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Phys. Rev. E 73, 022101 (2006) [4 pages]

Comprehensive study of pattern formation in relaxational systems

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Kevin Wood1,2, Javier Buceta3, and Katja Lindenberg1
1Department of Chemistry and Biochemistry 0340, and Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
2Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
3Centre de Recerca en Química Teòrica (CeRQT), Parc Científic de Barcelona, Campus Diagonal—Universitat de Barcelona, Edifici Modular, C/Josep Samitier 1-5, 08028 Barcelona, Spain

Received 7 October 2005; published 8 February 2006

We present a comprehensive study of pattern formation in single-field relaxational systems with field-dependent coefficients. A modulated mean-field theory leads to a form amenable to analysis via the geometric architecture developed in our earlier work for systems that exhibit phase transitions between global steady states [ Phys. Rev. E 69 011102 (2004)]. We demonstrate that the phase diagrams for these systems are entirely determined by a few geometric properties of the field-dependent relaxational coefficient and the local potential. Numerical simulations support the theoretical predictions.

© 2006 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.73.022101
DOI:
10.1103/PhysRevE.73.022101
PACS:
05.40.−a, 47.54.-r, 05.10.Gg, 89.75.Kd
 
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