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DY: Fachverband Dynamik und Statistische Physik

DY 44: Pattern Formation

DY 44.4: Talk

Thursday, March 19, 2015, 10:15–10:30, BH-N 333

Localized states in the conserved Swift-Hohenberg equation (aka the Phase Field Crystal quation) — •Uwe Thiele¹, Andrew J. Archer², Mark J. Robbins², Hector Gomez³, and Edgar Knobloch⁴ — ¹Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Germany — ²Department of Mathematical Sciences, Loughborough University, Loughborough, UK — ³University of A Coruna, 15192 A Coruna, Spain — ⁴Department of Physics, University of California, Berkeley, CA, USA

We consider the structure of localised states for the phase field crystal (PFC) model [aka conserved Swift-Hohenberg (cSH) equation with cubic nonlinearity] that may be obtained as a local approximation of a dynamical density functional theory (DDFT) for colloidal crystallisation [1].

We determine the location of steady spatially localized structures in the temperature vs. mean order parameter plane combining numerical continuation in 1d and direct numerical simulation in 2d and 3d. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential [2].

[1] H. Emmerich et al., Adv. Phys. 61, 665 (2012). [2] U. Thiele, A. J. Archer, M. J. Robbins, H. Gomez, and E. Knobloch, Phys. Rev. E. 87, 042915 (2013).