Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 59: Posters - Nonlinear General

DY 59.3: Poster

Thursday, March 23, 2017, 17:00–19:30, P1A

Rodlike Localized States in a Swift-Hohenberg Model — •Felix Tabbert¹, Ignacio Bordeu², and Svetlana Gurevich¹ — ¹Institute for Theoretical Physics, Münster — ²Imperial College, London

We study the existence of localized rodlike solutions in a Swift-Hohenberg model which have been reported in [1]. We provide a linear stability analysis and a bifurcation analysis in two dimensions of rodlike and other stationary solutions which bifurcate by breaking the rotational symmetry of a single localized solution. To this aim, we deploy numerical pathway continuation in two spatial dimensions in combination with direct numerical simulations. Since the Swift-Hohenberg equation possesses the same stationary solutions as the conserved Swift-Hohenberg equation, most of the results can also be applied to phase field crystal models of this type [2][3].

Further analysis includes the destabilization of the aforementioned solutions by time-delayed feedback leading to complex dynamics, e.g. drift or rotations. A stability analysis of the time-delayed system is also performed and shows good agreement with the results from direct numerical simulations.

[1] I. Bordeu and M. G. Clerc, Phys. Rev. E 92, 042915 (2015).

[2] A.M. Menzel and H. Löwen, Phys. Rev. Lett. 110, 055702 (2013).

[3] M.J. Robbins et al., Phys Rev E 85, 061408 (2012).