Journal article

Structure preserving schemes for the continuum Kuramoto model: phase transitions

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.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Carrillo, J. A., Choi, Y. P., & Pareschi, L. (2018). Structure preserving schemes for the continuum Kuramoto model: phase transitions. Journal of Computational Physics, 376, 365–389.

MLA Style

Carrillo, J. A., et al. “Structure Preserving Schemes for the Continuum Kuramoto Model: Phase Transitions.” Journal of Computational Physics, vol. 376, Elsevier, 2018, pp. 365–89.

Chicago Style

Carrillo, JA, YP Choi, and L Pareschi. 2018. “Structure Preserving Schemes for the Continuum Kuramoto Model: Phase Transitions.” Journal of Computational Physics 376: 365–89.
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Files:: Structure_preserving_schemes.pdf

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Publisher copy:: 10.1016/j.jcp.2018.09.049

Authors

+ Carrillo, JA More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Choi, YP More by this author

Role:: Author

+ Pareschi, L More by this author

Role:: Author

Publisher:: Elsevier
Journal:: Journal of Computational Physics More from this journal
Volume:: 376
Pages:: 365-389
Publication date:: 2018-10-02
Acceptance date:: 2018-09-27
DOI:: 10.1016/j.jcp.2018.09.049
EISSN:: 1090-2716
ISSN:: 0021-9991

Language:: English
Keywords:: phase transitions

Kuramoto oscillators

kinetic equations

structure preserving
Pubs id:: 1098235
Local pid:: pubs:1098235
Deposit date:: 2020-04-07

Terms of use

Copyright holder:: Carrillo et al.
Copyright date:: 2018
Rights 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/).

Licence:: CC Attribution (CC BY)

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