Related papers: The Asymmetric Avalanche Process
Functionals of a stochastic process Y(t) model many physical time-extensive observables, e.g. particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are…
Amorphous solids display numerous universal features in their mechanics, structure, and response. Current models assume heterogeneity in mesoscale elastic properties, but require fine-tuning in order to quantitatively explain vibrational…
Assume that each species $l$ has its own jump rate $b_l$ in the multi-species totally asymmetric simple exclusion process. We show that this model is \textit{integrable} in the sense that the Bethe Ansatz method is applicable to obtain the…
In this paper, the operation of totally asymmetric simple exclusion process with one or two shortcuts under open boundary conditions is discussed. Using both mathematical analysis and numerical simulations, we have found that, according to…
We investigate shock formation in an asymmetric exclusion process with creation and annihilation of particles in the bulk. We show how the continuum mean-field equations can be studied analytically and hence derive the phase diagrams of the…
In a series of papers, Bartelt and co-workers developed novel snow-avalanche models in which \emph{random kinetic energy} $R_K$ (a.k.a.\ granular temperature) is a key concept. The earliest models were for a single, constant density layer,…
Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump $l$ sites ahead with the probability $p_l\sim 1/l^{\sigma+1}$ is studied by Monte Carlo…
For a driven elastic object near depinning, we derive from first principles the distribution of instantaneous velocities in an avalanche. We prove that above the upper critical dimension, d >= d_uc, the n-times distribution of the…
A {\it heuristic} approach is proposed to estimate the average speed of particles during binary encounters by using the macroscopic variables with their extended gradient-type which are the fundamental independent variables in {\it extended…
We consider the zero-temperature single-spin-flip dynamics of the random-field Ising model on a Bethe lattice in the presence of an external field h. We derive the exact self-consistent equations to determine the distribution Prob(s) of…
We give contour integral formulas for the generating function of the joint distribution of the PushASEP on a ring. We obtained these formulas through a rigorous treatment of Bethe Ansatz. The approach relies on residue computations and…
We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a…
Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We describe the hydrodynamic behavior of the $k$-step exclusion process. Since the flux appearing in the hydrodynamic equation for this particle system is neither convex nor concave, the set of possible solutions include in addition to…
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
We study the coarsening dynamics of a two dimensional system via lattice Boltzmann numerical simulations. The system under consideration is a biphasic system consisting of domains of a dispersed phase closely packed together in a continuous…