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RANDOM PERTURBATIONS FOR THE CHEMOTAXIS-FLUID MODEL WITH FRACTIONAL DISSIPATION: GLOBAL PATHWISE WEAK SOLUTIONS

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arXiv 2023年

作者： Zhang, Lei 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

This paper considers a stochastically perturbed Keller-Segel-Navier-Stokes (KS-SNS) system arising from the biomathematics in two dimensions, where the diffusion of fluid is expressed by a fractional Laplacian with an exponent in [1/2, 1]. Our main result demonstrates that, under appropriate assumptions, the Cauchy problem of the KS-SNS system has a unique global probabilistically strong and analytically weak solution, which also confirms that the quadratic logistic source authentically contributes to the global existence of solutions. First, a three-layer approximate system is introduced, this system seems to be new in the studying of chemotaxis-fluid model and it enables one to construct approximate solutions in regular Hilbert spaces Hs(R2). Second, to accomplish the convergence progressively, a series of crucial entropy-energy inequalities for the approximations are derived, whose derivation strongly depends on the fine structure of the system and requires a novel strategy to adapt to the appearance of fractional dissipation and the unboundedness of domain. Third, based on these uniform bounds, we establish the existence of global martingale weak solutions by virtue of a stochastic compactness method. Finally, by applying the Littlewood-Paley theory, we show that the pathwise uniqueness holds for these martingale solution. As a by-product, a few interpolation inequalities in Besov spaces are obtained, which seems to be new and may have their own interest. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

Harnessing Graphene Plasmons by Accessing the Retardation Regime

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ACS Applied Materials and Interfaces 2025年第22期17卷 32782-32789页

作者： Zhang, Jiasheng Xing, Qiaoxia Zhao, Tuoyu Wang, Shunjia Ma, Junwei Wang, Chong Wang, Jiajun Xie, Yuangang Huang, Shenyang Song, Chaoyu Wan, Quan Shi, Lei Tao, Zhensheng Shi, Wu Li, Xuesong Zhou, Lei Yan, Hugen State Key Laboratory of Surface Physics Key Laboratory of Micro- and Nano-Photonic Structures Ministry of Education Shanghai Key Laboratory of Metasurfaces for Light Manipulation Department of Physics Fudan University Shanghai 200433 China Inner Mongolia Key Laboratory of Microscale Physics and Atom Innovation School of Physical Science and Technology Inner Mongolia University Hohhot 010021 China State Key Laboratory of Surface Physics Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai 200433 China Zhangjiang Fudan International Innovation Center Fudan University Shanghai 201210 China Centre for Quantum Physics Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE) School of Physics Beijing Institute of Technology Beijing 100081 China Beijing Key Lab of Nanophotonics & Ultrafine Optoelectronic Systems School of Physics Beijing Institute of Technology Beijing 100081 China School of Integrated Circuit Science and Engineering Exemplary School of Microelectronics University of Electronic Science and Technology of China Chengdu 611731 China Shenzhen Institute for Advanced Study University of Electronic Science and Technology of China Shenzhen 518110 China

Plasmons in graphene are highly tunable, mainly by leveraging the carrier density and Drude scattering. Here, we introduce another scheme, i.e., accessing the retardation regime (originated from the finite speed of light), to engineer the lifetime and dispersion of plasmons in graphene in the terahertz regime. We find that the retardation regime can be approached by reducing plasmon momentum in artificially stacked multilayer graphene systems with large Drude weight, and this can significantly increase the plasmon lifetime. In addition, an explicit theoretical model along with finite-element simulation was given, consistent with the experimental findings. Our work opens another avenue to manipulate terahertz plasmons in graphene. © 2025 American Chemical Society.

