Related papers: Interface motion in random media

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with…

We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case,…

The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…

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…

An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…

The steady state structure of an interface in an Ising system on a square lattice placed in a {\em non-uniform} external field, shows a commensurate -incommensurate transition driven by the velocity of the interface. The non-uniform field…

We present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some wide assumptions, we show the joint distribution of the position…

We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from…

Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…

Using stability arguments, this Brief Report suggests that a term that enhances the surface tension in the presence of large height fluctuations should be included in the Kardar-Parisi-Zhang equation. A one-loop renormalization group…

We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition,…

Purely repulsive active particles spontaneously undergo motility-induced phase separation (MIPS) into condensed and dilute phases. Remarkably, the mechanical tension measured along the interface between these phases is negative. In…

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…

We study the dynamical behavior of a one dimensional interface interacting with a sticky unpenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contact between the interface and the substrate…

Interfaces of phase-separated systems roughen in time due to capillary waves. Because of fluxes in the bulk, their dynamics is nonlocal in real space and is not described by the Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) equations, nor…

We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely…

The static and dynamic properties of a Cosserat-type lattice interface of finite thickness are studied, so that both displacements and rotational degrees of freedom are taken into account. The model allows considering interfaces with a…

We present theoretical and dynamic Monte Carlo simulation results for the mobility and microscopic structure of 1+1-dimensional Ising interfaces moving far from equilibrium in an applied field under a single-spin-flip ``soft'' stochastic…

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 the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…