Related papers: Mathematics of random growing interfaces
We study the mean-field version of a model proposed by Leschhorn to describe the depinning transition of interfaces in random media. We show that evolution equations for the distribution of forces felt by the interface sites can be written…
We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal fluctuation $<m> \sim…
In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process.…
In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
Fluctuations of the interface between coexisting colloidal fluid phases have been measured with confocal microscopy. Due to a very low surface tension, the thermal motions of the interface are so slow, that a record can be made of the…
We investigate the behaviour of solutions of a fractional semilinear partial differential equation that models the evolution of an interface in a random medium. We show a pinning result and apply it to the related homogenizing process.
We consider the equilibrium surface of the Random Average Process started from an inclined plane, as seen from the height of the origin, obtained in [Ferrari & Fontes, 1998], where its fluctuations were shown to be of order of the square…
Test area deformations are used to analyse vapour-liquid interfaces of Lennard-Jones particles by molecular dynamics simulation. For planar vapour-liquid interfaces the change in free energy is captured by the average of the corresponding…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
Consider the Ising model at low-temperatures and positive external field $\lambda$ on an $N\times N$ box with Dobrushin boundary conditions that are plus on the north, east, and west boundaries and minus on the south boundary. If $\lambda =…
Surface growth in random media is usually governed by both the surface tension and the random local forces. Simulations on lattices mimic the former by imposing a maximum gradient $m$ on the surface heights, and the latter by site-dependent…
I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour,…
We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory \cite{Herminghaus2012,…
We study large deviations of the one-point height distribution, $\mathcal{P}(H,T)$, of a stochastic interface, governed by the Golubovi\'{c}-Bruinsma equation $$…
We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability…
Consider a stationary Poisson process $\eta$ in the $d$-dimensional Euclidean or hyperbolic space and construct a random graph with vertex set $\eta$ as follows. First, each point $x\in\eta$ is connected by an edge to its nearest neighbour,…
Following Barany et al., who proved that large random lattice zonotopes converge to a deterministic shape in any dimension after rescaling, we establish a central limit theorem for finite-dimensional marginals of the boundary of the…
We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from…
The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the…