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The temporal evolution of equilibrium fluctuations for surface steps of monoatomic height is analyzed studying one-dimensional solid-on-solid models. Using Monte Carlo simulations, fluctuations due to periphery-diffusion (PD) as well as due to evaporation-condensation (EC) are considered, both for isolated steps and steps confined by the presence of straight steps. For isolated steps, the dependence of the characteristic power-laws, their exponents and prefactors, on temperature, slope, and curvature is elucidated, with the main emphasis on PD, taking into account finite-size effects. The entropic repulsion due to a second straight step may lead, among others, to an interesting transient power-law like growth of the fluctuations, for PD. Findings are compared to results of previous Monte Carlo simulations and predictions based, mostly, on scaling arguments and Langevin theory.
We report on the investigation of height distributions (HDs) and spatial covariances of two-dimensional surfaces obtained from extensive numerical simulations of the celebrated Clarke-Vvedensky (CV) model for homoepitaxial thin film growth. In this m
Crystallization from an amorphous atomic structure is usually seen as a spontaneous process in pursuit of a lower energy state, but for alloy systems it is often hard to elucidate because of the intrinsic structural and compositional complexity. Here
We study the early time and coarsening dynamics in the Light-Heavy model, a system consisting of two species of particles ($light$ and $heavy$) coupled to a fluctuating surface (described by tilt fields). The dynamics of particles and tilts are coupl
An equilibrium random surface multistep height model proposed in [Abraham and Newman, EPL, 86, 16002 (2009)] is studied using a variant of the worm algorithm. In one limit, the model reduces to the two-dimensional Ising model in the height representa
We revisit the classical stability versus accuracy dilemma for the lattice Boltzmann methods (LBM). Our goal is a stable method of second-order accuracy for fluid dynamics based on the lattice Bhatnager--Gross--Krook method (LBGK). The LBGK scheme