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Localized States in the Conserved Swift-Hohenberg Equation

Wednesday, June 5, 2013 - 10:15am - 11:00am
Keller 3-180
Edgar Knobloch (University of California, Berkeley)
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the
simplest microscopic description of the thermodynamic transition from a
fluid state to a crystalline state. The resulting phase field crystal
model describes a variety of spatially localized structures, in addition
to different spatially extended periodic structures. The location of these
structures in the temperature versus mean order parameter plane is
determined using a combination of numerical continuation in one
dimension and direct numerical simulation in two and three dimensions.
Localized states are found in the region of thermodynamic coexistence
between the homogeneous and structured phases, and may lie outside of the
binodal for these states. 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,
and are expected to carry over to related models with a conserved order
parameter.

This work is joint work with U Thiele, A J Archer, M J Robbins and H Gomez.
MSC Code: 
74A15
Keywords: