Related papers: Coarsening in surface growth models without slope …
We use a stochastic model and direct numerical simulation to study the impact of turbulence on cloud droplet growth by condensation. We show that the variance of the droplet size distribution increases in time as t^{1/2}, with growth rate…
The phenomenon of stochastic growth of a surface on a two-dimensional substrate occurs in Nature in a variety of circumstances and its statistical characterization requires the study of higher order cumulants. Here, we consider the…
Stylolites are spectacular rough dissolution surfaces that are found in many rock types. Despite many studies, their genesis is still debated, particularly the time scales of their formation and the relationship between this time and their…
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…
We present some results of Monte Carlo simulations for the deposition of particles of different sizes on a two-dimensional substrate. The particles are linear, height one, and can be deposited randomly only in the two, $x$ and $y$…
The meander instability of a vicinal surface growing under step flow conditions is studied within a solid-on-solid model. In the absence of edge diffusion the selected meander wavelength agrees quantitatively with the continuum linear…
We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height…
We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is…
A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential…
One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…
The conserved Kuramoto-Sivashinsky equation is considered as the evolution equation of amorphous thin film growth in one- and in two-dimensions. The role of the nonlinear term $\Delta (\ | \nabla u\ | ^{2})$ and the properties of the…
We describe laboratory-grown snow crystals that exhibit a triangular, plate-like morphology, and we show that the occurrence of these crystals is much more frequent than one would expect from random growth perturbations of the more-typical…
Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…
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…
We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian…
We examine the conjectured asymptotic shape of the three dimensional corner growth model [Olejarz et. al.,PRL, 108, 016102 (2012)] by mapping the model onto a restricted solid on solid model on a triangular lattice. By choosing appropriate…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…
We investigate the nonlinear evolution of the Bales-Zangwill instability, responsible for the meandering of atomic steps on a growing vicinal surface. We develop an asymptotic method to derive, in the continuous limit, an evolution equation…
For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 dimensions, fluctuations grow as t^{1/3} during time t and the correlation length at a fixed time scales as t^{2/3}. In this note we discuss the scale of time…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…