The role of pinning and instability in a class of non-equilibrium growth models

Chattopadhyay, A.K. (2002). The role of pinning and instability in a class of non-equilibrium growth models. European Physical Journal B: Condensed Matter and Complex Systems, 29 (4), pp. 567-576.

Abstract

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed.

Publication DOI: https://doi.org/10.1140/epjb/e2002-00341-4
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Uncontrolled Keywords: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion,05.70.Ln Nonequilibrium and irreversible thermodynamics,64.60.Ht Dynamic critical phenomena
Full Text Link: http://link.springer.com/article/10.1140%2Fepjb%2Fe2002-00341-4
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Published Date: 2002-10
Authors: Chattopadhyay, A.K.

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