the second scenario, existence and regularity are assumed while the H1-gradient flow is treated in full generality (for short time). The methods developed here are a blueprint for the more physical setting of linearized isotropic *** Codes 35K93, 35Q74, 74N05 Copyright © 2020, The Authors. All rights reserved.

关键词： Elasticity

Multiscale PHATE Exploration of SARS-CoV-2 Data Reveals Multimodal Signatures of Disease

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Research Square

Research Square 2021年

作者： Kuchroo, Manik Huang, Jessie Wong, Patrick Grenier, Jean-Christophe Shung, Dennis Tong, Alexander Lucas, Carolina Klein, Jon Burkhardt, Daniel B. Gigante, Scott Godavarthi, Abhinav Rieck, Bastian Israelow, Benjamin Simonov, Michael Mao, Tianyang Oh, Ji Eun Silva, Julio Takahashi, Takehiro Odio, Camila D. Casanovas-Massana, Arnau Fournier, John Farhadian, Shelli Dela Cruz, Charles S. Ko, Albert I. Hirn, Matthew J. Wilson, F. Perry Hussin, Julie Wolf, Guy Iwasaki, Akiko Krishnaswamy, Smita Department of Neuroscience Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States Department of Immunobiology Yale University New HavenCT United States Montreal Heart Institute MontréalQC Canada Department of Medicine Yale University New HavenCT United States Department of Genetics Yale University New HavenCT United States Computational Biology Bioinformatics Program Yale University New HavenCT United States Department of Applied Mathematics Yale University New HavenCT United States Department of Biosystems Science and Engineering ETH Zurich Switzerland Department of Epidemiology of Microbial Diseases Yale School of Public Health New HavenCT United States Department of Medicine Section of Infectious Diseases Yale University School of Medicine New HavenCT United States Department of Medicine Section of Pulmonary and Critical Care Medicine Yale University School of Medicine New HavenCT United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI United States Department of Mathematics Michigan State University East LansingMI United States Clinical and Translational Research Accelerator Department of Medicine Yale University New HavenCT United States Faculty of Medicine Université de Montréal Québec Canada Mila – Quebec AI institute MontréalQC Canada Department of Mathematics and Statistics Université de Montréal MontréalQC Canada Howard Hughes Medical Institute Chevy ChaseMD United States

The biomedical community is producing increasingly high dimensional datasets, integrated from hundreds of patient samples, which current computational techniques struggle to explore. To uncover biological meaning from these complex datasets, we present an approach called Multiscale PHATE, which learns abstracted biological features from data that can be directly predictive of disease. Built on a coarse graining process called diffusion condensation, Multiscale PHATE learns a data topology that can be analyzed at coarse levels for high level summarizations of data, as well as at fine levels for detailed representations on subsets. We apply Multiscale PHATE to study the immune response to COVID-19 in 54 million cells from 168 hospitalized patients. Through our analysis of patient samples, we identify CD16hiCD66blo neutrophil and IFNγ+GranzymeB+ Th17 cell responses enriched in patients who die. Furthermore, we show that population groupings Multiscale PHATE discovers can be directly fed into a classifier to predict disease outcome. We also use Multiscale PHATE-derived features to construct two different manifolds of patients, one from abstracted flow cytometry features and another directly on patient clinical features, both associating immune subsets and clinical markers with outcome. © 2021, CC BY.

关键词： Coronavirus

mathematics for cryo-electron microscopy

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arXiv 2018年

作者： Singer, Amit Department of Mathematics Program in Applied and Computational Mathematics Princeton University

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Methods as Method of the Year 2015, large scale investments in cryo-EM facilities are being made all over the world, and the Nobel Prize in Chemistry 2017 was awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM.92C55, 68U10, 44A12, 62H12, 33C55, 90C22 Copyright © 2018, The Authors. All rights reserved.

关键词： Electron microscopes