Langevin equations for competitive growth models

Silveira, Flavio A.; Reis, F. D. A. Aarão

doi:10.1103/physreve.85.011601

Cited by 11 publications

(10 citation statements)

References 54 publications

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“…By construction, h → h − h , then f (h, t) has zero mean, so its skewness and kurtosis are the most important quantities to observe [147,[178][179][180][181]. In addition, Langevin equations for growth models have been discussed by some authors [182][183][184]. Several works have been done in the weakly asymmetric simple exclusion process [136], the totally asymmetric exclusion process [137,185], and the direct d-mer diffusion model [138]: for a review see [170,181,186,187].…”

Section: Scaling Invariancementioning

confidence: 99%

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

et al. 2019

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In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be given to some methods applied in the analysis and characterization of diffusive regimes through the memory function, the mixing condition (or irreversibility), and ergodicity. Those methods can be used in the study of small-scale systems, ranging in size from single-molecule to particle clusters and including among others polymers, proteins, ion channels and biological cells, whose diffusive properties have received much attention lately.

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Section: Scaling Invariancementioning

confidence: 99%

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

et al. 2019

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“…the KPZ class) scales with λ −4 [22]. In competitive models, λ grows at least linearly with the difference p − p * [26], and the crossover time is expect to depend on p with (p − p * ) −4 . This result is corroborated by evaluating the local growth exponent β(t) ≡ d ln W/d ln t (or effective growth exponent) illustrated in Figure 4.…”

Section: (B))mentioning

confidence: 99%

Height distribution of equipotential lines in a region confined by a rough conducting boundary

Castro¹,

Assis²,

Castilho³

et al. 2014

J. Phys.: Condens. Matter

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Abstract.This work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces: a cathode with an irregular interface and a distant flat anode.Both boundaries, which are maintained at distinct and constant potential values, are assumed to be conductors. The morphology of the cathode interface results from the deposit of 2 × 10 4 monolayers that are produced using a single competitive growth model based on the rules of the Restricted Solid on Solid and Ballistic Deposition models, both of which belong to the Kadar-Parisi-Zhang (KPZ) universality class. At each time step, these rules are selected with probability p and q = 1 − p. For several irregular profiles that depend on p, a family of equipotential lines is evaluated. The lines are characterized by the skewness and kurtosis of the height distribution. The results indicate that the skewness of the equipotential line increases when they approach the flat anode, and this increase has a non-trivial convergence to a delta distribution that characterizes the equipotential line in a uniform electric field. The morphology of the equipotential lines is discussed; the discussion emphasizes their features for different ranges of p that correspond to positive, null and negative values of the coefficient of the non-linear term in the KPZ equation.Height distribution of equipotential lines in a region confined by a rough conducting boundary2

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“…the intrinsic roughness. In BD-RDSR in 2D, long crossovers from EW to KPZ scaling were already shown for small p [39][40][41] .…”

Section: Previous Results On the Bd-rdsr Modelmentioning

confidence: 85%

Effects of the growth kinetics on solute diffusion in porous films

Correa,

Almeida,

Reis

2021

Preprint

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For the development of porous materials with improved transport properties, a key ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here we address these relations by studying solute diffusion through three-dimensional porous films produced by deposition models with controlled thickness and porosity. A competition between pore formation by lateral particle aggregation and surface relaxation that favors compaction is simulated by the lattice models of ballistic deposition and of random deposition with surface relaxation, respectively, with relative rates proportional to p and 1 − p. Effective diffusion coefficients are determined in steady state simulations with a solute source at the basis and a drain at the top outer surface of the films. For a given film thickness, the increase of the relative rate of lateral aggregation leads to the increase of the effective porosity and of the diffusivity, while the tortuosity decreases. With constant growth conditions, the increase of the film thickness always leads to the increase of the effective porosity, but a nontrivial behavior of the diffusivity is observed. For deposition with p ≤ 0.7, in which the porosity is below 0.6, the diffusion coefficient is larger in thicker films; the decrease of the tortuosity with the thickness quantitatively confirms that the growth continuously improves the pore structure for the diffusion. Microscopically, this result is associated with narrower distributions of the local solute current at higher points of the deposits. For deposition with p ≥ 0.9, in which the films are in the narrow porosity range ∼ 0.65 − 0.7, the tortuosity is between 1.3 and 2, increases with the thickness, and has maximal changes near 25%. Pairs of values of porosity and tortuosity obtained in some porous electrodes are close to the pairs obtained here in the thickest films, which suggests that our results may be applied to deposition of materials of technological interest. Noteworthy, the increase of the film thickness is generally favorable for diffusion in their pores, and the exceptions have small losses in tortuosity.

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Langevin equations for competitive growth models

Cited by 11 publications

References 54 publications

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

Height distribution of equipotential lines in a region confined by a rough conducting boundary

Effects of the growth kinetics on solute diffusion in porous films

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