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Analysis of a Mathematical Model for Fluid Transport in Poroelastic Materials in 2D Space 分析二维空间中波弹性材料中的流体传输数学模型
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-18 DOI: arxiv-2409.11949
Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka, Jacek Waniewski
{"title":"Analysis of a Mathematical Model for Fluid Transport in Poroelastic Materials in 2D Space","authors":"Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka, Jacek Waniewski","doi":"arxiv-2409.11949","DOIUrl":"https://doi.org/arxiv-2409.11949","url":null,"abstract":"A mathematical model for the poroelastic materials (PEM) with the variable\u0000volume is developed in multidimensional case. Governing equations of the model\u0000are constructed using the continuity equations, which reflect the well-known\u0000physical laws. The deformation vector is specified using the Terzaghi effective\u0000stress tensor. In the two-dimensional space case, the model is studied by\u0000analytical methods. Using the classical Lie method, it is proved that the\u0000relevant nonlinear system of the (1+2)-dimensional governing equations admits\u0000highly nontrivial Lie symmetries leading to an infinite-dimensional Lie\u0000algebra. The radially-symmetric case is studied in details. It is shown how\u0000correct boundary conditions in the case of PEM in the form of a ring and an\u0000annulus are constructed. As a result, boundary-value problems with a moving\u0000boundary describing the ring (annulus) deformation are constructed. The relevant nonlinear boundary-value problems are analytically solved in the\u0000stationary case. In particular, the analytical formulae for unknown\u0000deformations and an unknown radius of the annulus are presented.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260378","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
Principal binets 主要二进制
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.11322
Niklas Christoph Affolter, Jan Techter
{"title":"Principal binets","authors":"Niklas Christoph Affolter, Jan Techter","doi":"arxiv-2409.11322","DOIUrl":"https://doi.org/arxiv-2409.11322","url":null,"abstract":"Conjugate line parametrizations of surfaces were first discretized almost a\u0000century ago as quad meshes with planar faces. With the recent development of\u0000discrete differential geometry, two discretizations of principal curvature line\u0000parametrizations were discovered: circular nets and conical nets, both of which\u0000are special cases of discrete conjugate nets. Subsequently, circular and\u0000conical nets were given a unified description as isotropic line congruences in\u0000the Lie quadric. We propose a generalization by considering polar pairs of line\u0000congruences in the ambient space of the Lie quadric. These correspond to pairs\u0000of discrete conjugate nets with orthogonal edges, which we call principal\u0000binets, a new and more general discretization of principal curvature line\u0000parametrizations. We also introduce two new discretizations of orthogonal and\u0000Gauss-orthogonal parametrizations. All our discretizations are subject to the\u0000transformation group principle, which means that they satisfy the corresponding\u0000Lie, M\"obius, or Laguerre invariance respectively, in analogy to the smooth\u0000theory. Finally, we show that they satisfy the consistency principle, which\u0000means that our definitions generalize to higher dimensional square lattices.\u0000Our work expands on recent work by Dellinger on checkerboard patterns.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260394","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
A gradient flow model for ground state calculations in Wigner formalism based on density functional theory 基于密度泛函理论的维格纳基态计算梯度流模型
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.10851
Guanghui Hu, Ruo Li, Hongfei Zhan
{"title":"A gradient flow model for ground state calculations in Wigner formalism based on density functional theory","authors":"Guanghui Hu, Ruo Li, Hongfei Zhan","doi":"arxiv-2409.10851","DOIUrl":"https://doi.org/arxiv-2409.10851","url":null,"abstract":"In this paper, a gradient flow model is proposed for conducting ground state\u0000calculations in Wigner formalism of many-body system in the framework of\u0000density functional theory. More specifically, an energy functional for the\u0000ground state in Wigner formalism is proposed to provide a new perspective for\u0000ground state calculations of the Wigner function. Employing density functional\u0000theory, a gradient flow model is designed based on the energy functional to\u0000obtain the ground state Wigner function representing the whole many-body\u0000system. Subsequently, an efficient algorithm is developed using the operator\u0000splitting method and the Fourier spectral collocation method, whose numerical\u0000complexity of single iteration is $O(n_{rm DoF}log n_{rm DoF})$. Numerical\u0000experiments demonstrate the anticipated accuracy, encompassing the\u0000one-dimensional system with up to $2^{21}$ particles and the three-dimensional\u0000system with defect, showcasing the potential of our approach to large-scale\u0000simulations and computations of systems with defect.