Related papers: Singularities and Avalanches in Interface Growth w…
Simulations with more than $10^{12}$ spins are used to study the motion of a domain wall driven through a three-dimensional random-field Ising magnet (RFIM) by an external field $H$. The interface advances in a series of avalanches whose…
We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid…
We study the recently-introduced directed percolation depinning (DPD) model for interface roughening with quenched disorder for which the interface becomes pinned by a directed percolation (DP) cluster for $d = 1$, or a directed surface…
We consider a model for haptotaxis with bistable growth and study its singular limit. This yiels an interface motion where the normal velocity of the interface depends on the mean curvature and on some nonlocal haptotaxis term. We prove the…
When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the…
The kinetic roughening of a stable oil--air interface, moving in a Hele--Shaw cell which contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough…
An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche…
Although scaling phenomena have long been documented in crystalline plasticity, the universality class has been difficult to identify due to the rarity of avalanche events, which require large system sizes and long times in order to…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
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…
The response of spatially extended systems to a force leading their steady state out of equilibrium is strongly affected by the presence of disorder. We focus on the mean velocity induced by a constant force applied on one-dimensional…
Cascading large-amplitude bursts in neural activity, termed avalanches, are thought to provide insight into the complex spatially distributed interactions in neural systems. In human neuroimaging, for example, avalanches occurring during…
Cahn-Hilliard models are central for describing the evolution of interfaces in phase separation processes and free boundary problems. In general, they have non-constant and often degenerate mobilities. However, in the latter case, the…
The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth,…
We perform large scale simulations of a two dimensional lattice model for amorphous plasticity with random local yield stresses and long-range quadrupolar elastic interactions. We show that as the external stress increases towards the…
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled…
In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by T = T_N and is allowed to grow with the size N of…
Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the…