TY - JOUR

T1 - Phase Transition in a Periodic Tubular Structure

AU - Рядовкин, Кирилл Сергеевич

AU - Киселев, Александр

PY - 2024

Y1 - 2024

N2 - We consider an \varepsilon-periodic (\varepsilon \rightarrow 0) 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 \BbbR 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.

AB - We consider an \varepsilon-periodic (\varepsilon \rightarrow 0) 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 \BbbR 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.

KW - asymptotic analysis

KW - homogenization

KW - periodic graphs

KW - phase transitions

UR - https://www.mendeley.com/catalogue/c2fbab87-f178-36fc-8de1-09eb1c0ee02b/

U2 - 10.1137/23M157274X

DO - 10.1137/23M157274X

M3 - Article

VL - 84

SP - 890

EP - 914

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

M1 - 3

ER -