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Structure preserving schemes for the continuum Kuramoto model: Phase transitions

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Title: Structure preserving schemes for the continuum Kuramoto model: Phase transitions
Authors: Carrillo de la Plata, J
Choi, Y-P
Pareschi, L
Item Type: Journal Article
Abstract: The construction of numerical schemes for the Kuramoto model is challenging due to the structural properties of the system which are essential in order to capture the correct physical behavior, like the description of stationary states and phase transitions. Additional difficulties are represented by the high dimensionality of the problem in presence of multiple frequencies. In this paper, we develop numerical methods which are capable to preserve these structural properties of the Kuramoto equation in the presence of diffusion and to solve efficiently the multiple frequencies case. The novel schemes are then used to numerically investigate the phase transitions in the case of identical and nonidentical oscillators.
Issue Date: 1-Jan-2019
Date of Acceptance: 27-Sep-2018
URI: http://hdl.handle.net/10044/1/65069
DOI: https://dx.doi.org/10.1016/j.jcp.2018.09.049
ISSN: 0021-9991
Publisher: Elsevier
Start Page: 365
End Page: 389
Journal / Book Title: Journal of Computational Physics
Volume: 376
Copyright Statement: © 2018 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: 01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status: Published
Online Publication Date: 2018-10-02
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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