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Phase-field simulations of the effect of temperature and interface for zirconiumδ-hydrides

Chinese Physics B 2024年第4期33卷 701-710页

作者：陈子航盛杰刘瑜施小明黄厚兵许可王越超武帅孙博刘海风宋海峰 School of Materials Science and Engineering Beijing Institute of TechnologyBeijing 100081China Advanced Research Institute of Multidisciplinary Science Beijing Institute of TechnologyBeijing 100081China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Department of Physics University of Science and Technology BeijingBeijing 100083China

Hydride precipitation in zirconium cladding materials can damage their integrity and *** temperature and material defects have a significant effect on the dynamic growth of *** this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium *** results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride *** ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree *** escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection ***,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial ***,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack *** research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.

关键词： zirconium hydride phase-field method temperature effect mismatch degree

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Some mathematical aspects of Anderson localization:boundary effect,multimodality,and bifurcation

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Communications in Theoretical Physics 2022年第11期74卷 45-64页

作者： Chen Jia Ziqi Liu Zhimin Zhang Applied and Computational Mathematics Division Beijing Computational Science Research CenterBeijing 100193China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Department of Mathematics Wayne State UniversityDetroitMichigan 48202United States of America

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered *** we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach,and further investigate some mathematical aspects of Anderson localization that are rarely discussed ***,we observe that under the Neumann boundary condition,the low energy quantum states are localized on the boundary of the domain with high *** provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional ***,we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary ***,we examine a bifurcation phenomenon of the localization subregion as the strength of disorder *** critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.

关键词： landscape spectrum eigenvalue eigenmode eigenfunction elliptic operator Schr?dinger operator confinement

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Fast decisions reflect biases;slow decisions do not

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Physical Review E 2024年第2期110卷 024305-024305页

作者： Samantha Linn Sean D. Lawley Bhargav R. Karamched Zachary P. Kilpatrick Krešimir Josić Department of Mathematics Institute of Molecular Biophysics Program in Neuroscience Department of Applied Mathematics Department of Biology and Biochemistry

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased and hence make better choices. We obtain asymptotic expressions in the large population limit quantifying how agents' initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in nontrivial ways to determine the reliability of decisions in a group.

关键词： Social networks Diffusion & random walks Extreme event statistics First passage problems Fokker–Planck equation Langevin equation Monte Carlo methods Stochastic analysis Stochastic differential equations

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A localized Fourier collocation method for 2D and 3D elliptic partial differential equations:Theory and MATLAB code

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International Journal of Mechanical System Dynamics 2022年第4期2卷 339-351页

作者： Yan Gu Zhuojia Fu Mikhail V.Golub Department of Computational Mathematics School of Mathematics and StatisticsQingdao UniversityQingdaoChina Department of Engineering Mechanics College of Mechanics and MaterialsHohai UniversityNanjingChina Department of Applied Mathematics Institute for MathematicsMechanics and InformaticsKuban State UniversityKrasnodarRussian Federation

A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value *** method first discretizes the entire domain into a set of overlapping small subdomains,and then in each of the subdomains,the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation *** key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale *** present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape *** numerical experiments involving Poisson,Helmholtz,and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.

关键词： meshless method collocation method Fourier basis functions large-scale problem

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A Flow Artist for High-Dimensional Cellular Data 33

A Flow Artist for High-Dimensional Cellular Data

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33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Yale University Department of Mathematics United States Pomona College Department of Mathematics United States University of Washington Department of Statistics United States Boise State University Department of Mathematics United States Yale University Department of Computer Science United States Yale University Applied Mathematics Program United States Yale University Computational Biology and Bioinformatics Program United States

ISBN: (纸本)9798350324112

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023 IEEE.

