周期管状结构中的相变

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-05-06 DOI:10.1137/23m157274x

Alexander V. Kiselev, Kirill Ryadovkin

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引用次数: 0

摘要

SIAM 应用数学杂志》第 84 卷第 3 期第 890-914 页，2024 年 6 月。摘要。我们考虑了一个[math]-周期（[math]）管状结构，它被建模为一个度量图上的磁拉普拉奇，它沿单轴是周期性的。我们证明，相应的哈密顿方程可以收敛到[math]上的一个 ODE 的规范残差，在磁势的一组离散值（临界点）上是四阶的，而在一般情况下是二阶的。在临界点附近，我们建立了混合阶渐近线。我们还估算了收敛速率。这代表了一个随着（恒定）磁场强度增加而发生相变的物理可行模型。

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Phase Transition in a Periodic Tubular Structure

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.

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

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.