@article{83f0dc7be74940f6a4543aae55d264fd,
title = "Phase Transition in a Periodic Tubular Structure",
abstract = "We consider an ε-periodic (ε→0) tubular structure, modelled 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 R which is fourth order at a discrete set of values of the magnetic potential (\emph{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.",
keywords = "asymptotic analysis, homogenization, periodic graphs, phase transitions",
author = "Kiselev, {Alexander V.} and Kirill Ryadovkin",
year = "2024",
month = jun,
day = "30",
doi = "10.1137/23M157274X",
language = "English",
volume = "84",
pages = "890--914",
journal = "SIAM Journal on Applied Mathematics ",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}