关键词： Drude weight graphene plasmon retardation effects terahertz

Social Lode: Human Trajectory Prediction with Latent Odes

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Social Lode: Human Trajectory Prediction with Latent Odes

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Kexin Ke Jian Yang Yingjie Liu Mingsong Chen Xian Wei Xuan Tang MoE Engineering Research MOE Center of SW/HW Co-Design Technology and Application Shanghai Key Laboratory of Trustworthy Computing East China Normal University China School of Geospatial Information Information Engineering University China School of Communications and Electronic Engineering East China Normal University China

Human trajectory prediction is crucial in human-computer interaction and even in the safety of autonomous driving. In this work, A new method, called Social Latent Ordinary Differential Equation (Social LODE), is introduced for predicting human trajectories. The backbone of Social LODE consists of a conditional Variational Autoencoder (VAE) architecture based on Recurrent Neural Network (RNN). The hidden state updated by RNN is often discrete, but the human trajectory is continuous and uncertain. Thus, we use Latent ODEs as the decoder of VAE to overcome the limitation of RNN. Finally, we demonstrate that Social LODE achieves state-of-the-art compared to other methods, such as those involving the ETH/UCY and SDD datasets.

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Incomplete crossing and semi-topological horseshoes

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arXiv 2025年

作者： Cheng, Junfeng Yang, Xiao-Song 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

This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrative examples are provided: one from the perturbed Duffing system and another from a polynomial system proposed by Chen, demonstrating the prevalence of semi-horseshoes in chaotic systems. Moreover, the semi-topological horseshoe theory enhances the detection of chaos and improves the accuracy of topological entropy estimation. Copyright © 2025, The Authors. All rights reserved.

关键词： Topology

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应变梯度引起的极化畴结构减少铁电材料脆性

Acta Mechanica Sinica 2023年第5期39卷 13-18页

作者：陈玉峻王鸿宇楼旭辉郭浩李晓雁王清远范海冬田晓宝 MOE Key Laboratory of Deep Earth Science and Engineering College of Architecture and EnvironmentSichuan UniversityChengdu610065China Department of Mechanics Sichuan UniversityChengdu610065China School of Urban Construction Material Simulation and Computing LaboratoryHebei Normal University of Science&TechnologyQinhuangdao066004China Center for Advanced Mechanics and Materials Applied Mechanics LaboratoryDepartment of Engineering MechanicsTsinghua UniversityBeijing100084China

铁电材料的力电耦合特性以及在纳米尺度的快速失效导致其剪切过程很难研究,而材料的脆性也限制了这些材料在铁电器件中的潜在应用.在这项工作中,我们使用分子动力学方法模拟了剪切和畴演变的动态过程,揭示了这些畴结构如何影响材料的力... 详细信息

铁电材料的力电耦合特性以及在纳米尺度的快速失效导致其剪切过程很难研究,而材料的脆性也限制了这些材料在铁电器件中的潜在应用.在这项工作中,我们使用分子动力学方法模拟了剪切和畴演变的动态过程,揭示了这些畴结构如何影响材料的力电性能.在原子尺度上,一个明显的极化旋涡状的畴结构出现在剪切带的尖端,两侧分别有180°和90°的畴壁.由应变梯度引起的挠曲电效应导致了这些复杂的畴结构.施加外部电场阻碍畴的翻转,并通过减少积累的能量减少了失配应变区域,加速了剪切过程.结果表明极化旋涡畴阻碍了剪切破坏过程,这启示我们可以通过设计畴结构来增韧铁电材料.

关键词： Ferroelectric toughening Molecular dynamics Vortex domain structure Strain gradient

An Optimization Method for Renewable Energy and Energy Storage Capacity Allocation Based on Temporal Production Simulation 7

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An Optimization Method for Renewable Energy and Energy Stora...

7th IEEE Conference on Energy Internet and Energy System Integration, EI2 2023

作者： Du, Hongbo Li, Chi Chen, Liang Zhang, Jinping Kou, Caixia College of Sciences Beijing University of Posts and Telecommunications Beijing China National Key Laboratory of Renewable Energy Grid-Integration China Electric Power Research Institute Beijing China Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

