Related papers: A solvable model of interface depinning in random …
We consider statistical mechanics models of continuous height effective interfaces in the presence of a delta-pinning at height zero. There is a detailed mathematical understanding of the depinning transition in 2 dimensions without…
We analyse features of the patterns formed from a simple model for a martensitic phase transition. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
We study a broad class of high-dimensional mean-field exchange models, encompassing both noisy and singular dynamics, along with their dual processes. This includes a generalized version of the averaging process as well as some…
We consider a discretized version of the quenched Edwards-Wilkinson model for the propagation of a driven interface through a random field of obstacles. Our model consists of a system of ordinary differential equations on a $d$-dimensional…
In this paper, a phase-field model is introduced to describe the evolution of a deformable, self-propelled object driven by surface-tension effects. The model couples an Allen-Cahn-type equation, which distinguishes the body from the…
We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be…
The precise determination of the universality classes in self-organized critical phenomena (SOC) is still an unsolved problem. Different SOC models like sandpile, linear interface depinning, and the Barkhausen effect have been investigated…
We consider the dynamics and kinetic roughening of wetting fronts in the case of forced wetting driven by a constant mass flux into a 2D disordered medium. We employ a coarse-grained phase field model with local conservation of density,…
We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain…
Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties…
The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure…
A simple model for an interface moving in a disordered medium is presented. The model exhibits a transition between the two universality classes of interface growth phenomena. Using this model, it is shown that the application of…
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We study a coarsening model describing the dynamics of interfaces in the one-dimensional Allen-Cahn equation. Given a partition of the real line into intervals of length greater than one, the model consists in constantly eliminating the…