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STRESS CONCENTRATION FOR NONLINEAR INSULATED CONDUCTIVITY PROBLEM WITH ADJACENT INCLUSIONS

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arXiv 2023年

作者： Chen, Qionglei Zhao, Zhiwen Institute of Applied Physics and Computational Mathematics Beijing100088 China Beijing Computational Science Research Center Beijing100193 China

A high-contrast two-phase nonlinear composite material with adjacent inclusions of m-convex shapes is considered for m > 2. The mathematical formulation consists of the insulated conductivity problem with p-Laplace operator in dfor p > 1 and d ≥ 2. The stress, which is the gradient of the solution, always blows up with respect to the distance ϵ between two inclusions as ϵ goes to zero. We first establish the pointwise upper bound on the gradient possessing the singularity of order ϵ-βwith β = (1 - α)/m for some α ≥ 0, where α = 0 if d = 2 and α > 0 if d ≥ 3. In particular, we give a quantitative description for the range of horizontal length of the narrow channel in the process of establishing the gradient estimates, which provides a clear understanding for the applied techniques and methods. For d ≥ 2, we further construct a supersolution to sharpen the upper bound with any β > (d + m - 2)/(m(p - 1)) when p > d + m - 1. Finally, a subsolution is also constructed to show the almost optimality of the blow-up rate ϵ-1/ max{p-1,m}in the presence of curvilinear squares. This fact reveals a novel dichotomy phenomena that the singularity of the gradient is uniquely determined by one of the convexity parameter m and the nonlinear exponent p except for the critical case of p = m + 1 in two dimensions. Copyright © 2023, The Authors. All rights reserved.

关键词： Mathematical operators

Effects of the initial perturbations on the Rayleigh–Taylor–Kelvin–Helmholtz instability system

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Frontiers of physics 2022年第3期17卷 77-89页

作者： Feng Chen Aiguo Xu Yudong Zhang Yanbiao Gan Bingbing Liu Shuang Wang School of Aeronautics Shan Dong Jiaotong UniversityJinan 250357China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009-26Beijing 100088China HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory of Explosion Science and Technology Beijing Institute of TechnologyBeijing 100081China School of Mechanics and Safety Engineering Zhengzhou UniversityZhengzhou 450001China Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle North China Institute of Aerospace EngineeringLangfang 065000China Naval Architecture and Port Engineering College Shan Dong Jiaotong UniversityWeihai 264200China School of Science Shandong Jianzhu UniversityJinan 250101China

The effects of initial perturbations on the Rayleigh–Taylor instability (RTI), Kelvin–Helmholtz instability (KHI), and the coupled Rayleigh–Taylor–Kelvin–Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. It is found that the initial perturbation has a significant influence on the evolution of RTI. The sharper the interface, the faster the growth of bubble or spike. While the influence of initial interface shape on KHI evolution can be ignored. Based on the mean heat flux strength D3,1, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle θ_(1) and the middle contact angle θ_(2). The increase of θ_(1) and the decrease of θ_(2) have opposite effects on the critical velocity. When θ_(2) remains roughly unchanged at 90 degrees, if θ_(1) is greater than 90 degrees (such as the parabolic interface), the critical shear velocity increases with the increase of θ_(1), and the ellipse perturbation is its limiting case;If θ_(1) is less than 90 degrees (such as the inverted parabolic and the inverted ellipse disturbances), the critical shear velocities are basically the same, which is less than that of the sinusoidal and sawtooth disturbances. The influence of inverted parabolic and inverted ellipse perturbations on the transition point of the RTKHI system is greater than that of other interfaces: (i) For the same amplitude, the smaller the contact angle θ_(1), the later the transitio

关键词： discrete Boltzmann method hydrodynamic instability non-equilibrium characteristic initial perturbation

Multiple Auger Decay Following Xe+(4p3^(−1)/2)Ionization

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Chinese physics Letters 2021年第2期38卷 12-17页

作者： Zhenqi Liu Qing Liu Yulong Ma Fuyang Zhou Yizhi Qu School of Optoelectronics University of Chinese Academy of SciencesBeijing 100049China College of Physics and Electronic Engineering Northwest Normal UniversityLanzhou 730070China Data Center for High Energy Density Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China

The Auger decay for the many-electron Xe+(4p3^(−1)/2)state is studied in detail,using multistep *** is found that the single Auger decay channels are primarily Coster–Kronig processes,which is in accord with other theoretical and experimental *** double and triple Auger decays result primarily from cascade processes,i.e.,the sequential two-step and three-step Auger decay,and as such,the contributions from direct processes can be ***-to-level rates for single,double,and triple decays are obtained,based on which comprehensive Auger electron spectra and ion yields are *** decay paths and Auger electron spectra are in agreement with the experimental analysis[Hikosaka et al.,***.A 76(2007)032708],and our ion yield ratios(Xe^(2+):Xe^(3+):Xe^(4+)=4.6:87.0:8.4)are also in line with their values(5.0:86.0:9.0).However,with respect to the ion yield ratios,a discrepancy still remains among the experimental and theoretical *** into account the complexity of Xe’s electronic structure,further,more detailed experiments are still required.

