Mathematical Physics, Analysis and Geometry最新文献_第2页

Correction to: Geometric analysis of Ising Models, Part III 修正：伊辛模型的几何分析，第三部分

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-09-05 DOI: 10.1007/s11040-026-09583-x

Michael Aizenman

引用次数: 0

Universal Cumulants and Conformal Invariance in Annihilating Random Walks with Pair Deposition 具有对沉积的湮灭随机游动中的普适累积量和保形不变性

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-26 DOI: 10.1007/s11040-026-09588-6

D. Karevski, G. M. Schütz, A. Zahra

引用次数: 0

(L^p)-Boltzmann–Gibbs Principle via Littlewood–Paley–Stein Inequality (L^p)-由littlewood - paly - stein不等式推导的boltzmann - gibbs原理

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-25 DOI: 10.1007/s11040-026-09587-7

Tadahisa Funaki

引用次数: 0

Boundary Thermalization in Superdiffusive Energy Transport 超扩散能量输运中的边界热化

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-24 DOI: 10.1007/s11040-026-09586-8

Tomasz Komorowski, Stefano Olla

{"title":"Boundary Thermalization in Superdiffusive Energy Transport","authors":"Tomasz Komorowski, Stefano Olla","doi":"10.1007/s11040-026-09586-8","DOIUrl":"10.1007/s11040-026-09586-8","url":null,"abstract":"<div><p>We study energy transport in a finite one-dimensional unpinned harmonic chain with stochastic nearest-neighbor momentum exchanges and Langevin heat baths at its endpoints. Such systems are known to exhibit superdiffusive transport driven by long-wavelength acoustic modes, leading to fractional macroscopic behavior. While fractional heat equations have been rigorously derived for infinite chains, the corresponding boundary conditions for finite systems in contact with heat baths remain unclear due to the nonlocality of the fractional Laplacian. Under the superdiffusive time scaling <span>(tsim n^{3/2})</span>, where <i>n</i> is the system size, we prove that the averaged microscopic energy profile converges, as <span>(nrightarrow +infty )</span>, to a temperature field solving a fractional heat equation on [0, 1], with the generator given by a Neumann fractional Laplacian and additional nonlocal boundary terms induced by the heat baths. Our results provide a rigorous derivation of macroscopic boundary conditions for superdiffusive heat transport in open chains and introduce new boundary conditions for fractional Laplacians, that are motivated by a physical model.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09586-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stochastic Heterogeneous SIR Model with Infection-Age Dependent Infectivity on Large Random Graphs 大随机图上感染年龄依赖的随机异构SIR模型

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-21 DOI: 10.1007/s11040-026-09582-y

Guodong Pang, Étienne Pardoux, Aurélien Velleret

{"title":"Stochastic Heterogeneous SIR Model with Infection-Age Dependent Infectivity on Large Random Graphs","authors":"Guodong Pang, Étienne Pardoux, Aurélien Velleret","doi":"10.1007/s11040-026-09582-y","DOIUrl":"10.1007/s11040-026-09582-y","url":null,"abstract":"<div><p>We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous connectivity. Each individual is associated with particular characteristics (for example, spatial location and age structure), which may not be i.i.d., and is represented by a particular node. The connectivities among the individuals are given by a non-homogeneous random graph, whose connecting probabilities may depend on the individual characteristics of the edge. To each individual is associated a random infectivity function of its infection age, which is allowed to depend upon the individual characteristics. We use measure-valued processes to describe the epidemic evolution dynamics, tracking the infection age of all individuals, and their associated characteristics. We consider the epidemic dynamics as the population size grows to infinity under a specific scaling of the connectivity graph related to the convergence to a graphon. In the limit, we obtain a system of measure-valued equations, which can be also represented as a PDE model on graphon, and reflects the heterogeneities in individual characteristics and social connectivity.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Gradient Estimates for a Nonlinear Parabolic Equation Under the Yamabe Flow Yamabe流下非线性抛物方程的梯度估计

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-06 DOI: 10.1007/s11040-026-09585-9

Chenlin Huang, Fei Yang

引用次数: 0

Lie Symmetry Analysis, Conservation Laws and Stability Analysis for the Nonhomogeneous Monge–ampère equation 非齐次monge - ampantre方程的Lie对称性分析、守恒律和稳定性分析

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-05 DOI: 10.1007/s11040-026-09575-x

Germán F. Escobar F., Oscar M. Londoño D., Julio C. Duarte V.

