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arXiv 2020年

作者： Hou, Xiaobo Tian, Xueting Zhang, Yiwei School of Mathematical Sciences Fudan University Shanghai200433 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

Pfister and Sullivan proved that if a topological dynamical system (X, T) satisfies almost product property and uniform separation property, then for each nonempty compact subset K of invariant measures, the entropy of saturated set GK satisfies (0.1) hBtop(T, GK) = inf{h(T, µ): µ ∈ K}, where hBtop(T, GK) is Bowen's topological entropy of T on GK, and h(T, µ) is the Kolmogorov-Sinai entropy of µ. In this paper, we investigate topological complexity of GK by replacing Bowen's topological entropy with upper capacity entropy and packing entropy in (0.1) and obtain the following formulas: hUCtop (T, GK) = htop(T, X) and hPtop(T, GK) = sup{h(T, µ): µ ∈ K}, where hUCtop (T, GK) is the upper capacity entropy of T on GK and hPtop(T, GK) is the packing entropy of T on GK. In the proof of these two formulas, uniform separation property is unnecessary. As applications, when (X, T) is a transitive Anosov diffeomorphism on a compact manifold, we show that (1) for any continuous function f, hUCtop (T, Sfop) = htop(T, X) where Sfop is the set of initial values of f-optimal orbits;(2) there exists a Baire generic subset F in the space of continuous functions and an open and dense subset G in the space of Hölder continuous or C1 smooth functions such that for any f ∈ F or f ∈ G, hBtop(T, Sfop) = hPtop(T, Sfop) = 0;(3) for any f ∈ G, hUCtop (T, SfMR) = 0 where SfMR is the set of initial values of measure-recurrent optimal orbits;(4) there exists a dense subset in the space of continuous functions such that for any f in the subset, hBtop(T, Sfop) = hPtop(T, Sfop) > 0. For equilibrium states, we prove that (1) for any continuous function f and equilibrium state µ of f, hUCtop (T, Gµ) = htop(T, X);(2) if f is Hölder continuous and is not cohomologous to a constant, then hBtop(T, Gµ) = hPtop(T, Gµ) fopMSC Codes 37C50, 37B20, 37B05, 37D45, 37C45 © 2020, CC BY.

关键词： Entropy

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Graph denoising with framelet regularizer

arXiv

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arXiv 2021年

作者： Zhou, Bingxin Li, Ruikun Zheng, Xuebin Wang, Yu Guang Gao, Junbin The University of Sydney Business School The University of Sydney NSW Australia Institute of Natural Sciences Shanghai Jiao Tong University Shanghai China Institute of Natural Sciences School of Mathematical Sciences Key Laboratory of Scientific and Engineering Computing of Ministry of Education Center for Mathematics of Artificial Intelligence Institute Shanghai Jiao Tong University Shanghai China Shanghai Artificial Intelligence Laboratory Shanghai China School of Mathematics and Statistics The University of New South Wales Australia

As graph data collected from the real world is merely noise-free, a practical representation of graphs should be robust to noise. Existing research usually focuses on feature smoothing but leaves the geometric structure untouched. Furthermore, most work takes L2-norm that pursues a global smoothness, which limits the expressivity of graph neural networks. This paper tailors regularizers for graph data in terms of both feature and structure noises, where the objective function is efficiently solved with the alternating direction method of multipliers (ADMM). The proposed scheme allows to take multiple layers without the concern of over-smoothing, and it guarantees convergence to the optimal solutions. Empirical study proves that our model achieves significantly better performance compared with popular graph convolutions even when the graph is heavily contaminated. © 2021, CC BY.

关键词： Constrained optimization

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Seeking Consensus on Subspaces in Federated Principal Component Analysis

arXiv

引用

arXiv 2020年

作者： Wang, Lei Liu, Xin Zhang, Yin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper, we develop an algorithm for federated principal component analysis (PCA) with emphases on both communication efficiency and data privacy. Generally speaking, federated PCA algorithms based on direct adaptations of classic iterative methods, such as simultaneous subspace iterations (SSI), are unable to preserve data privacy, while algorithms based on variable-splitting and consensus-seeking, such as alternating direction methods of multipliers (ADMM), lack in communication-efficiency. In this work, we propose a novel consensus-seeking formulation by equalizing subspaces spanned by splitting variables instead of equalizing variables themselves, thus greatly relaxing feasibility restrictions and allowing much faster convergence. Then we develop an ADMM-like algorithm with several special features to make it practically efficient, including a low-rank multiplier formula and techniques for treating subproblems. We establish that the proposed algorithm can better protect data privacy than classic methods adapted to the federated PCA setting. We derive convergence results, including a worst-case complexity estimate, for the proposed ADMM-like algorithm in the presence of the nonlinear equality constraints. Extensive empirical results are presented to show that the new algorithm, while enhancing data privacy, requires far fewer rounds of communication than existing peer algorithms for federated PCA. Copyright © 2020, The Authors. All rights reserved.

