Related papers: On two continuous models for the dynamics of sandp…

We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit shape exists and show via a family of counterexamples that…

The Crump-Young model consists of two fully coupled stochastic processes modeling the substrate and microorganisms dynamics in a chemostat. Substrate evolves following an ordinary differential equation whose coefficients depend of…

This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…

We prove a precise relationship between the threshold state of the fixed-energy sandpile and the stationary state of Dhar's abelian sandpile: In the limit as the initial condition tends to negative infinity, the former is obtained by…

We present a sandpile model, in which the instability of a site is determined also by the variables in a neighbourhood. This is a modification of the Abelian Sandpile Model, in which abelianity is preserved: it shares several mathematical…

Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of…

We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…

The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…

In this work we survey selected theoretical developments for models of deposition of extended particles, with and without surface diffusion, on linear and planar substrates, of interest in colloid, polymer, and certain biological systems.

In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…

Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the…

We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and oblique incidence. After considering the current limitations of more standard descriptions in…

We study an inhomogeneous sandpile model in which two different toppling rules are defined. For any site only one rule is applied corresponding to either the Bak, Tang and Wiesenfeld model {[}P.Bak, C. Tang, and K. Wiesenfeld, Phys. Rev.…

Genetic systems with multiple loci can have complex dynamics. For example, mean fitness need not always increase and stable cycling is possible. Here, we study the dynamics of a genetic system inspired by the molecular biology of…

We establish an $\varepsilon$-regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth, and, as a consequence, the partial regularity of such BV…

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…

The article [Phys. Rev. E {\bf 73}, 031111 (2006)] by Horowitz and Albano reports on simulations of competitive surface-growth models RD+X that combine random deposition (RD) with another deposition X that occurs with probability $p$. The…

We present a fixed energy sandpile (FES) model which, by increasing the initial energy,undergoes, at the level of individual configurations, a discontinuous transition.The model is obtained by modifying the toppling procedure in the BTW…

We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…