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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

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

Jacobi polynomials on the Bernstein ellipse

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arXiv 2017年

作者： Wang, Haiyong Zhang, Lun 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 School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathe-matics Fudan University Shanghai200433

In this paper, we are concerned with Jacobi polynomials P(α,β)n(x) on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of P(α,β)n(x) is derived in the variable of parametrization. This formula further allows us to show that the maximum value of |P(α,β)n(z)| over the Bernstein ellipse is attained at one of the endpoints of the major axis if α+β ≥ -1. For the minimum value, we are able to show that for a large class of Gegenbauer polynomials (i.e., α = β), it is attained at two endpoints of the minor axis. These results particularly extend those previously known only for some special cases. Moreover, we obtain a more refined asymptotic estimate for Jacobi polynomials on the Bernstein ellipse.65N35, 65D05, 41A05, 41A25 Copyright © 2017, The Authors. All rights reserved.

关键词： Polynomials

Examining scientific writing styles from the perspective of linguistic complexity

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arXiv 2018年

作者： Lu, Chao Bu, Yi Wang, Jie Ding, Ying Torvik, Vetle Schnaars, Matthew Zhang, Chengzhi School of Economics and Management Nanjing University of Science and Technology Nanjing Jiangsu China School of Informatics Computing and Engineering Indiana University BloomingtonIN United States Center for Complex Networks and Systems Research School of Informatics Computing and Engineering Indiana University BloomingtonIN United States School of Information Management Nanjing University Nanjing Jiangsu China School of Information Management Wuhan University Wuhan Hubei China School of Information Sciences University of Illinois UrbanaIL United States Jiangsu Key Laboratory of Data Engineering and Knowledge Service Nanjing University Nanjing Jiangsu China

Publishing articles in high-impact English journals is difficult for scholars around the world, especially for non-native English-speaking scholars (NNESs), most of whom struggle with proficiency in English. In order to uncover the differences in English scientific writing between native English-speaking scholars (NESs) and NNESs, we collected a large-scale data set containing more than 150,000 full-text articles published in PLoS between 2006 and 2015. We divided these articles into three groups according to the ethnic backgrounds of the first and corresponding authors, obtained by Ethnea, and examined the scientific writing styles in English from a two-fold perspective of linguistic complexity: (1) syntactic complexity, including measurements of sentence length and sentence complexity;and (2) lexical complexity, including measurements of lexical diversity, lexical density, and lexical sophistication. The observations suggest marginal differences between groups in syntactical and lexical complexity. Copyright © 2018, The Authors. All rights reserved.

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Lattice boltzmann modeling of wall-bounded ternary fluid flows

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arXiv 2017年

作者： Liang, Hong Xu, Jiangrong Chen, Jiangxing Chai, Zhenhua Shi, Baochang Department of Physics Hangzhou Dianzi University Hangzhou310018 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

In this paper, a wetting boundary scheme used to describe the interactions among ternary fluids and solid is proposed in the framework of the lattice Boltzmann method. This scheme for three-phase fluids can preserve the reduction consistency property with the diphasic situation such that it could give physically relevant results. Combining this wetting boundary scheme and the lattice Boltzmann (LB) ternary fluid model based on the multicomponent phase-field theory, we simulated several ternary fluid flow problems involving solid substrate, including the spreading of binary drops on the substrate, the spreading of a compound drop on the substrate, and the shear of a compound liquid drop on the substrate. The numerical results are found to be good agreement with the analytical solutions or some available results. Finally, as an application, we use the LB model coupled with the present wetting boundary scheme to numerically investigate the impact of a compound drop on a solid circular cylinder. It is found that the dynamics of a compound drop can be remarkably influenced by the wettability of the solid surface and the dimensionless Weber number. Copyright © 2017, The Authors. All rights reserved.

关键词： Circular cylinders

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

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arXiv 2017年

作者： Liang, Hong Xu, Jiangrong Chen, Jiangxing Wang, Huili Chai, Zhenhua Shi, Baochang Department of Physics Hangzhou Dianzi University Hangzhou310018 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

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and Spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. At last, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Navier Stokes equations

A third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

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arXiv 2017年

作者： Wu, Chen Shu, Chang Shi, Baochang Chen, Zhen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore119260 Singapore 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

An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third-order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation LBE based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second-order (or lower-order) of accuracy in time splitting scheme as in the conventional high-order Runge-Kutta (RK) based kinetic methods, the present method solves the original BE, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows. Copyright © 2017, The Authors. All rights reserved.

关键词： Boltzmann equation

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arXiv 2018年

作者： Yang, Peng Zhang, Ning Zhang, Shan Yu, Li Zhang, Junshan Shen, Xuemin School of Electronic Information and Communications Huazhong University of Science and Technology Wuhan Hubei430074 China Department of Computing Sciences Texas A and M University-Corpus Christi Corpus ChristiTX78412 United States Beijing Key Laboratory of Computer Networks School of Computer Science and Engineering Beihang University Beijing100191 China School of Electrical Computer and Energy Engineering Arizona State University TempeAZ85287 United States Department of Electrical and Computer Engineering University of Waterloo WaterlooONN2L 3G1 Canada

Mobile edge caching enables content delivery within the radio access network, which effectively alleviates the backhaul burden and reduces response time. To fully exploit edge storage resources, the most popular contents should be identified and cached. Observing that user demands on certain contents vary greatly at different locations, this paper devises location-customized caching schemes to maximize the total content hit rate. Specifically, a linear model is used to estimate the future content hit rate. For the case where the model noise is zero-mean, a ridge regression based online algorithm with positive perturbation is proposed. Regret analysis indicates that the proposed algorithm asymptotically approaches the optimal caching strategy in the long run. When the noise structure is unknown, an H1 filter based online algorithm is further proposed by taking a prescribed threshold as input, which guarantees prediction accuracy even under the worst-case noise process. Both online algorithms require no training phases, and hence are robust to the time-varying user demands. The underlying causes of estimation errors of both algorithms are numerically analyzed. Moreover, extensive experiments on real world dataset are conducted to validate the applicability of the proposed algorithms. It is demonstrated that those algorithms can be applied to scenarios with different noise features, and are able to make adaptive caching decisions, achieving content hit rate that is comparable to that via the hindsight optimal strategy. Copyright © 2018, The Authors. All rights reserved.

关键词： Mobile edge computing