Related papers: Steady state of Stochastic Sandpile Models
We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense…
Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order…
The Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur when the grains topple over a graph. In this study, we allow the graph to evolve…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
We define two general classes of nonabelian sandpile models on directed trees (or arborescences) as models of nonequilibrium statistical phenomena. These models have the property that sand grains can enter only through specified reservoirs,…
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…
We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently…
The Abelian sandpile model is the simplest analytically tractable model of self-organized criticality. This paper presents a brief review of known results about the model. The abelian group structure allows an exact calculation of many of…
We show that the one-dimensional Oslo rice-pile model is a special case of the abelian distributed processors model. The exact steady state of the model is determined. We show that the time evolution operator W for the system satisfies the…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are…
We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
Simulations of a stochastic fixed-energy sandpile in one and two dimensions reveal slow relaxation of the order parameter, even far from the critical point. The decay of the activity is best described by a stretched-exponential form. The…
The non-equilibrium steady states emerging from stochastic resetting to a distribution is studied. We show that for a range of processes, the steady-state moments can be expressed as a linear combination of the moments of the distribution…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters…
We study the dynamical steady-states of a monolayer of chemically active self-phoretic colloids as a function of packing fraction and self-propulsion speed by means of Brownian dynamics simulations. We focus on the case that a chemical…
An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach…
We experimentally investigate the steady states of two granular assemblies differing in their material properties and allowed to exchange volume with each other under external agitation in the vicinity of their jamming transition. We…