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Kinetic and Related Models最新文献

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On the thermal relaxation of a dense gas described by the modified Enskog equation in a closed system in contact with a heat bath 用修正Enskog方程描述稠密气体在与热浴接触的封闭系统中的热弛豫
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2023-05-19 DOI: 10.3934/krm.2023025
S. Takata
{"title":"On the thermal relaxation of a dense gas described by the modified Enskog equation in a closed system in contact with a heat bath","authors":"S. Takata","doi":"10.3934/krm.2023025","DOIUrl":"https://doi.org/10.3934/krm.2023025","url":null,"abstract":"The thermal relaxation of a dense gas described by the modified Enskog equation is studied for a closed system in contact with a heat bath. As in the case of the Boltzmann equation, the Helmholtz free energy $mathcal{F}$ that decreases monotonically in time is found under the conventional kinetic boundary condition that satisfies the Darrozes--Guiraud inequality. The extension to the modified Enskog--Vlasov equation is also presented.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82869636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system 一维修正Vlasov-Poisson-Boltzmann系统的Green函数和点态行为
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2023-03-23 DOI: 10.3934/krm.2023004
Yanchao Li, Mingying Zhong
{"title":"Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system","authors":"Yanchao Li, Mingying Zhong","doi":"10.3934/krm.2023004","DOIUrl":"https://doi.org/10.3934/krm.2023004","url":null,"abstract":"The pointwise space-time behaviors of the Green's function and the global solution to the modified Vlasov- Poisson-Boltzmann (mVPB) system in one-dimensional space are studied in this paper. It is shown that, the Green's function admits the diffusion wave, the Huygens's type sound wave, the singular kinetic wave and the remainder term decaying exponentially in space-time. These behaviors are similar to the Boltzmann equation (Liu and Yu in Comm. Pure Appl. Math. 57: 1543-1608, 2004). Furthermore, we establish the pointwise space-time nonlinear diffusive behaviors of the global solution to the nonlinear mVPB system in terms of the Green's function.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86051015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interface layers and coupling conditions on networks for linearized kinetic BGK equation 线性化动力学BGK方程网络的界面层和耦合条件
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023029
Ikrom Akramov, R. Borsche, Nils Eckhard, A. Klar
{"title":"Interface layers and coupling conditions on networks for linearized kinetic BGK equation","authors":"Ikrom Akramov, R. Borsche, Nils Eckhard, A. Klar","doi":"10.3934/krm.2023029","DOIUrl":"https://doi.org/10.3934/krm.2023029","url":null,"abstract":"","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82165003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solutions of the 2D radially symmetric Vlasov-Maxwell system with an initial focusing phase 具有初始聚焦相位的二维径向对称Vlasov-Maxwell系统的解
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023011
K. Z. Zhang
{"title":"Solutions of the 2D radially symmetric Vlasov-Maxwell system with an initial focusing phase","authors":"K. Z. Zhang","doi":"10.3934/krm.2023011","DOIUrl":"https://doi.org/10.3934/krm.2023011","url":null,"abstract":"","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87868743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Galerkin type method for kinetic Fokker-Planck equations based on Hermite expansions 基于Hermite展开的动力学Fokker-Planck方程的Galerkin型方法
4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023035
Benny Avelin, Mingyi Hou, Kaj Nyström
{"title":"A Galerkin type method for kinetic Fokker-Planck equations based on Hermite expansions","authors":"Benny Avelin, Mingyi Hou, Kaj Nyström","doi":"10.3934/krm.2023035","DOIUrl":"https://doi.org/10.3934/krm.2023035","url":null,"abstract":"In this paper, we develop a Galerkin-type approximation, with quantitative error estimates, for weak solutions to the Cauchy problem for kinetic Fokker-Planck equations in the domain $ (0, T) times D times mathbb{R}^d $, where $ D $ is either $ mathbb{T}^d $ or $ mathbb{R}^d $. Our approach is based on a Hermite expansion in the velocity variable only, with a hyperbolic system that appears as the truncation of the Brinkman hierarchy, as well as ideas from [2] and additional energy-type estimates that we have developed. We also establish the regularity of the solution based on the regularity of the initial data and the source term.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis of kinetic models for label switching and stochastic gradient descent 标签切换和随机梯度下降的动力学模型分析