ISBN: (纸本)9798350345094

With the rapid expansion of large-scale renewable energy bases in China, optimizing the allocation of renewable energy and energy storage capacity is crucial for improving system efficiency. In this paper, a joint optimal configuration method of wind-photovoltaic-energy storage capacity based on time series production simulation is proposed for renewable energy transmission base. Its aim is to minimize the total investment cost of the system under certain constraints about the proportion of renewable energy power generation, renewable energy utilization rate, conventional thermal power operation, energy storage power station operation, ultra-high voltage direct current (UHVDC) regulation and power transmission. To handle the nonlinear constraints, linearization is achieved by introducing integer variables. For the complex operation constraints of conventional thermal power and UHVDC channel, a simplified modeling method of start-stop cycle and adjustment cycle is proposed, which can effectively reduce the number of integer variables and improve the solving efficiency. The effectiveness of the proposed method is tested on the data of a renewable energy base in Northwest China. © 2023 IEEE.

关键词： Energy utilization

A New Multi-point Stepsize Gradient Method for Optimization 5th

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A New Multi-point Stepsize Gradient Method for Optimization

5th International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOV 2020

作者： Huang, Yakui Dai, Yu-Hong Liu, Xin-Wei Institute of Mathematics Hebei University of Technology Tianjin300401 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

ISBN: (纸本)9783030720391

The Barzilai-Borwein (BB) gradient method, which employs two-point stepsizes computed by the information of two consecutive iterations, is efficient in solving large-scale unconstrained optimization. In this paper, motivated by the success of BB method and the multi-point stepsize proposed by Dai and Fletcher (Mathematical Programming, 2006, 106: 403–421), we develop a new efficient gradient method, called MPSG, which adaptively uses the Dai-Fletcher long stepsize and Dai-Fletcher short stepsize. The R-linear convergence of MPSG for general n-dimensional strictly convex quadratic functions is established. By making use of two modified multi-point stepsizes and nonmonotone line searches, MPSG is extended to solve general unconstrained optimization. Moreover, the proposed MPSG method is further generalized for solving extreme eigenvalue problems. Numerical experiments on quadratic optimization, general unconstrained optimization and extreme eigenvalue problems demonstrate the efficiency of our method. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Gradient methods

The Exploration of Neural Collapse under Imbalanced Data

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arXiv 2024年

作者： Liu, Haixia 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

Neural collapse, a newly identified characteristic, describes a property of solutions during model training. In this paper, we explore neural collapse in the context of imbalanced data. We consider the L-extended unconstrained feature model with a bias term and provide a theoretical analysis of global minimizer. Our findings include: (1) Features within the same class converge to their class mean, similar to both the balanced case and the imbalanced case without bias. (2) The geometric structure is mainly on the left orthonormal transformation of the product of L linear classifiers and the right transformation of the class-mean matrix. (3) Some rows of the left orthonormal transformation of the product of L linear classifiers collapse to zeros and others are orthogonal, which relies on the singular values of Ŷ = (IK − 1/Nn1TK)D, where K is class size, n is the vector of sample size for each class, D is the diagonal matrix whose diagonal entries are given by √n. Similar results are for the columns of the right orthonormal transformation of the product of class-mean matrix and D. (4) The i-th row of the left orthonormal transformation of the product of L linear classifiers aligns with the i-th column of the right orthonormal transformation of the product of class-mean matrix and D. (5) We provide the estimation of singular values about Ŷ . Our numerical experiments support these theoretical *** Codes ***, *** Copyright © 2024, The Authors. All rights reserved.

关键词： Linear transformations

Quasiperiodic Symmetric Tilt FCC Grain Boundaries

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arXiv 2024年

作者： Zou, Wenwen Zhang, Juan Xu, Jie Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we investigate [110] symmetric tilt FCC grain boundaries (GBs) by a recently developed approach for quasiperiodic interfaces using the Landau-Brazovskii model. On special tilt angles associated with quadratic algebraic numbers, quasiperiodic GBs exhibit generalized Fibonacci substitution rules. The transition mechanism from quasiperiodic GBs to periodic GBs is explored through sphere offsets and spectral coalescence. We also propose an accurate method to calculate the GB energy for arbitrary tilt angle and analyze the factors affecting the GB energy. The revealing GB energy change is continue along with tilt angle except periodic GBs. © 2024, CC BY-NC-SA.

关键词： Grain boundaries