{"title":"Phase Transition in a Periodic Tubular Structure","authors":"Alexander V. Kiselev, Kirill Ryadovkin","doi":"10.1137/23m157274x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 890-914, June 2024. <br/> Abstract. We consider an [math]-periodic ([math]) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on [math] which is fourth order at a discrete set of values of the magnetic potential (critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m157274x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 890-914, June 2024. Abstract. We consider an [math]-periodic ([math]) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on [math] which is fourth order at a discrete set of values of the magnetic potential (critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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