| Issue |
Europhys. Lett.
Volume 57, Number 4, February 2002
|
|
|---|---|---|
| Page(s) | 480 - 486 | |
| Section | Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics | |
| DOI | https://doi.org/10.1209/epl/i2002-00487-7 | |
| Published online | 01 September 2002 | |
Multiplication of defects in hexagonal patterns
1
Université Libre de Bruxelles, Service de Chimie Physique
EP C.P. 165/62, 50 Av. F. D. Roosevelt, 1050 Brussels, Belgium
2
Department of Mathematics and Minerva Center
for Nonlinear Physics of Complex Systems,
Technion-Israel Institute of Technology - 32000 Haifa, Israel
Corresponding author: pcolinet@ulb.ac.be
Received:
26
January
2001
Accepted:
28
November
2001
A typical object in hexagonal patterns is a penta-hepta defect (PHD), i.e. a bound state of two dislocations on different roll subsystems. In the frame of a generic non-variational system of amplitude equations, a new phenomenon of multiplication of PHDs is predicted. Typically, a PHD can multiply through creation of a new dislocation pair on the dislocation-free roll subsystem, and recombination of dislocations into PHDs of the next generation. The long-run evolution displays wavelength selection mediated by moving PHDs, even within the Busse stability balloon of perfect hexagonal patterns. Defect-mediated wave number adjustment is also predicted for the damped Kuramoto-Sivashinsky equation.
PACS: 47.54.+r – Pattern selection; pattern formation / 47.20.Dr – Surface-tension-driven instability / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems
© EDP Sciences, 2002
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