Crystallization kinetics and self-induced pinning in cellular patterns

Journal Article · Sat Jul 01 00:00:00 EDT 2000 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.62.R5· OSTI ID:20217090

Aranson, Igor S ^[1]; Malomed, Boris A ^[2]; Pismen, Len M ^[3]; Tsimring, Lev S ^[4]

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1. Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439 (United States)
2. Department of Interdisciplinary Studies, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, (Israel)
3. Department of Chemical Engineering, Technion, 32000 Haifa, (Israel)
4. Institute for Nonlinear Science, University of California at San Diego, La Jolla, California 92093-0402 (United States)

Within the framework of the Swift-Hohenberg model it is shown numerically and analytically that the front propagation between cellular and uniform states is determined by periodic nucleation events triggered by the explosive growth of the localized zero-eigenvalue mode of the corresponding linear problem. We derive an evolution equation for this mode using asymptotic analysis, and evaluate the time interval between nucleation events, and hence the front speed. In the presence of noise, we find the velocity exponent of ''thermally activated'' front propagation (creep) beyond the pinning threshold. (c) 2000 The American Physical Society.

• OSTI ID: 20217090
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 62, Issue 1; Other Information: PBD: Jul 2000; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CRYSTALLIZATION
NUCLEATION
EIGENVALUES
ASYMPTOTIC SOLUTIONS
THEORETICAL DATA