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

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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.
Original languageEnglish
Pages (from-to)567-576
Number of pages10
JournalEuropean Physical Journal B: Condensed Matter and Complex Systems
Volume29
Issue number4
DOIs
Publication statusPublished - Oct 2002

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curvature
continuums
numerical integration
flat surfaces
nonlinearity
Crystalline materials
deviation
scaling
Geometry
geometry

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

Cite this

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title = "The role of pinning and instability in a class of non-equilibrium growth models",
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.",
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",
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issn = "1434-6028",
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AB - 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.

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KW - 64.60.Ht Dynamic critical phenomena

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