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260453","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
Foundations on k-contact geometry k 接触几何学基础
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.11001
Javier de Lucas, Xavier Rivas, Tomasz Sobczak
{"title":"Foundations on k-contact geometry","authors":"Javier de Lucas, Xavier Rivas, Tomasz Sobczak","doi":"arxiv-2409.11001","DOIUrl":"https://doi.org/arxiv-2409.11001","url":null,"abstract":"k-Contact geometry appeared as a generalisation of contact geometry to\u0000analyse field theories. This work provides a new insightful approach to\u0000k-contact geometry by devising a theory of k-contact forms and proving that the\u0000kernel of a k-contact form is locally equivalent to a distribution of corank k\u0000that is distributionally maximally non-integrable and admits k commuting Lie\u0000symmetries: a so-called k-contact distribution. Compact manifolds admitting a\u0000global k-contact form are analysed, we give necessary topological conditions\u0000for their existence, k-contact Lie groups are defined and studied, we extend\u0000the Weinstein conjecture for the existence of closed orbits of Reeb vector\u0000fields in compact manifolds to the k-contact setting after studying compact\u0000low-dimensional manifolds endowed with a global k-contact form, and we provide\u0000some physical applications of some of our results. Polarisations for k-contact\u0000distributions are introduced and it is shown that a polarised k-contact\u0000distribution is locally diffeomorphic to the Cartan distribution of the\u0000first-order jet bundle over a fibre bundle of order k, which is a globally\u0000defined polarised k-contact distribution. Then, we relate k-contact manifolds\u0000to presymplectic and k-symplectic manifolds on fibre bundles of larger\u0000dimension and define for the first time types of submanifolds in k-contact\u0000geometry. We also review the theory of Hamiltonian k-vector fields, studying\u0000Hamilton-De Donder-Weyl equations in general and in Lie groups, which are here\u0000studied in an unprecedented manner. A theory of k-contact Hamiltonian vector\u0000fields is developed, which describes the theory of characteristics for Lie\u0000symmetries for first-order partial differential equations in a k-contact\u0000Hamiltonian manner. Our new Hamiltonian k-contact techniques are illustrated by\u0000analysing Hamilton-Jacobi and Dirac equations.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260450","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
Off-shell color-kinematics duality from codifferentials 从代差分出发的壳外色彩运动学对偶性
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.11484
Maor Ben-Shahar, Francesco Bonechi, Maxim Zabzine
{"title":"Off-shell color-kinematics duality from codifferentials","authors":"Maor Ben-Shahar, Francesco Bonechi, Maxim Zabzine","doi":"arxiv-2409.11484","DOIUrl":"https://doi.org/arxiv-2409.11484","url":null,"abstract":"We examine the color-kinematics duality within the BV formalism, highlighting\u0000its emergence as a feature of specific gauge-fixed actions. Our goal is to\u0000establish a general framework for studying the duality while investigating\u0000straightforward examples of off-shell color-kinematics duality. In this\u0000context, we revisit Chern-Simons theory as well as introduce new examples,\u0000including BF theory and 2D Yang-Mills theory, which are shown to exhibit the\u0000duality off-shell. We emphasize that the geometric structures responsible for\u0000flat-space color-kinematics duality appear for general curved spaces as well.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260391","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
Stability and eigenvalue bounds for micropolar shear flows 微波剪切流的稳定性和特征值边界
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.11584
Pablo Braz e Silva, Jackellyny Carvalho