关键词： decay primarily neglected

Towards large-scale and spatiotemporally resolved diagnosis of electronic density of states by deep learning

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Physical Review B 2022年第17期105卷 174109-174109页

作者： Qiyu Zeng Bo Chen Xiaoxiang Yu Shen Zhang Dongdong Kang Han Wang Jiayu Dai Department of Physics National University of Defense Technology Changsha Hunan 410073 People's Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 People's Republic of China

Modern laboratory techniques such as ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization, and dissociation dynamics. To understand and model the dramatic change of both electronic structures and ion dynamics during such dynamic processes, the traditional method faces difficulties. Here, we demonstrate the ability of a deep neural network (DNN) to capture the atomic local-environment dependence of the electronic density of states (DOS) for both multicomponent systems under exoplanet thermodynamic conditions and nonequilibrium systems during superheated melting processes. Large-scale and time-resolved diagnosis of DOS can be efficiently achieved within the accuracy of the ab initio method. Moreover, the atomic contribution to DOS given by the DNN model accurately reveals the information of the local neighborhood for the selected atom, which thus can serve as robust order parameters to identify different phases and intermediate local structures, strongly highlighting the efficacy of this DNN model in studying dynamic processes.

关键词： Density of states Phase transitions Ab initio molecular dynamics First-principles calculations Machine learning

Ill-posedness of the Kelvin-Helmholtz problem for compressible Euler fluids

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arXiv 2024年

作者： Xie, Binqiang Zhao, Bin School of Mathematics and Statistics Guangdong University of Technology Guangzhou510006 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, when the magnitude of the Mach number is strictly between some fixed small enough constant and √2, we can prove the linear and nonlinear ill-posedness of the Kelvin-Helmholtz problem for compressible ideal fluids. To our best knowledge, this is the first reslult that proves the nonlinear ill-posedness to the Kelvin-Helmholtz problem for the compressible Euler *** Codes 14J60(primary) Copyright © 2024, The Authors. All rights reserved.

关键词：

Lp MAXIMAL ESTIMATES FOR WEYL SUMS WITH k ≥ 3 ON T

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arXiv 2024年

作者： Chen, Xuezhi Miao, Changxing Yuan, Jiye Zhao, Tengfei Institute of Applied Physics and Computational Mathematics Beijing100088 China Beijing100083 China School of Mathematics and Physics University of Science and Technology Beijing Beijing100083 China

In this paper, we study the Lp maximal estimates for the Weyl sums ∑N/n=1e2πi(nx+nkt) with higher-order k ≥ 3 on T, and obtain the positive and negative results. Especially for the case k = 3, our result is sharp up to the endpoint. The main idea is to investigate the structure of the set where large values of Weyl sums are achieved by making use of the rational approximation and the refined estimate for the exponential *** Codes 42B25, 42B37, 35Q41 © 2024, CC BY.

关键词： Schrodinger equation

Effect of weak elasticity on the Kelvin-Helmholtz instability

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arXiv 2024年

作者： Xie, Binqiang Guo, Boling Zhao, Bin School of Mathematics and Statistics Guangdong University of Technology Guangzhou510006 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, we present an analysis of the Kelvin-Helmholtz instability in two-dimensional ideal compressible elastic flows, providing a rigorous confirmation that weak elasticity has a destabilizing effect on the Kelvin-Helmholtz instability. There are two critical velocities, Ulow and Uupp, where Ulow and Uupp represent the lower and upper critical velocities, respectively. We demonstrate that when the magnitude of the rectilinear solutions satisfies Ulow + cǫ0 ≤ |v1+| ≤ Uupp−cǫ0, the linear and nonlinear ill-posedness of the piecewise smooth solutions of the Kelvin-Helmholtz problem for two-dimensional ideal compressible elastic fluids is established uniformly, where c is the sound speed and ǫ0 is some small enough positive *** Codes 35Q35, 35D35 Copyright © 2024, The Authors. All rights reserved.

关键词： Compressible flow

Gradient-weighted physics-informed neural networks for one-dimensional Euler equation

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TechRxiv

TechRxiv 2022年

作者： Xiong, Fansheng Liu, Li Liu, Shengping Wang, Han Yong, Heng Institute of Applied Physics and Computational Mathematics Beijing100094 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100094 China HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China

physics informed neural networks (PINNs) have been a well-known tool in solving forward and inverse partial differential equations (PDEs) problem. In particular, for the forward problem, only the initial/boundary conditions and the equation itself as the physical information are needed to obtain the predicted solution within the definition domain. However, some existing works show that the standard PINN method is insufficient for solving complex problems. For the relatively complex one-dimensional Euler equation problem, due to the limited accuracy of the standard PINN method, the algorithm is improved in two aspects in this study. First, a gradient-related weight function is introduced into the loss function and the framework of gradient-weighted physics-informed neural networks (gwPINNs) is proposed. In particular, the weight function is carefully designed. Second, the sequence-to-sequence (seq2seq) learning is applied in the training process to improve the precision. Then, four cases of Riemann problems are solved using the improved algorithm. The results show that the improved algorithm can obtain high accuracy in solving these problems, and verify the feasibility of solving one-dimensional Euler equation based on the improved PINN method. © 2022, CC BY.

关键词： Euler equations

Stochastic Schrödinger-Korteweg de Vries systems driven by multiplicative noises

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arXiv 2024年

作者： Chen, Jie Gu, Fan Guo, Boling Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Sciences Jimei University Xiamen361021 China

In this paper, we consider the well-posedness of stochastic S-KdV driven by multiplicative noises in Hx1 × Hx1. To get the local well-posedness, we first develop the bilinear and trilinear Bourgain norm estimates of the nonlinear terms with b ∈ (0, 1/2). Then, to overcome the lack of the maximum functional estimate, we introduce a series of approximation equations with localized nonlinear terms, which are also cutted-off in both the physical and the Fourier space. By limitations, these approximation equations will help us get a priori estimate in the Bourgain space and finish the proof of the global well-posedness of the initial *** Codes 60H15, 35Q53, 35Q55 Copyright © 2024, The Authors. All rights reserved.

关键词： Fourier series