关键词： Principal component analysis

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Liouville-type theorems for steady Navier-Stokes system in a slab with Navier boundary conditions

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Journal of Differential Equations 2025年 443卷

作者： Jingwen Han Yun Wang Chunjing Xie School of Mathematical Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China School of Mathematical Sciences Center for dynamical systems and differential equations Soochow University Suzhou China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing and CMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

In this paper, the Liouville-type theorems for the steady Navier-Stokes system in a slab supplemented with Navier boundary conditions are investigated. Specifically, we prove that any bounded smooth solution must be zero if either the swirl or radial velocity is axisymmetric, or r u r decays to zero as r tends to infinity. When the velocity is not big in L ∞ -space, the general three-dimensional steady Navier-Stokes flow in a slab with the Navier boundary conditions must be a Poiseuille type flow. The key idea of the proof is to establish the Saint-Venant type estimates that characterize the growth of Dirichlet integral of nontrivial solutions.

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Manipulation of cholesteric liquid crystal phase behavior and molecular assembly by molecular chirality

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Physical Review E 2019年第2期100卷 022703-022703页

作者： Liang Wu Huai Sun School of Chemistry and Chemical Engineering Materials Genome Initiative Center and Key Laboratory of Scientific and Engineering Computing of Ministry of Education Shanghai Jiao Tong University Shanghai 200240 China

Molecular simulation is used to study the effect of molecular chirality on liquid crystalline phase transition and molecular assembly behavior. Based on a flexible chain (FCh) model with helical arrangement of side beads, the phase behavior of FCh models with various molecular chiralities are studied as functions of pressure (or density). By modifying the molecular chirality of FCh, we can manipulate the relative stability of the nematic and cholesteric phases continuously; and we found that increasing molecular chirality may destabilize cholesteric order due to the effective reduction of chiral interactions. A semismectic phase is identified in the high-density region, in which the two-dimensional fluid layers overlap due to shift alignment formed by FCh particles. The global phase diagram of the FCh model is constructed and the potential energy surface is calculated to elucidate the formation of cholesteric phase in terms of two-body interactions.

关键词： Liquid crystal phase transitions Liquid crystals Molecular dynamics

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Low-order moments of the velocity gradient in homogeneous compressible turbulence

arXiv

引用

arXiv 2022年

作者： Yang, PingFan Fang, Jian Fang, Le Pumir, Alain Xu, Haitao The State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing100190 China School of Engineering Sciences University of Chinese Academy of Sciences Beijing100049 China Center for Combustion Energy School of Aerospace Engineering Tsinghua University Beijing100084 China Scientific Computing Department STFC Daresbury Laboratory WarringtonWA4 4AD United Kingdom LCS Ecole Centrale de Pékin Beihang University Beijing100191 China Laboratoire de Physique Ecole Normale Supérieure de Lyon CNRS Université de Lyon LyonF-69007 France Max Planck Institute for Dynamics and Self-Organization GöttingenD-37077 Germany

We derive from first principles analytic relations for the second and third order moments of the velocity gradient mij = ∂ui/∂xj in compressible turbulence, which generalize known relations in incompressible flows. These relations, although derived for homogeneous flows, hold approximately for a mixing layer. We also discuss how to apply these relations to determine all the second and third moments of the velocity gradient experimentally. Copyright © 2022, The Authors. All rights reserved.

关键词： Incompressible flow

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The Role of Permanent and Induced Electrostatic Dipole Moments for Schottky Barriersin Janus MXY/Graphene Heterostructures: A First Principles Study

arXiv

引用

arXiv 2022年

作者： Chen, Yu-Qi Zhang, Huan-Huan Wen, Bo Li, Xi-Bo Chai, Yi-Feng Xu, Ying Wei, Xiao-Lin Yin, Wen-Jin Teobaldi, Gilberto School of Physics and Electronic Science Hunan University of Science and Technology Xiangtan411201 China Key Laboratory of Intelligent Sensors and Advanced Sensing Materials of Hunan Province Hunan University of Science and Technology Xiangtan411201 China School of Physics and Electronics Henan University Kaifeng475001 China Department of Physics Jinan University Guangzhou510632 China Department of Physics Laboratory for Quantum Engineering and Micro-Nano Energy Technology Xiangtan University Hunan Xiangtan411105 China Scientific Computing Department STFC UKRI Rutherford Appleton Laboratory Harwell Campus DidcotOX11 0QX United Kingdom School of Chemistry University of Southampton High Field Southampton SO17 1BJ United Kingdom

