Kinetics of interface growth in driven systems

Guo, Hong; Grossmann, B.; Grant, Martin

doi:10.1103/physrevlett.64.1262

Cited by 64 publications

(18 citation statements)

References 20 publications

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“…Our best values for the roughness exponent χ are χ = 0.38 ± 0.02 from the correlation function and χ = 0.40 ± 0.01 from the structure factor. Both these values are, within the error bars, compatible with previous numerical results on the continuum KPZ equation in real space [12,13,14,31,32] and with recent extensive simulations on RSOS models [11]. As explained in Ref.…”

Section: B Pseudo-spectral Methodssupporting

confidence: 92%

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Pseudospectral method for the Kardar-Parisi-Zhang equation

2002

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We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the non-linear term. The method is tested in (1 + 1)-and (2 + 1)-dimensions, where it is shown to reproduce the current most reliable estimates of the critical exponents based on Restricted Solid-on-Solid simulations. In particular it allows the computations of various correlation and structure functions with high degree of numerical accuracy. Some deficiencies which are common to all previously used finite-difference schemes are pointed out and the usefulness of the present approach in this respect is discussed.

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Section: B Pseudo-spectral Methodssupporting

confidence: 92%

“…It has been computed after averaging over many realizations of noise (typically of the order of 50 − 100). The value λ = 3 numerically corresponds to the optimal choice used in previous works [12,13,14,31,32] in which the strong coupling regime is well displayed (see Fig. 4).…”

Section: B Pseudo-spectral Methodsmentioning

confidence: 73%

Pseudospectral method for the Kardar-Parisi-Zhang equation

2002

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“…Even in cases where soft dynamics are the more appropriate choice, as for solidification or adsorption problems where the driving force is a chemical-potential difference, [12,13,27,28,29] the results can depend significantly on which soft dynamics are chosen. The spin classes in the anisotropic square-lattice SOS model.…”

Section: Discussionmentioning

confidence: 99%

Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

2006

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We study the microscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (electro)chemical potential. We use an analytic nonlinear-response approximation [P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] together with kinetic Monte Carlo simulations. Here we consider interfaces that move under Arrhenius dynamics, which include a microscopic energy barrier between the allowed Ising/latticegas states. Two different dynamics are studied: the standard one-step dynamics (OSD) [H. C. Kang and W. Weinberg, J. Chem. Phys. 90, 2824Phys. 90, (1992] and the two-step transition-dynamics approximation (TDA) [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)]. In the OSD the effects of the applied force and the interaction energies in the model factorize in the transition rates (soft dynamics), while in the TDA such factorization is not possible (hard dynamics). In full agreement with previous general theoretical results we find that the local interface width under the TDA increases dramatically with the applied force. In contrast, the interface structure with the OSD is only weakly influenced by the force, in qualitative agreement with the theoretical expectations. Results are also obtained for the force-dependence and anisotropy of the interface velocity, which also show differences in good agreement with the theoretical expectations for the differences between soft and hard dynamics. Our results confirm that different stochastic interface dynamics that all obey detailed balance and the same conservation laws nevertheless can lead to radically different interface responses to an applied force.

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“…In two dimensions the values of the KPZ systems are not known exactly. There is a large diver-*Electronic address: eytak@post.tau.ac.il † Electronic address: mosh@tarazan.tau.ac.il 3 + 1 0.12 [13] sity of results that range between 0.18 and 0.4 for ␣ and 0.1 and 0.25 for ␤ [16] (these results were obtained by a direct integration of the KPZ equation or the equivalent directed polymer problem). However, it usually accepted that ␣ = ϳ 0.4 and ␤ = 0.24 are the KPZ exponents in 2 + 1 dimensions.…”

Section: Introductionmentioning

confidence: 99%

What is the connection between ballistic deposition and the Kardar-Parisi-Zhang equation?

Katzav

Schwartz

2004

Phys. Rev. E

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Ballistic deposition (BD) is believed to belong to the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we study the validity of this belief by rigorously deriving a continuum equation from the BD microscopic rules, which deviates from the KPZ equation. We show that in one dimension and in the presence of noise the deviation is not important. This is not the case in the absence of noise. In more than one dimension and in the presence of noise we obtain an equation that superficially seems to be a continuum equation but in which the symmetry under rotations around the growth direction is broken.

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Kinetics of interface growth in driven systems

Cited by 64 publications

References 20 publications

Pseudospectral method for the Kardar-Parisi-Zhang equation

Pseudospectral method for the Kardar-Parisi-Zhang equation

Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

What is the connection between ballistic deposition and the Kardar-Parisi-Zhang equation?

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