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Phys. Rev. E 69, 016215 (2004) [8 pages]

Pattern formation capacity of spatially extended systems

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Serguei Vakulenko*
Institute for Mechanical Engineering Problems, Russian Academy of Sciences, Bolshoy prospekt V.O. 61, Saint Petersburg 199178, Russia

Bogdan Kazmierczak†,‡
Polish Academy of Sciences, IPPT PAN, Świetokrzyska 21, PL 00-049 Warszawa, Poland

Stéphane Génieys§
MAPLY, UMR 5585 CNRS, Université Lyon I, 43 Boulevard du 11 Novembre, 69622 Villeurbanne Cedex, France

Received 18 August 2003; published 30 January 2004

We analyze a class of spatially extended systems which are capable of generating many complicated patterns. These systems are given by the Ginzburg-Landau equation coupled with a system of two linear equations and describe nonlinear media with localized defects. We find a connection between these systems and spin-glass systems. We show that the system is capable to produce many patterns and describe patterning algorithms.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.69.016215
DOI:
10.1103/PhysRevE.69.016215
PACS:
89.75.Kd, 74.20.De

*Electronic address: vakul@mech.ipme.ru

†Electronic address: bkazmier@ippt.gov.pl

‡Also at Department of Mathematics and the Interdisciplinary Center for the Study of Biocomplexity, University of Notre Dame, Notre Dame, IN 46556-5670.

§Electronic address: genieys@maply.univ-lyon1.fr

 
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