4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023005
Martin Burger, Alex Rossi
{"title":"Analysis of kinetic models for label switching and stochastic gradient descent","authors":"Martin Burger, Alex Rossi","doi":"10.3934/krm.2023005","DOIUrl":"https://doi.org/10.3934/krm.2023005","url":null,"abstract":"In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes. Besides problems in biology and physics, we also demonstrate that stochastic gradient descent, the most popular technique in machine learning, can be understood in this setting, when considering a time-continuous variant.Our analysis is focusing on the case of evolution in a collection of external potentials, for which we provide analytical and numerical results about the evolution as well as the stationary problem.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135470253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Two kinetic models for non-instantaneous binary alignment collisions 非瞬时二元对准碰撞的两种动力学模型
4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023038
Laura Kanzler, Christian Schmeiser, Veronica Tora
{"title":"Two kinetic models for non-instantaneous binary alignment collisions","authors":"Laura Kanzler, Christian Schmeiser, Veronica Tora","doi":"10.3934/krm.2023038","DOIUrl":"https://doi.org/10.3934/krm.2023038","url":null,"abstract":"A new type of kinetic models with non-instantaneous binary collisions is considered. Collisions are described by a transport process in the joint state space of a pair of particles. The interactions are of alignment type, where the states of the particles approach each other. For two spatially homogeneous models with deterministic or stochastic collision times existence and uniqueness of solutions, the long time behavior, and the instantaneous limit are considered, where the latter leads to standard kinetic models of Boltzmann type.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135559630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Low–dimensional reduction of the non-Abelian quantum synchronization models on the unitary group 酉群上非阿贝尔量子同步模型的低维约化
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023028
Dohyun Kim, Jeongho Kim
{"title":"Low–dimensional reduction of the non-Abelian quantum synchronization models on the unitary group","authors":"Dohyun Kim, Jeongho Kim","doi":"10.3934/krm.2023028","DOIUrl":"https://doi.org/10.3934/krm.2023028","url":null,"abstract":"","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81408786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Incompressible Navier-Stokes-Fourier limit of 3D stationary Boltzmann equation 三维平稳Boltzmann方程的不可压缩Navier-Stokes-Fourier极限
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023026
L. Wu, Zhimeng Ouyang
{"title":"Incompressible Navier-Stokes-Fourier limit of 3D stationary Boltzmann equation","authors":"L. Wu, Zhimeng Ouyang","doi":"10.3934/krm.2023026","DOIUrl":"https://doi.org/10.3934/krm.2023026","url":null,"abstract":"","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73249666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-posedness for systems of self-propelled particles 自推进粒子系统的适定性
4区 数学
Kinetic and Related Models Pub Date : 2023-01-01 DOI: 10.3934/krm.2023036
Marc Briant, Nicolas Meunier
{"title":"Well-posedness for systems of self-propelled particles","authors":"Marc Briant, Nicolas Meunier","doi":"10.3934/krm.2023036","DOIUrl":"https://doi.org/10.3934/krm.2023036","url":null,"abstract":"This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the Euclidean space but constrained on the unit sphere (the self-propulsion constraint). Two related equations are considered: the first one, in which the alignment mechanism is nonlocal, using an observation kernel depending on the space variable, and a second form, which is purely local, corresponding to the principal order of a scaling limit of the first one. We prove local existence and uniqueness of weak solutions in both cases for bounded initial conditions (in space and velocity) with finite total mass. The solution is proven to depend continuously on the initial data in $ L^p $ spaces with finite $ p $. In the case of a bounded kernel of observation, we obtain that the solution is global in time. Finally, by exploiting the fact that the second equation corresponds to the principal order of a scaling limit of the first one, we deduce a Cauchy theory for an approximate problem approaching the second one.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134882270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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