相关论文: Weak pinning: Surface growth in presence of a defe…
We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning…
The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with…
We consider a simple model for the growth of isolated steps on a vicinal crystal surface. It incorporates diffusion and drift of adatoms on the terrace, and strong step and kink edge barriers. Using a combination of analytic methods and…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson…
We consider the facilitated exclusion process, an interacting particle system on the integer line where particles hop to one of their left or right neighbouring site only when the other neighbouring site is occupied by a particle. A…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
The shape of a liquid-air interface advancing on a heterogeneous surface was studied experimentally, together with the force induced by the pinning of the contact line to surface defects. Different surfaces were considered with circular…
A discrete solid-on-solid model of epitaxial growth is introduced which, in a simple manner, takes into account the effect of an Ehrlich-Schwoebel barrier at step edges as well as the local relaxation of incoming particles. Furthermore a…
An evolution partial differential equation for the surface of a non-wetting single-crystal film in an attractive substrate potential is derived and used to study the dynamics of a pinhole for the varying initial depth of a pinhole and the…
Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the…
This study proposes a new analytical model for grain boundary pinning by second phase particles in two-dimensional polycrystals. This approach not only considers how particles impede grain growth, but also elucidates their role in…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of…
We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…
We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…
The propagation of an adhesive crack through an anisotropic heterogeneous interface is considered. Tuning the local toughness distribution function and spatial correlation is numerically shown to induce a transition between weak to strong…
We investigate numerically the dynamics of crack propagation along a weak plane using a model consisting of fibers connecting a soft and a hard clamp. This bottom-up model has previously been shown to contain the competition of two crack…
Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant…
The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…