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Localized states in passive and active phase-field-crystal models

journal contribution
posted on 13.07.2021, 14:18 by Max Philipp Holl, Andrew ArcherAndrew Archer, Svetlana V Gurevich, Edgar Knobloch, Lukas Ophaus, Uwe Thiele
The passive conserved Swift–Hohenberg equation (or phase-field-crystal [PFC] model) describes gradient dynamics of a single-order parameter field related to density. It provides a simple microscopic description of the thermodynamic transition between liquid and crystalline states. In addition to spatially extended periodic structures, the model describes a large variety of steady spatially localized structures. In appropriate bifurcation diagrams the corresponding solution branches exhibit characteristic slanted homoclinic snaking. In an active PFC model, encoding for instance the active motion of self-propelled colloidal particles, the gradient dynamics structure is broken by a coupling between density and an additional polarization field. Then, resting and traveling localized states are found with transitions characterized by parity-breaking drift bifurcations. Here, we briefly review the snaking behavior of localized states in passive and active PFC models before discussing the bifurcation behavior of localized states in systems of (i) two coupled passive PFC models with common gradient dynamics, (ii) two coupled passive PFC models where the coupling breaks the gradient dynamics structure and (iii) a passive PFC model coupled to an active PFC model.

Funding

Franco-German University (CDFA-01-14)

National Science Foundation (DMS1908891)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

IMA Journal of Applied Mathematics

Publisher

Oxford University Press (OUP)

Version

AM (Accepted Manuscript)

Rights holder

© The Authors

Publisher statement

This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Max Philipp Holl, Andrew J Archer, Svetlana V Gurevich, Edgar Knobloch, Lukas Ophaus, Uwe Thiele, Localized states in passive and active phase-field-crystal models, IMA Journal of Applied Mathematics, 2021;, hxab025, https://doi.org/10.1093/imamat/hxab025 is available online at: https://doi.org/10.1093/imamat/hxab025.

Acceptance date

10/06/2021

Publication date

2021-07-09

Copyright date

2021

Notes

Submitted to the IMA Journal of Applied Mathematics' Special Issue on Homoclinic Snaking at 21, in memory of Patrick Woods.

ISSN

0272-4960

eISSN

1464-3634

Language

en

Depositor

Prof Andrew Archer. Deposit date: 13 July 2021