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Spectral gap of sparse bistochastic matrices with exchangeable rows

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arXiv 2018年

作者： Bordenave, Charles Qiu, Yanqi Zhang, Yiwei Institut de Mathématiques de Marseille CNRS Aix-Marseille University 39 Rue Frédéric Joliot Curie Marseille13013 France Institute of Mathematics and Hua Loo-Keng Key Laboratory of Mathematics AMSS Chinese Academy of Sciences Beijing100190 China CNRS Institut de Mathématiques de Toulouse University of Toulouse III 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

We consider a random bistochastic matrix of size n of the form MQ where M is a uniformly distributed permutation matrix and Q is a given bistochastic matrix. Under sparsity and regularity assumptions on Q, we prove that the second largest eigenvalue of MQ is essentially bounded by the normalized Hilbert-Schmidt norm of Q when n grows large. We apply this result to random walks on random regular digraphs.60B20, 60C05, 05C80, 05C38 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Anomalous time-scaling of extreme events in infinite systems and birkhoff sums of infinite observables

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arXiv 2018年

作者： Galatolo, Stefano Holland, Mark Persson, Tomas Zhang, Yiwei Dipartimento di Matematica Via Buonattoti 1 Pisa56127 Italy North Park Road EXETEREX4 4QF United Kingdom Centre for Mathematical Sciences Lund University Box 118 Lund221 00 Sweden Scool 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

We establish quantitative results for the statistical behaviour of infinite systems. We consider two kinds of infinite system: i) a conservative dynamical system (f, X, µ) preserving a σ-finite measure µ such that µ(X) = ∞;ii) the case where µ is a probability measure but we consider the statistical behaviour of an observable φ: X → [0, ∞) which is non-integrable: R φ dµ = ∞. In the first part of this work we study the behaviour of Birkhoff sums of systems of the kind ii). For certain weakly chaotic systems, we show that these sums can be strongly oscillating. However, if the system has superpolynomial decay of correlations or has a Markov structure, then we show this oscillation cannot happen. In this case we prove a general relation between the behavior of φ, the local dimension of µ, and the scaling rate of the growth of Birkhoff sums of φ as time tends to infinity. We then establish several important consequences which apply to infinite systems of the kind i). This includes showing anomalous scalings in extreme event limit laws, or entrance time statistics. We apply our findings to non-uniformly hyperbolic systems preserving an infinite measure, establishing anomalous scalings in the case of logarithm laws of entrance times, dynamical Borel-Cantelli lemmas, almost sure growth rates of extremes, and dynamical run length functions.37A40, 37A50, 37A25, 60G75, 37D25 Copyright © 2018, The Authors. All rights reserved.

关键词： Chaotic systems

ON COMPUTABILITY OF EQUILIBRIUM STATES

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arXiv 2023年

作者： Binder, Ilia He, Qiandu Li, Zhiqiang Zhang, Yiwei Department of Mathematics University of Toronto Bahen Centre 40 St. George St. TorontoONM5S 2E4 Canada School of Mathematical Sciences Peking University Beijing100871 China School of Mathematical Sciences Beijing International Center for Mathematical Research Peking University Beijing100871 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

Equilibrium states are natural dynamical analogs of Gibbs states in thermodynamic formalism. This paper is devoted to the study of their computability in the sense of Computable Analysis. We show that the unique equilibrium state associated to a pair of a computable, topologically exact, distance-expanding, open map T: X → X and a computable Hölder continuous potential : X → R is always computable. Furthermore, the Hausdorff dimension of the Julia set and the equilibrium state for the geometric potential of a computable hyperbolic rational map are computable. On the other hand, we introduce a mechanism to establish non-uniqueness of equilibrium states. We also present some computable dynamical systems whose equilibrium states are all *** Codes Primary: 03D78, Secondary: 37D35, 37D20, 37F15 Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamical systems

A fully discrete energy stable scheme for a phase-field moving contact line model with variabledensities and viscosities

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arXiv 2018年

作者： Zhu, Guangpu Chen, Huangxin Sun, Shuyu Yao, Jun Qingdao266580 China Sch. of Math. Sci. and Fujian Prov. Key Lab. on Math. Modeling and High Perf. Scientific Computing Xiamen University Xiamen361005 China Computational Transport Phenomena Laboratory Division of Physical Science and Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this work, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model consists of a Cahn-Hilliard equation, a Navier-Stokes equation and the generalized Navier boundary condition. A scalar auxiliary variable is introduced to transform the nonlinear potential into an equivalent form, allowing the nonlinear potential to be treated effectively and semi-explicitly. A pressure stabilization method is used to decouple the computation of velocity and pressure. Some subtle implicit-explicit treatments are adopted to deal with convention and stress terms. An artificial term is added to balance the explicit nonlinear term originating from the surface energy at fluid-solid interface. We establisharigorous proof of energy stability for the proposed time-marching *** a finite difference methodon staggered grids isusedto spatially discretize the constructed time-marchingscheme. We prove that the fully discrete scheme satisfiesthe discrete energy dissipationlaw. Numerical results demonstrate accuracy and energy stability of the proposed scheme. Using our numerical scheme, we analyze theevolution of kinetic energy, mixing energy and surface energy at fluid-solid interfaceduring the bubble rising process. Three-dimensional droplet spreading is also investigated onachemically patterned surface. Our numerical simulation accurately predicts the expected energy evolutions and it successfully reproduces expected phenomenathat an oil droplet contractsinwardson a hydrophobiczone and spreadsoutwards quickly on a hydrophiliczone. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite difference method

