Related papers: Controlling anisotropy in 2D microscopic models of…
We use a lattice gas cellular automata model in the presence of random dynamic scattering sites and quenched disorder in the two-phase immiscible model with the aim of producing an interface dynamics similar to that observed in Hele-Shaw…
This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…
Based on a high temperature expansion, we compute the two-point correlation function and the critical line of an Ising lattice gas driven into a non-equilibrium steady state by a uniform bias E. The lowest nontrivial order already…
Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form…
Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using…
We study numerically a stochastic differential equation describing an interface driven along the hard direction of an anisotropic random medium. The interface is subject to a homogeneous driving force, random pinning forces and the surface…
We calculate the two-point correlation function and magnetic susceptibility in the anisotropic 2D Ising model on a lattice with one infinite and the other finite dimension, along which periodic boundary conditions are imposed. Using exact…
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which…
The lectures examine several problems related to non-equilibrium fluctuations of interfaces and flux lines. The first two introduce the phenomenology of depinning, with particular emphasis on interfaces and contact lines. The role of the…
Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…
In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the…
We investigate the stability of electrodeposition at solid-solid interfaces for materials exhibiting an anisotropic mechanical response. The stability of electrodeposition or resistance to the formation of dendrites is studied within a…
The surface morphology of faults controls the spatial anisotropy of their frictional properties, and hence their mechanical stability. Such anisotropy is only rarely studied in seismology models of fault slip, although it might be paramount…
Instability of a binary eutectic solidification front to morphological perturbations due to rejection of a ternary impurity leads to the formation of eutectic colonies. Whereas, the instability dynamics and the resultant mi- crostructural…
We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings,…
Optimal growth of structures governed by spatially stochastic dynamics arises in many scientific settings, for example in processes such as solution-based crystallization and the formation of microbial biofilms on patterned substrates or…
We propose a sharp interface model for simulating solid-state dewetting where the surface energy is (weakly) anisotropic. The morphology evolution of thin films is governed by surface diffusion and contact line migration. The mathematical…
Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a…
We associate to each unit volume lattice of $\R^d$ the Ising model with bond variables equal to the inverse successive minima of that lattice. This induces the notion of a critical temperature for a random lattice for which integrability…
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…