Multiplication of defects in hexagonal patterns

Author： Colinet P. Nepomnyashchy A. A. Legros J. C.

E-ISSN： 1286-4854|57|4|480-486

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.57, Iss.4, 2010-03, pp. : 480-486

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Abstract

A typical object in hexagonal patterns is a penta-hepta defect (PHD),i.e. a bound state of two dislocations on different rollsubsystems. In the frame of a generic non-variational system ofamplitude equations, a new phenomenon of multiplication of PHDs ispredicted. Typically, a PHD can multiply through creation of a newdislocation pair on the dislocation-free roll subsystem, andrecombination of dislocations into PHDs of the next generation. Thelong-run evolution displays wavelength selection mediated by movingPHDs, even within the Busse stability balloon of perfect hexagonalpatterns. Defect-mediated wave number adjustment is also predicted forthe damped Kuramoto-Sivashinsky equation.