{"title":"Stability and eigenvalue bounds for micropolar shear flows","authors":"Pablo Braz e Silva, Jackellyny Carvalho","doi":"arxiv-2409.11584","DOIUrl":"https://doi.org/arxiv-2409.11584","url":null,"abstract":"We prove eigenvalue bounds for two-dimensional linearized disturbances of\u0000parallel flows of micropolar fluids, deriving the Orr-Sommerfeld equations and\u0000providing a sufficient condition for linear stability of such flows. We also\u0000derive wave speed bounds.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260390","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
Hyperboloidal Approach to Quasinormal Modes 准正模的超波状方法
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.11478
Rodrigo Panosso Macedo, Anil Zenginoglu
{"title":"Hyperboloidal Approach to Quasinormal Modes","authors":"Rodrigo Panosso Macedo, Anil Zenginoglu","doi":"arxiv-2409.11478","DOIUrl":"https://doi.org/arxiv-2409.11478","url":null,"abstract":"Oscillations of black hole spacetimes exhibit divergent behavior toward the\u0000bifurcation sphere and spatial infinity. This divergence can be understood as a\u0000consequence of the geometry in these spacetime regions. In contrast, black-hole\u0000oscillations are regular when evaluated toward the event horizon and null\u0000infinity. Hyperboloidal surfaces naturally connect these regions, providing a\u0000geometric regularization of time-harmonic oscillations called quasinormal modes\u0000(QNMs). This review traces the historical development of the hyperboloidal\u0000approach to QNMs. We discuss the physical motivation for the hyperboloidal\u0000approach and highlight current developments in the field.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260392","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
A tale of two $q$-deformations : connecting dual polar spaces and weighted hypercubes 两个 q$ 变形的故事：连接对偶极空间和加权超立方体
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.11243
Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet
{"title":"A tale of two $q$-deformations : connecting dual polar spaces and weighted hypercubes","authors":"Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet","doi":"arxiv-2409.11243","DOIUrl":"https://doi.org/arxiv-2409.11243","url":null,"abstract":"Two $q$-analogs of the hypercube graph are introduced and shown to be related\u0000through a graph quotient. The roles of the subspace lattice graph, of a twisted\u0000primitive elements of $U_q(mathfrak{su}(2))$ and of the dual $q$-Krawtchouk\u0000polynomials are elaborated upon. This paper is dedicated to Tom Koornwinder.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260462","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
Asymptotics of the divisor for the good Boussinesq equation 良好布辛斯方程除数的渐近性
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.10988
Andrey Badanin, Andrey Badanin
{"title":"Asymptotics of the divisor for the good Boussinesq equation","authors":"Andrey Badanin, Andrey Badanin","doi":"arxiv-2409.10988","DOIUrl":"https://doi.org/arxiv-2409.10988","url":null,"abstract":"We consider a third order operator under the three-point Dirichlet condition.\u0000Its spectrum is the so-called auxiliary spectrum for the good Boussinesq\u0000equation, as well as the Dirichlet spectrum for the Schr\"odinger operator on\u0000the unit interval is the auxiliary spectrum for the periodic KdV equation. The\u0000auxiliary spectrum is formed by projections of the points of the divisor onto\u0000the spectral plane. We estimate the spectrum and the corresponding norming\u0000constants in terms of small operator coefficients. This work is the first in a\u0000series of papers devoted to solving the inverse problem for the Boussinesq\u0000equation.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260398","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
Three lectures on Fourier analysis and learning theory 关于傅立叶分析和学习理论的三场讲座
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.10886
Haonan Zhang
{"title":"Three lectures on Fourier analysis and learning theory","authors":"Haonan Zhang","doi":"arxiv-2409.10886","DOIUrl":"https://doi.org/arxiv-2409.10886","url":null,"abstract":"Fourier analysis on the discrete hypercubes ${-1,1}^n$ has found numerous\u0000applications in learning theory. A recent breakthrough involves the use of a\u0000classical result from Fourier analysis, the Bohnenblust--Hille inequality, in\u0000the context of learning low-degree Boolean functions. In these lecture notes,\u0000we explore this line of research and discuss recent progress in discrete\u0000quantum systems and classical Fourier analysis.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260452","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
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