Crystallization kinetics and self-induced pinning in cellular patterns

Igor Aronson, Boris A. Malomed, Len M. Pismen, Lev S. Tsimring

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

The aspect of pattern formation in nonequilibrium media such as self-induced pinning and stick-and-slip motion of the interphase boundary, as a particular kind of crystallization or melting is modelled by the Swift-Hohenberg (SH) equation. Within the SH model, the front propagation between cellular and uniform states can be evaluated by periodic nucleation events initiated by a violent growth of the localized zero-eigenvalue mode of the corresponding linear problem. An evolution equation for this mode is estimated using asymptotic analysis wherein the time interval between nucleation events and the front speed are estimated. The creep velocity exponent of `thermally activated' front propagation beyond the pinning threshold is derived.

Original languageEnglish (US)
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume62
Issue number1 A
DOIs
StatePublished - Jul 1 2000

Fingerprint

Front Propagation
Crystallization
Nucleation
Kinetics
crystallization
Swift-Hohenberg Equation
kinetics
Creep
Pattern Formation
Melting
Asymptotic Analysis
nucleation
Slip
Non-equilibrium
Evolution Equation
propagation
Exponent
Eigenvalue
Interval
Motion

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

Cite this

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Crystallization kinetics and self-induced pinning in cellular patterns. / Aronson, Igor; Malomed, Boris A.; Pismen, Len M.; Tsimring, Lev S.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 62, No. 1 A, 01.07.2000.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Crystallization kinetics and self-induced pinning in cellular patterns

AU - Aronson, Igor

AU - Malomed, Boris A.

AU - Pismen, Len M.

AU - Tsimring, Lev S.

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AB - The aspect of pattern formation in nonequilibrium media such as self-induced pinning and stick-and-slip motion of the interphase boundary, as a particular kind of crystallization or melting is modelled by the Swift-Hohenberg (SH) equation. Within the SH model, the front propagation between cellular and uniform states can be evaluated by periodic nucleation events initiated by a violent growth of the localized zero-eigenvalue mode of the corresponding linear problem. An evolution equation for this mode is estimated using asymptotic analysis wherein the time interval between nucleation events and the front speed are estimated. The creep velocity exponent of `thermally activated' front propagation beyond the pinning threshold is derived.

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