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Uniform structural stability and uniqueness of poiseuille flows in a two dimensional periodic strip

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arXiv 2020年

作者： Kaijian, S.H.A. Wang, Yun Chunjing, X.I.E. Department of mathematics East China University of Science and Technology 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 SHL-MAC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

In this paper, we prove the uniform nonlinear structural stability of Poiseuille flows with arbitrarily large flux for the Navier-Stokes system in a two dimensional periodic strip when the period is not large. The key point is to establish the a priori estimate for the associated linearized problem via the careful analysis for the associated boundary layers. Furthermore, the well-posedness theory for the Navier-Stokes system is also proved even when the external force is large in L2. Finally, if the vertical velocity is suitably small where the smallness is independent of the flux, then Poiseuille flow is the unique solution of the steady Navier-Stokes system in the periodic strip. Copyright © 2020, The Authors. All rights reserved.

关键词： Boundary layers

A Hybrid Supramolecular Polymeric Nanomedicine for Cascade-Amplified Synergetic Cancer Therapy

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Angewandte Chemie 2022年第27期134卷

作者： Kai Yang Dr. Shaolong Qi Dr. Xinyang Yu Dr. Bing Bai Xueyan Zhang Prof. Dr. Zhengwei Mao Prof. Dr. Feihe Huang Prof. Dr. Guocan Yu Key Laboratory of Bioorganic Phosphorus Chemistry & Chemical Biology Department of Chemistry Tsinghua University Beijing 100084 P. R. China State Key Laboratory of Chemical Engineering Stoddart Institute of Molecular Science Department of Chemistry Zhejiang University Hangzhou 310027 P. R. China ZJU-Hangzhou Global Scientific and Technological Innovation Center Hangzhou 311215 P. R. China Green Catalysis Center and College of Chemistry Zhengzhou University Zhengzhou 450001 P. R. China Key Laboratory of Precision Diagnosis and Treatment for Hepatobiliary and Pancreatic Tumor of Zhejiang Province the Second Affiliated Hospital School of Medicine MOE Key Laboratory of Macromolecular Synthesis and Functionalization Department of Polymer Science and Engineering Zhejiang University Hangzhou Zhejiang 310027 P. R. China

Discrete effects on some boundary schemes of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations

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arXiv 2019年

作者： Wu, Yao Zhao, Yong Chai, Zhenhua Shi, Baochang 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

In this paper, we perform a more general analysis on the discrete effects of some boundary schemes of the popular one- to three-dimensional DnQq multiple-relaxation-time lattice Boltzmann model for convection-diffusion equation (CDE). Investigated boundary schemes include anti-bounce-back(ABB) boundary scheme, bounce-back(BB) boundary scheme and non-equilibrium extrapolation(NEE) boundary scheme. In the analysis, we adopt a transform matrix M constructed by natural moments in the evolution equation, and the result of ABB boundary scheme is consistent with the existing work of orthogonal matrix M. We also find that the discrete effect does not rely on the choice of transform matrix, and obtain a relation to determine some of the relaxation-time parameters which can be used to eliminate the numerical slip completely under some assumptions. In this relation, the weight coefficient is considered as an adjustable parameter which makes the parameter adjustment more flexible. The relaxation factors associated with second moments can be used to eliminate the numerical slip of ABB boundary scheme and BB boundary scheme while the numerical slip can not be eliminated of NEE boundary scheme. Furthermore, we extend the relations to complex-valued CDE, several numerical examples are used to test the relations. Copyright © 2019, The Authors. All rights reserved.

