Kinetic growth with surface relaxation: Continuum versus atomistic models

Lai, Zaizhi; Sarma, S. Das

doi:10.1103/physrevlett.66.2348

Cited by 637 publications

(496 citation statements)

References 17 publications

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“…Nevertheless, since the numerical estimation is based on finite-size systems, it is not clear what the value is in the thermodynamic limit. Thus, it is worthwhile to check through the renormalization group approach if the proposed dynamic equation generates a new universality class other than the Lai and Das Sarma one [11] when 1 is sufficiently small but not zero. …”

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confidence: 99%

Kimet al.Reply:

Kim

2005

Phys. Rev. Lett.

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Kim et al. Reply:We investigated the kinetic roughening of a sputter-eroded Pd(001) surface experimentally and also introduced a dynamic equation to illustrate the pattern formation thereof [1]. The conserved KPZ (CKPZ) term of the form r 2 rh 2 was derived by extending the KuramotoSivashinsky (KS) equation to higher order, addressing the necessity of the higher order term for the first time. In the preceding Comment [2], however, Castro and Cuerno pointed out that Eq. (1) of Ref.[1] is not relevant to the moundlike pattern formation for 1 < 0 and 2 > 0, which we obtained via the TRIM Monte Carlo simulations [3]. From the explicit functional form of 1 , unseen in our previous Letter,

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confidence: 99%

Kimet al.Reply:

Kim

2005

Phys. Rev. Lett.

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“…If we consider higher order corrections to (8), we obtain additional martingale terms of order ε in (9) from the Itô-formula argument. These terms depend on b and the fast OU-process.…”

Section: Higher Order Correctionsmentioning

confidence: 99%

“…Moreover, we briefly discuss a model from surface growth proposed by Lai & Das Sarma (cf. [8] and see also [9]). …”

Section: Introductionmentioning

confidence: 99%

Amplitude equations for SPDEs with cubic nonlinearities

Blömker

Mohammed

2011

Stochastics

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For a quite general class of SPDEs with cubic nonlinearities we derive rigorously amplitude equations describing the essential dynamics using the natural separation of time-scales near a change of stability. Typical examples are the Swift-Hohenberg equation, the Ginzburg-Landau (or Allen-Cahn) equation and some model from surface growth.We discuss the impact of degenerate noise on the dominant behavior, and see that additive noise has the potential to stabilize the dynamics of the dominant modes. Furthermore, we discuss higher order corrections to the amplitude equation.

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“…The continuum ones are based on the stochastic differential Langevin equations [3,4,5,6] which group models to the various classes of universality associated with the some set of critical exponents. In discrete approach computational methods may be applied, with cellular automata technique (CA) [9,10] among others.…”

Section: Introductionmentioning

confidence: 99%

New cellular automaton designed to simulate epitaxial films growth

Kosturek

Malarz

2005

Physica A: Statistical Mechanics and its Applications

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In this paper a simple (2+1) solid-on-solid model of the epitaxial films growth based on random deposition followed by breaking particle-particle lateral bonds and particles surface diffusion is introduced. The influence of the critical number of the particle-particle lateral bonds z and the deposition rate on the surface roughness dynamics and possible surface morphology anisotropy is presented. The roughness exponent α and the growth exponent β are (0.863, 0.357), (0.215, 0.123), (0.101, 0.0405) and (0.0718, 0.0228) for z = 1, 2, 3 and 4, respectively.Snapshots from simulations of the growth process are included.

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Kinetic growth with surface relaxation: Continuum versus atomistic models

Cited by 637 publications

References 17 publications

Kimet al.Reply:

Kimet al.Reply:

Amplitude equations for SPDEs with cubic nonlinearities

New cellular automaton designed to simulate epitaxial films growth

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