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A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This…

Condensed Matter · Physics 2009-10-28 Uri Alon , Martin Evans , Haye Hinrichsen , David Mukamel

Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…

Analysis of PDEs · Mathematics 2022-02-01 Stephan Gärttner , Peter Knabner , Nadja Ray

There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…

Statistical Mechanics · Physics 2007-05-23 Juan R. Sanchez

We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory,…

Materials Science · Physics 2009-11-10 G. Russo , L. M. Sander , P. Smereka

We report a kinetic Monte Carlo modeling study of nanocrystal layer sintering. Features that are of interest for the dynamics of the layer as a whole, especially the morphology of the evolving structure, are considered. It is found that the…

Materials Science · Physics 2014-11-11 Vyacheslav Gorshkov , Vasily Kuzmenko , Vladimir Privman

Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…

Soft Condensed Matter · Physics 2019-03-06 Rami Abi-Akl , Rohan Abeyaratne , Tal Cohen

We study, using noise reduction techniques, layer by layer epitaxial growth in limited mobility solid-on-solid nonequilibrium surface growth models, which have been introduced in the context of kinetic surface roughening in ideal molecular…

Statistical Mechanics · Physics 2007-05-23 P. Punyindu Chatraphorn , S. Das Sarma

We provide a quantitative picture of non-conserved interface growth from a diffusive field making special emphasis on two main issues, the range of validity of the effective small-slopes (interfacial) theories and the interplay between the…

Statistical Mechanics · Physics 2009-11-13 Matteo Nicoli , Mario Castro , Rodolfo Cuerno

Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…

Materials Science · Physics 2020-11-11 Kamyar M. Davoudi , Joost J. Vlassak

A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…

Statistical Mechanics · Physics 2009-10-30 Uri Alon , Martin Evans , Haye Hinrichsen , David Mukamel

We investigate the late coarsening stages of one dimensional adsorption processes with diffusional relaxation. The nonequilibrium domain size distribution is studied by means of the field theory associated to the stochastic evolution. An…

Statistical Mechanics · Physics 2007-05-23 M. D. Grynberg

We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…

Statistical Mechanics · Physics 2007-05-23 A. Kolakowska , M. A. Novotny

A continuum model for growth of solids is developed, considering adatom deposition, surface diffusion, and configuration dependent incorporation rate. For amorphous solids it is related to surface energy densities. The high adatom density…

Statistical Mechanics · Physics 2007-05-23 Martin Rost

The growth of a rough and porous thin surface by deposition of randomly shaped clusters with different sizes over an initially flat linear substrate is simulated, using Monte Carlo technique. Unlike the ordinary Random Deposition, our…

Mesoscale and Nanoscale Physics · Physics 2012-11-09 ZH. Ebrahiminejad , Seyed Farhad Masoudi , R. S. Dariani , Saeed S. Jahromi

We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase…

Materials Science · Physics 2008-11-18 M. Fleck , C. Hueter , D. Pilipenko , R. Spatschek , E. A. Brener

Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the…

Analysis of PDEs · Mathematics 2021-05-27 Kiana Naghibzadeh , Noel Walkington , Kaushik Dayal

We present a lattice-gas (generalised Ising) model for liquid droplets on solid surfaces. The time evolution in the model involves two processes: (i) Single-particle moves which are determined by a kinetic Monte Carlo algorithm. These…

Soft Condensed Matter · Physics 2019-11-06 Mounirah Areshi , Dmitri Tseluiko , Andrew J. Archer

We investigate the influence of step edge diffusion (SED) and desorption on Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the solid-on-solid (SOS) model. Based on these investigations we propose two strategies to…

Statistical Mechanics · Physics 2009-10-31 S. Schinzer , M. Sokolowski , M. Biehl , W. Kinzel

We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…

Soft Condensed Matter · Physics 2025-05-07 Jaemin Kim , Keon Ho Kim , Nikolaos Bouklas

A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum…

Statistical Mechanics · Physics 2007-09-27 M. D. Grynberg