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

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Chattopadhyay,  A. K.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Chattopadhyay, A. K. (2002). The role of pinning and instability in a class of non- equilibrium growth models. European Physical Journal B, 29(4), 567-576. Retrieved from http://link.springer.de/link/service/journals/10051/bibs/2029004/20290567.htm.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-36D5-6
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.