关键词： RNA

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A folding preprocess for the max k-cut problem

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Optimization Letters 2025年第5期19卷 899-917页

作者： Fakhimi, Ramin Validi, Hamidreza Hicks, Illya V. Terlaky, Tamás Zuluaga, Luis F. Department of Industrial and Systems Engineering Lehigh University Bethlehem United States Department of Industrial Manufacturing & Systems Engineering Texas Tech University Lubbock United States Department of Computational Applied Mathematics & Operations Research Rice University Houston United States

Given graph G=(V,E) with vertex set V and edge set E, the max k-cut problem seeks to partition the vertex set V into at most k subsets that maximize the weight (number) of edges with endpoints in different parts. This paper proposes a graph folding procedure (i.e., a procedure that reduces the number of the vertices and edges of graph G) for the weighted max k-cut problem that may help reduce the problem’s dimensionality. While our theoretical results hold for any k≥2, our computational results show the effectiveness of the proposed preprocess only for k=2 and on two sets of instances. Furthermore, we observe that the preprocess improves the performance of a MIP solver on a set of large-scale instances of the max cut problem. © The Author(s) 2025.

关键词： Network theory (graphs)

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Machine learning potential assisted exploration of complex defect potential energy surfaces

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npj computational Materials 2024年第1期10卷 3017-3023页

作者： Chao Jiang Chris A.Marianetti Marat Khafizov David H.Hurley Computational Mechanics and Materials Department Idaho National LaboratoryIdaho FallsID 83415USA Department of Applied Physics and Applied Mathematics Columbia UniversityNew YorkNY 10027USA Department of Mechanical and Aerospace Engineering The Ohio State UniversityColumbusOH 43210USA Materials Science and Engineering Department Idaho National LaboratoryIdaho FallsID 83415USA

Atomic-scale defects generated in materials under both equilibrium and irradiation conditions can significantly impact their physical and mechanical *** the energetically most favorable ground-state configurations of these defects is an important step towards the fundamental understanding of their influence on the performance of materials ranging from photovoltaics to advanced nuclear ***,using fluorite-structured thorium dioxide(ThO_(2))as an exemplar,we demonstrate how density functional theory and machine learning interatomic potential can be synergistically combined into a powerful tool that enables exhaustive exploration of the large configuration spaces of small point defect *** study leads to several unexpected discoveries,including defect polymorphism and ground-state structures that defy our physical *** physical origins of these unexpected findings are elucidated using a local cluster expansion model developed in this work.

关键词： properties defect potential

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Essentially Commuting with a Unitary

arXiv

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arXiv 2025年

作者： Chung, Jui-Hui Shapiro, Jacob Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States

Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the set of path-connected components of the orthogonal projections which essentially commute with R and obey a non-triviality condition, and prove it is bijective with Z. Copyright © 2025, The Authors. All rights reserved.

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Generalized Multiscale Finite Element Method for Multicontinuum Coupled Flow and Transport Model

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Lobachevskii Journal of mathematics 2024年第11期45卷 5343-5356页

作者： Ammosov, D.A. Huang, J. Leung, W.T. Shan, B. Computational Technologies and Artificial Intelligence North-Eastern Federal University Yakutsk 677980 Russian Federation School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Hunan Xiangtan 411105 China Department of Mathematics City University of Hong Kong Hong Kong Department of Mathematics Texas A & M University College Station 77843 TX United States

Abstract: In this paper, we consider a coupled flow and transport process described by partial differential equations for pressure and concentration. We derive the multicontinuum coupled flow and transport model using the multicontinuum homogenization method. We formulate cell problems with constraints that take into account various homogenized effects. For the resulting multicontinuum model, we develop a multiscale solver based on the Generalized Multiscale Finite Element Method. The combined approach of multicontinuum and multiscale modeling makes it possible to consider complex heterogeneous media with high contrast. We present numerical results for a model problem with two continua and heterogeneous coefficients separable into microscopic and macroscopic parts. The results show the high efficiency of the proposed multiscale approach. © Pleiades Publishing, Ltd. 2024.

关键词： coupled flow and transport generalized multiscale finite element method homogenization miscible displacement multicontinuum

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Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

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Physical Review Research 2024年第3期6卷 033029-033029页

作者： Zhiyan Ding Taehee Ko Jiahao Yao Lin Lin Xiantao Li Department of Mathematics School of Computational Sciences Applied Mathematics and Computational Research Division Challenge Institute for Quantum Computation

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings.

关键词： Machine learning Quantum algorithms & computation Quantum simulation

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