{"title":"Lie Symmetry Analysis, Conservation Laws and Stability Analysis for the Nonhomogeneous Monge–ampère equation","authors":"Germán F. Escobar F., Oscar M. Londoño D., Julio C. Duarte V.","doi":"10.1007/s11040-026-09575-x","DOIUrl":"10.1007/s11040-026-09575-x","url":null,"abstract":"<div><p>This work presents a symmetry analysis of the nonhomogeneous Monge–Ampère equation <span>(varvec{det D^{2} u = x^{p} y^{q}})</span> in <span>(varvec{Omega subset } pmb {mathbb {R}}^{textbf{2}})</span>, with <span>(varvec{p, q in } pmb {mathbb {R}})</span>. Using Lie group theory, we classify all point symmetries, obtaining a five-dimensional Lie algebra in the generic case, which is solvable and isomorphic to <span>({mathbb {R}}^3 ltimes {mathbb {R}}^2)</span>. We prove the equation is nonlinearly self-adjoint and apply Ibragimov’s theorem to derive explicit conservation laws for each symmetry generator. The adjoint representation of the Lie algebra is constructed, and a one-dimensional optimal system of subalgebras is determined, enabling classification of all distinct symmetry reductions. These reductions yield nonlinear ordinary differential equations, analyzed qualitatively via Poincaré compactification to identify critical points at infinity and their stability. The results provide a comprehensive structural description of the equation’s symmetries, conservation laws, and invariant solutions, enhancing understanding of its geometric and analytical properties.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09575-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Gradient Measures on Cayley Trees Associated with Two Periodic Homogeneous and Inhomogeneous Boundary Laws for the SOS Model 基于两个周期齐次和非齐次边界律的Cayley树的梯度测度

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-04 DOI: 10.1007/s11040-026-09581-z

R. A. Ilyasova

引用次数: 0

Affine Weyl Groups and Non-Abelian Discrete Systems: An Application to the d-Painlevé Equations 仿射Weyl群与非阿贝尔离散系统：在d- painlevleve方程中的应用

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-03 DOI: 10.1007/s11040-026-09573-z

Irina Bobrova

引用次数: 0

On the Large-Time Asymptotics of the Defocusing mKdV Equation with Step-Like Initial Data 具有步长初始数据的散焦mKdV方程的大时间渐近性

IF 1.2 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-28 DOI: 10.1007/s11040-026-09579-7

Taiyang Xu, Yidan Zhang

{"title":"On the Large-Time Asymptotics of the Defocusing mKdV Equation with Step-Like Initial Data","authors":"Taiyang Xu, Yidan Zhang","doi":"10.1007/s11040-026-09579-7","DOIUrl":"10.1007/s11040-026-09579-7","url":null,"abstract":"<div><p>We study the Cauchy problem for the defocusing modified Korteweg–de Vries (mKdV) equation with step-like initial data approaching nonzero constants <span>(c_l)</span> and <span>(c_r)</span> as <span>(x rightarrow -infty )</span> and <span>(xrightarrow +infty )</span>, respectively. Assuming <span>(c_l>c_r>0)</span>, the solution exhibits a rarefaction wave structure. We first develop the inverse scattering transform for the solution satisfying these step-like boundary conditions. Using the associated scattering data, we prove that there exists a unique global solution of the Cauchy problem and characterize it in terms of a Riemann–Hilbert (RH) problem. By applying the nonlinear steepest descent method to this RH problem, we rigorously obtain large-time asymptotics of rarefaction wave solution in three distinct space-time regions, each characterized by a different leading order behavior. They are: (I) a left-field region where the solution approaches the left background constant, modulo a small oscillatory correction, (II) a central region where the solution exhibits a slowly varying profile that transitions between the two constants, and (III) a right-field region where the solution tends to the right background constant, up to an algebraically small correction. Rigorous derivations of the leading terms, sub-leading terms as well as the error bounds are presented.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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