检索结果-内蒙古大学图书馆

Improved hybrid Allen-Cahn phase-field-based lattice Boltzmann method for incompressible two-phase flows

学校读者我要写书评

暂无评论

Physical Review E 2023年第3期107卷 035308-035308页

作者： Xi Liu Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan 430074 China and Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.

关键词： Multiphase flows Lattice-Boltzmann methods Two-fluid & multi-fluid model

Auto-ejection of liquid from a nozzle

学校读者我要写书评

暂无评论

Physical Review E 2024年第4期109卷 045302-045302页

作者： Fang Shan 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 Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan 430074 China

Auto-ejection of liquid is an important process in engineering applications, and is also very complicated since it involves interface moving, deforming, and jet breaking up. In this work, a theoretical velocity of meniscus at nozzle exit is first derived, which can be used to analyze the critical condition for auto-ejection of liquid. Then a consistent and conservative axisymmetric lattice Boltzmann (LB) method is proposed to study the auto-ejection process of liquid jet from a nozzle. We test the LB model by conducting some simulations, and find that the numerical results agree well with the theoretical and experimental data. We further consider the effects of contraction ratio, length ratio, contact angle, and nozzle structure on the auto-ejection, and observe some distinct phenomena during the ejection process, including the deformation of meniscus, capillary necking, and droplet pinch off. Finally, the results reported in the present work may play an instructive role on the design of droplet ejectors and the understanding of jetting dynamics in microgravity environment.

关键词： Lattice-Boltzmann methods

SAMPLE PATH MDP FOR THE CURRENT AND THE TAGGED PARTICLE IN THE SSEP

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Xue, Xiaofeng Zhao, Linjie School of Mathematics and Statistics Beijing Jiaotong University Beijing100044 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We prove sample path moderate deviation principles (MDP) for the current and the tagged particle in the symmetric simple exclusion process, which extends the results in [39], where the MDP was only proved at any fixed...

关键词：

GLOBAL SOLVABILITY IN A TWO-SPECIES CHEMOTAXIS SYSTEM WITH SIGNAL PRODUCTION

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Ren, Guoqiang Xiang, Tian School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Institute for Mathematical Sciences Renmin University of China Bejing100872 China

In this paper, we study the following prototypical two-species chemotaxis system with Lotka-Volterra competition and signal production: (Equation presented). We show that if (Equation presented). the associated Neumann initial-boundary value problem for (∗) admits a global generalized solutions in a bounded and smooth domain Ω ⊂ N (N ≥ 2) under merely integrable initial *** Codes 35A01, 35K57, 35Q92, 92C17 © 2021, CC BY.

关键词： Initial value problems

GLOBAL SOLVABILITY AND ASYMPTOTICAL BEHAVIOR IN A TWO-SPECIES CHEMOTAXIS MODEL WITH SIGNAL ABSORPTION

学校读者我要写书评

暂无评论

arXiv 2021年

In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for the following two-species chemotaxis consumption model: ut = ∆u - χ1∇ · (u∇w), x ∈ Ω, t > 0, {{{{{{{ vt = ∆v - χ2∇ · (u∇w), x ∈ Ω, t > 0, wt = ∆w - (αu + βv)w, x ∈ Ω, t > 0, in a bounded smooth but not necessarily convex domain Ω ⊂ Rn(n = 2, 3, 4, 5) with nonnegative initial data u0, v0, w0 and homogeneous Neumann boundary data. Here, the parameters χ1, χ2 are positive and α, β are nonnegative. Under a smallness condition max{χ1, χ2}kw0kL∞ MSC Codes 35K59, 35K57 © 2021, CC BY.

关键词： Biochemistry

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

学校读者我要写书评

暂无评论

Physical Review E 2018年第2期97卷 023306-023306页

作者： Chen Wu Baochang Shi Chang Shu Zhen Chen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan 430074 China 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 Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore 119260 Singapore

An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a 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-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 the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, 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.

关键词： Boltzmann theory

Bridging Fairness Gaps: A (Conditional) Distance Covariance Perspective in Fairness Learning

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Huang, Ruifan Liu, Haixia School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan Hubei China School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China

We bridge fairness gaps from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We enhance fairness by incorporating sample (conditional) distance covariance as a manageable penalty term into the machine learning process. Additionally, we present the matrix form of empirical (conditional) distance covariance for parallel calculations to enhance computational efficiency. Theoretically, we provide a proof for the convergence between empirical and population (conditional) distance covariance, establishing necessary guarantees for batch computations. Through experiments conducted on a range of real-world datasets, we have demonstrated that our method effectively bridges the fairness gap in machine learning. Copyright © 2024, The Authors. All rights reserved.

关键词： Contrastive Learning

HEISENBERG UNIQUENESS PAIRS AND THE WAVE EQUATION

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Huang, Shanlin Yu, Jiaqi School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China

Given a curve Γ and a set Λ in the plane, the concept of the Heisenberg uniqueness pair (Γ, Λ) was first introduced by Hedenmalm and Motes-Rodrígez (Ann. of Math. 173(2),1507-1527, 2011, [11]) as a variant of the uncertainty principle for the Fourier transform. The main results in [11] concern the hyperbola Γ∊ = {(x1, x2) ∈ 2, x1x2 = ∊} (0 ≠ ∊ ∈ ) and lattice-crosses Λαβ = (α× {0}) ∪ ({0} × β) (α, β > 0), where it’s proved that (Γ∊, Λαβ) is a Heisenberg uniqueness pair if and only if αβ ≤ 1/|∊|. In this paper, we aim to study the endpoint case (i.e., ∊ = 0 in Γ∊) and investigate the following problem: what’s the minimal amount of information required on Λ (the zero set) to form a Heisenberg uniqueness pair? When Λ is contained in the union of two curves in the plane, we give characterizations in terms of some dynamical system conditions. The situation is quite different in higher dimensions and we obtain characterizations in the case that Λ is the union of two hyperplanes. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamical systems

Indices of equilibrium points of linear control systems with saturated state feedback

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Yang, Xiao-Song Huang, Weisheng School of Mathematics and Statistics Huazhong University of Science and Technology WuhanHubei430074 China Hubei Key Laboratory of Engineering Modeling and Science Computing Huazhong University of Science and Technology WuhanHubei430074 China

In this paper we investigate some properties of equilibrium points in n-dimensional linear control systems with saturated state feedback. We provide an index formula for equilibrium points and discuss its relation to boundaries of attraction basins in feedback systems with single input. In addition, we also touch upon convexity of attraction basin. © 2021, CC BY.

关键词： Linear control systems