关键词： Diffusion in liquids

Generalized lattice boltzmann method: modeling, analysis, and elements

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arXiv 2019年

作者： Shi, Baochang Chai, Zhenhua 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

In this paper, we first present a unified framework for the modelling of generalized lattice Boltzmann method (GLBM). We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansion and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes equations and nonlinear convection-diffusion equations from the GLBM, and show that from mathematical point of view, these four analysis methods are equivalent to each other. Finally, we give some elements that are needed in the implementation of the GLBM, and also find that some available LB models can be obtained from this GLBM. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear equations

Maxwell-Stefan-theory-based lattice Boltzmann model for diffusion in multicomponent mixtures

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Physical Review E 2019年第2期99卷 023312-023312页

作者： Zhenhua Chai Xiuya Guo Lei Wang 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

The phenomena of diffusion in multicomponent (more than two components) mixtures are universal in both science and engineering, and from the mathematical point of view, they are usually described by the Maxwell-Stefan (MS)-theory-based diffusion equations where the molar average velocity is assumed to be zero. In this paper, we propose a multiple-relaxation-time lattice Boltzmann (LB) model for the mass diffusion in multicomponent mixtures and also perform a Chapman-Enskog analysis to show that the MS continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS-theory-based diffusion equations are just a diffusion type of partial differential equations, we can also adopt much simpler lattice structures to reduce the computational cost of present LB model. We then conduct some simulations to test this model and find that the results are in good agreement with the previous work. Besides, the reverse diffusion, osmotic diffusion, and diffusion barrier phenomena are also captured. Finally, compared to the kinetic-theory-based LB models for multicomponent gas diffusion, the present model does not include any complicated interpolations, and its collision process can still be implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model.

关键词： Lattice-Boltzmann methods

An orthogonalization-free parallelizable framework for all-electron calculations in density functional theory

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arXiv 2020年

作者： Bin, G.A.O. Guanghui, H.U. Kuang, Yang Xin, L.I.U. ICTEAM Institute UCLouvain Louvain-la-Neuve Belgium Department of Mathematics University of Macau Macao SAR China Zhuhai UM Science & Technology Research Institute Guangdong Province China Department of Mathematics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and total energy minimization problem pursue orthogonal solutions. Most existing algorithms for solving these two models invoke orthogonalization process either explicitly or implicitly in each iteration. Their efficiency suffers from this process in view of its cubic complexity and low parallel scalability in terms of the number of electrons for large scale systems. To break through this bottleneck, we propose an orthogonalization-free algorithm framework based on the total energy minimization problem. It is shown that the desired orthogonality can be gradually achieved without invoking orthogonalization in each iteration. Moreover, this framework fully consists of Basic Linear Algebra Subprograms (BLAS) operations and thus can be naturally parallelized. The global convergence of the proposed algorithm is established. We also present a precondition technique which can dramatically accelerate the convergence of the algorithm. The numerical experiments on all-electron calculations show the efficiency and high scalability of the proposed algorithm. Copyright © 2020, The Authors. All rights reserved.

关键词： Density functional theory

The influence of stochastic forcing on strong solutions to the Incompressible Slice Model in 2D bounded domain

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arXiv 2020年

作者： Zhang, Lei Shi, Yu Hu, Chaozhu Wang, Weifeng Liu, Bin SCHOOL OF MATHEMATICS AND STATISTICS HUBEI KEY LABORATORY OF ENGINEERING MODELING AND SCIENTIFIC COMPUTING HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY HUBEI WUHAN430074 China SCHOOL OF SCIENCE WUHAN UNIVERSITY OF TECHNOLOGY HUBEI WUHAN 430070 China SCHOOL OF SCIENCE HUBEI UNIVERSITY OF TECHNOLOGY HUBEI WUHAN 430068 China SCHOOL OF MATHEMATICS AND STATISTICS SOUTH-CENTRAL UNIVERSITY FOR NATIONALITIES WUHAN430074 China