The Schottky barrier height (ESBH) is a crucialfactorin determining the transport properties of semiconductor materials as it directly regulatesthe carrier mobility in opto-electronics *** principle, van der Waals (vdW)Janusheterostructures offer an appealing avenue to controlling the ***, the underlying atomistic mechanismsare far from understood conclusively, which prompts for further research in the topic. To this end,here, we carryout an extensive first principles study of the electronic properties and ESHBof several vdW Janus MXY/Graphene(M=Mo, W;X, Y=S, Se, Te) *** results of the simulations show that by changing the composition and geometry of the heterostructure's interface, it is possible to controlitselectrical contact, thence electron transport properties, from Ohmicto Schottky with nearly one order of magnitude variationsin the *** analysis of the simulations enables rationalization of this highly attractive propertyon the basis of theinterplaybetween the permanent dipole moment of the Janus MXYsheet and the induced one due to interfacial charge redistribution at the MXY/Grinterface. Such an interplayis shown to be highly effectivein alteringthe electrostatic potential difference acrossthe vdW Janus heterostructure, determining its ESBH, thence Schottky (Ohmic) contact type. These computational findings contribute guidelines to control electrical contactsinJanus heterostructurestowardsrationaldesign of electrical contacts in nanoscale devices. © 2022, CC BY.

关键词： Van der Waals forces

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Formation of singularity for the rotating shallow water system

arXiv

引用

arXiv 2020年

作者： Huang, Yupei Chunjing, X.I.E. Department of mathematics Duke University United States School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing SHL-MAC Shanghai Jiao Tong Vniversity 800 Dongchuan Road Shanghai China

In this paper, we investigate the formation of singularity for general two dimensional and radially symmetric solutions for rotating shallow water system from different aspects. First, the formation of singularity is proved via the study for the associated moments for two dimensional solutions. For the radial symmetric solutions, the formation of singularity is established for the initial data with compact support. Finally, the global existence or formation of singularity for the radial symmetric solutions of the rotating shallow water system are analyzed in detail when the solutions are of the form with separated variables. Copyright © 2020, The Authors. All rights reserved.

关键词： Waterworks

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Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

arXiv

引用

arXiv 2021年

作者： Cao, Waixiang Li, Dongfang Zhang, Zhimin School of Mathematical Sciences Beijing Normal University Beijing100875 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Beijing Computational Science Research Center Beijing100193 China Department of Mathematics Wayne State University DetroitMI48202 United States

In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without time-step dependent on the spatial mesh size. The key is to estimate directly the solution bounds in the H2-norm for both the nonlinear wave equation and the corresponding fully discrete scheme, while the previous investigations rely on the temporal-spatial error splitting approach. Numerical examples are presented to confirm energy-conserving properties, unconditional convergence, and optimal error estimates, respectively, of the proposed fully discrete *** Codes 65M60, 65M12, 65N12 © 2021, CC0.

关键词： Wave equations

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High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state SN transport equation

arXiv

引用

arXiv 2021年

作者： Ren, Yupeng Xing, Yulong Wang, Dean Qiu, Jianxian School of Mathematical Sciences Xiamen University XiamenFujian361005 China Department of Mathematics Ohio State University ColumbusOH43210 United States Department of Mechanical and Aerospace Engineering Ohio State University ColumbusOH43210 United States School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University XiamenFujian361005 China

In this paper, we propose to combine the fifth order Hermite weighted essentially non-oscillatory (HWENO) scheme and fast sweeping method (FSM) for the solution of the steady-state SN transport equation in the finite volume framework. It is well-known that the SN transport equation asymptotically converges to a macroscopic diffusion equation in the limit of optically thick systems with small absorption and sources. Numerical methods which can preserve the asymptotic limit are referred to as asymptotic preserving methods. In the one-dimensional case, we provide the analysis to demonstrate the asymptotic preserving property of the high order finite volume HWENO method, by showing that its cell-edge and cell-average fluxes possess the thick diffusion limit. Numerical results in both one- and two- dimensions are presented to validate its asymptotic preserving property. A hybrid strategy to compute the nonlinear weights in the HWENO reconstruction is introduced to save computational cost. Extensive one- and two-dimensional numerical experiments are performed to verify the accuracy, asymptotic preserving property and positivity of the proposed HWENO FSM. Copyright © 2021, The Authors. All rights reserved.

关键词： Diffusion

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