Instability, intermittency, and multiscaling in discrete growth models of kinetic roughening

Dasgupta, C. ; Kim, J. M. ; Dutta, M. ; Das Sarma, S. (1997) Instability, intermittency, and multiscaling in discrete growth models of kinetic roughening Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 55 (3). pp. 2235-2254. ISSN 1539-3755

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We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma-Villain equation) and related atomistic models of epitaxial growth have a generic instability in which isolated pillars (or grooves) on an otherwise flat interface grow in time when their height (or depth) exceeds a critical value. Depending on the details of the model, the instability found in the discretized version may or may not be present in the truly continuum growth equation, indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts. This instability can be controlled either by the introduction of higher-order nonlinear terms with appropriate coefficients or by restricting the growth of pillars (or grooves) by other means. A number of such "controlled instability" models are studied by simulation. For appropriate choice of the parameters used for controlling the instability, these models exhibit intermittent behavior, characterized by multiexponent scaling of height fluctuations, over the time interval during which the instability is active. The behavior found in this regime is very similar to the "turbulent" behavior observed in recent simulations of several one- and two-dimensional atomistic models of epitaxial growth.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:83247
Deposited On:20 Feb 2012 12:09
Last Modified:20 Feb 2012 12:09

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