Kinetic & Related Models最新文献

A Lie algebra-theoretic approach to characterisation of collision invariants of the Boltzmann equation for general convex particles 一般凸粒子玻尔兹曼方程碰撞不变量特征的李代数方法

Kinetic & Related Models Pub Date : 2021-10-20 DOI: 10.3934/krm.2022008

Mark Wilkinson

{"title":"A Lie algebra-theoretic approach to characterisation of collision invariants of the Boltzmann equation for general convex particles","authors":"Mark Wilkinson","doi":"10.3934/krm.2022008","DOIUrl":"https://doi.org/10.3934/krm.2022008","url":null,"abstract":"By studying scattering Lie groups and their associated Lie algebras, we introduce a new method for the characterisation of collision invariants for physical scattering families associated to smooth, convex hard particles in the particular case that the collision invariant is of class <inline-formula><tex-math id=\"M1\">begin{document}$ mathscr{C}^{1} $end{document}</tex-math></inline-formula>. This work extends that of Saint-Raymond and Wilkinson (Communications on Pure and Applied Mathematics (2018), 71(8), pp. 1494–1534), in which the authors characterise collision invariants only in the case of the so-called canonical physical scattering family. Indeed, our method extends to the case of non-canonical physical scattering, whose existence was reported in Wilkinson (Archive for Rational Mechanics and Analysis (2020), 235(3), pp. 2055–2083). Moreover, our new method improves upon the work in Saint-Raymond and Wilkinson as we place no symmetry hypotheses on the underlying non-spherical particles which make up the gas under consideration. The techniques established in this paper also yield a new proof of the result of Boltzmann for collision invariants of class <inline-formula><tex-math id=\"M2\">begin{document}$ mathscr{C}^{1} $end{document}</tex-math></inline-formula> in the classical case of hard spheres.","PeriodicalId":393586,"journal":{"name":"Kinetic & Related Models","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126808420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Formal derivation of quantum drift-diffusion equations with spin-orbit interaction 具有自旋-轨道相互作用的量子漂移-扩散方程的形式推导

Kinetic & Related Models Pub Date : 2021-09-20 DOI: 10.3934/krm.2022007

L. Barletti, Philipp Holzinger, A. Jungel

引用次数: 0

Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium 收敛到给定平衡点的最优非对称Fokker-Planck方程

Kinetic & Related Models Pub Date : 2021-06-29 DOI: 10.3934/krm.2022009

A. Arnold, Beatrice Signorello

{"title":"Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium","authors":"A. Arnold, Beatrice Signorello","doi":"10.3934/krm.2022009","DOIUrl":"https://doi.org/10.3934/krm.2022009","url":null,"abstract":"This paper is concerned with finding Fokker-Planck equations in <inline-formula><tex-math id=\"M1\">begin{document}$ mathbb{R}^d $end{document}</tex-math></inline-formula> with the fastest exponential decay towards a given equilibrium. For a prescribed, anisotropic Gaussian we determine a non-symmetric Fokker-Planck equation with linear drift that shows the highest exponential decay rate for the convergence of its solutions towards equilibrium. At the same time it has to allow for a decay estimate with a multiplicative constant arbitrarily close to its infimum.Such an \"optimal\" Fokker-Planck equation is constructed explicitly with a diffusion matrix of rank one, hence being hypocoercive. In an <inline-formula><tex-math id=\"M2\">begin{document}$ L^2 $end{document}</tex-math></inline-formula>–analysis, we find that the maximum decay rate equals the maximum eigenvalue of the inverse covariance matrix, and that the infimum of the attainable multiplicative constant is 1, corresponding to the high-rotational limit in the Fokker-Planck drift. This analysis is complemented with numerical illustrations in 2D, and it includes a case study for time-dependent coefficient matrices.","PeriodicalId":393586,"journal":{"name":"Kinetic & Related Models","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127241292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Local conditional regularity for the Landau equation with Coulomb potential 具有库仑势的朗道方程的局部条件正则性

Kinetic & Related Models Pub Date : 2021-05-13 DOI: 10.3934/krm.2022010

Immanuel Ben Porat

引用次数: 3

Kinetic &amp; Related Models最新文献

Kinetic & Related Models最新文献