Fast IMEX time integration of nonlinear stiff fractional differential equations

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arXiv 2019年

作者： Zhou, Yongtao Suzuki, Jorge L. Zhang, Chengjian Zayernouri, Mohsen School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering Michigan State University East LansingMI48824 United States Department of Mechanical Engineering Michigan State University East LansingMI48824 United States 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 Department of Mechanical Engineering Department of Statistics and Probability Michigan State University East LansingMI48824 United States

Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the inverse power-law kernels deteriorates the accuracy and efficiency of many existing numerical methods. We develop two efficient first- and second-order implicit-explicit (IMEX) methods for accurate time-integration of stiff/nonlinear fractional differential equations with fractional order α ∈ (0, 1] and prove their convergence and linear stability properties. The developed methods are based on a linear multi-step fractional Adams-Moulton method (FAMM), followed by the extrapolation of the nonlinear force terms. In order to handle the singularities nearby the initial time, we employ Lubich-like corrections to the resulting fractional operators. The obtained linear stability regions of the developed IMEX methods are larger than existing IMEX methods in the literature. Furthermore, the size of the stability regions increase with the decrease of fractional order values, which is suitable for stiff problems. We also rewrite the resulting IMEX methods in the language of nonlinear Toeplitz systems, where we employ a fast inversion scheme to achieve a computational complexity of O(N log N), where N denotes the number of time-steps. Our computational results demonstrate that the developed schemes can achieve global first- and second-order accuracy for highly-oscillatory stiff/nonlinear problems with singularities. Copyright © 2019, The Authors. All rights reserved.

关键词： Matrix algebra

LOW MACH NUMBER LIMIT AND FAR FIELD CONVERGENCE RATES OF POTENTIAL FLOWS IN MULTI-DIMENSIONAL NOZZLES WITH AN OBSTACLE INSIDE

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arXiv 2020年

作者： Ma, Lei Wang, Tian-Yi Xie, Chunjing School of Mathematical Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China Department of Mathematics School of Science Wuhan University of Technology 122 Luoshi Road Wuhan Hubei430070 China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing and SHL-MAC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

This paper considers the low Mach number limit and far field convergence rates of steady Euler flows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First, the well-posedness theory for both incompressible and compressible subsonic flows with external forces in multidimensional nozzle with an obstacle inside are established by several uniform estimates. The uniformly subsonic compressible flows tend to the incompressible flows as quadratic order of Mach number as the compressibility parameter goes to zero. Furthermore, we also give the convergence rates of both incompressible flow and compressible flow at far fields as the boundary of nozzle goes to flat even when the forces do not admit convergence rate at far fields. The convergence rates obtained for the flows at far fields clearly describe the effects of the external force. Copyright © 2020, The Authors. All rights reserved.

关键词： Nozzles

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

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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

VARIATIONAL STRUCTURE AND TWO-DIMENSIONAL SUBSONIC JET FLOWS FOR COMPRESSIBLE EULER SYSTEM WITH GENERAL INCOMING FLOWS

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arXiv 2020年

作者： Li, Yan Shi, Wenhui Tang, Lan Xie, Chunjing School of Mathematical Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China School of Mathematics Monash University 9 Rainforest Walk ClaytonVIC3800 Australia School of Mathematics and Statistics Central China Normal University Hubei Wuhan430079 China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing CMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

In this paper, we proved the well-posedness theory of compressible subsonic jet flows for two-dimensional steady Euler system with general incoming horizontal velocity as long as the flux is larger than a critical value. One of the key observations is that the stream function formulation for two-dimensional compressible steady Euler system enjoys a variational structure even when the flows have nontrivial vorticity, so that the jet problem can be reformulated as a domain variation problem. This variational structure helps to adapt the framework developed by Alt, Caffarelli, and Friedman to study the jet problem, which is a Bernoulli type free boundary problem. A major technical point to analyze the jet flows is that the inhomogeneous terms in the rescaled equation near the free boundary are always small, even when the vorticity of the flows is big. Copyright © 2020, The Authors. All rights reserved.

关键词： Vorticity

Corrigendum to ‘Comparative study of natural convection melting inside a cubic cavity using an improved two-relaxation-time lattice Boltzmann model’ [International Journal of Heat and Mass Transfer, 143 (2019) 118449]

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International Journal of Heat and Mass Transfer 2021年 166卷

作者： Yong Zhao Lei Wang Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Physics China University of Geosciences Wuhan 430074 China