Related papers: Directed avalanche processes with underlying inter…
We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities vm during avalanches described by the mean field theory of the interface depinning transition. In…
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 thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful…
Elastic interfaces in quenched random media driven by external forces exhibit a continuous depinning phase transition between pinned and moving phases at a critical external force. Recent work [Phys. Rev. Lett. 129, 175701 (2022)] has shown…
The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889, (1986)] with…
In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
We provide a comprehensive view on the role of Abelian symmetry and stochasticity in the universality class of directed sandpile models, in context of the underlying spatial correlations of metastable patterns and scars. It is argued that…
We introduce and investigate a simple model to describe recent experiments by Douady and Daerr on flowing sand. The model reproduces experimentally observed compact avalanches, whose opening angle decreases linearly as a threshold is…
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…
We develop a phenomenological mapping between submonolayer polynuclear growth (PNG) and the interface dynamics at and below the depinning transition in the Kardar-Parisi-Zhang equation for a negative non-linearity \lambda. This is possible…
We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches…
In this study, we investigate the relationship between the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) equation and the stochastic Loewner equation (SLE), which is a one parameter family of the conformal mappings involving stochasticity.…
We perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed…
The ground state of an elastic interface in a disordered medium undergoes collective jumps upon variation of external parameters. These mesoscopic jumps are called shocks, or static avalanches. Submitting the interface to a parabolic…
Infinite hierarchy of exact equations are derived for the newly-observed f-avalanche in the Bak-Sneppen evolution model. By solving the first order exact equation, we found that the critical exponent which governs the divergence of the…
The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a…
Disordered systems under applied loading display slow creep flows at finite temperature, which can lead to the material rupture. Renormalization group arguments predicted that creep proceeds via thermal avalanches of activated events.…
We define a new model of interface roughening which has the property that the minimum of interface height is conserved locally during the growth. This model corresponds to the limit $q \to \infty$ of the q-color dimer deposition-evaporation…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…