The Cotter-Holm Slice Model (CHSM) was introduced to study the behavior of whether and specifically the formulation of atmospheric fronts, whose prediction is fundamental in meteorology. Considered herein is the influence of stochastic forcing on the Incompressible Slice Model (ISM) in a smooth 2D bounded domain, which can be derived by adapting the Lagrangian function in Hamilton’s principle for CHSM to the Euler-Boussinesq Eady incompressible case. First, we establish the existence and uniqueness of local pathwise solution (probability strong solution) to the ISM perturbed by nonlinear multiplicative stochastic forcing in Banach spaces Wk, p(D) with k > 1 + 1/ p and p ≥ 2. The solution is obtained by introducing suitable cut-off operators applied to the W1,∞-norm of the velocity and temperature fields, using the stochastic compactness method and the Yamada-Watanabe type argument based on the Gyöngy-Krylov characterization of convergence in probability. Then, when the ISM is perturbed by linear multiplicative stochastic forcing and the potential temperature does not vary linearly on the y-direction, we prove that the associated Cauchy problem admits a unique global-in-time pathwise solution with high probability, provided that the initial data is sufficiently small or the diffusion parameter is large enough. The results partially answer the problems left open in Alonso-Orán et al. (Physica D 392:99–118, 2019, pp. 117). Copyright © 2020, The Authors. All rights reserved.

关键词： Banach spaces

Conceptual model of real-time IoT systems

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Frontiers of Information Technology & Electronic engineering 2019年第11期20卷 1457-1464页

作者： Bo YUAN De-ji CHEN Dong-mei XU Ming CHEN Department of Computer Science and Technology Tongji UniversityShanghai 201804China School of Electronics and Information Engineering Jinggangshan UniversityJi'an 343009China MOE Key Laboratory of Embedded System and Service Computing Tongji UniversityShanghai 201804China China Electronics Standardization Institute Beijing 100007China Chinesisch-Deutsche Hochschule for Angewandte Wissenschaften Tongji UniversityShanghai 201804China

We address a special kind of Internet of Things (IoT) systems that are also real-time. We call them real-time IoT (RT-IoT) systems. An RT-IoT system needs to meet timing constraints of system delay, clock synchronization, deadline, and so on. The timing constraints turn to be more stringent as we get closer to the physical things. Based on the reference architecture of IoT (ISO/IEC 30141), the RT-IoT conceptual model is established. The idea of edge subsystem is introduced. The sensing & con-trolling domain is the basis of the edge subsystem, and the edge subsystem usually must meet the hard real-time constraints. The model includes four perspectives, the time view, computation view, communication view, and control view. Each view looks, from a different angle, at how the time parameters impact an RT-IoT system.

关键词： Internet of Things(IoT) Real-time system Conceptual model View Hard/Soft real-time

On Coupling Lemma and Stochastic Properties with Unbounded Observables for 1-d Expanding Maps

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arXiv 2020年

作者： Chen, Jianyu Zhang, Hong-Kun Zhang, Yiwei School of Mathematical Sciences Center for Dynamical Systems and Differential Equations Soochow University SuzhouJiangsu215006 China Department of Mathematics and Statistics University of Massachusetts Amherst AmherstMA01003 United States School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Hua-Zhong University of Sciences and Technology Wuhan430074 China

In this paper, we establish a coupling lemma for standard families in the setting of piecewise expanding interval maps with countably many branches. Our method merely requires that the expanding map satisfies Chernov’s one-step expansion at q-scale and eventually covers a magnet interval. Therefore, our approach is particularly powerful for maps whose inverse Jacobian has low regularity and those who does not satisfy the big image property. The main ingredients of our coupling method are two crucial lemmas: the growth lemma in terms of the characteristic Z function and the covering ratio lemma over the magnet interval. We first prove the existence of an absolutely continuous invariant measure. What is more important, we further show that the growth lemma enables the liftablity of the Lebesgue measure to the associated Hofbauer tower, and the resulting invariant measure on the tower admits a decomposition of Pesin-Sinai type. Furthermore, we obtain the exponential decay of correlations and the almost sure invariance principle (which is a functional version of the central limit theorem). For the first time, we are able to make a direct relation between the mixing rates and the Z function, see (2.7). The novelty of our results relies on establishing the regularity of invariant density, as well as verifying the stochastic properties for a large class of unbounded observables. Finally, we verify our assumptions for several well known examples that were previously studied in the literature, and unify results to these examples in our framework. Copyright © 2020, The Authors. All rights reserved.

关键词： Inverse problems