Steady state of Stochastic Sandpile
نویسندگان
چکیده
We study the steady state of the abelian sandpile models with stochastic toppling rules. The particle addition operators commute with each other, but in general these operators need not be diagonalizable. We use their abelian algebra to determine their eigenvalues, and the Jordan block structure. These are then used to determine the probability of different configurations in the steady state. We illustrate this procedure by explicitly determining the numerically exact steady state for a one dimensional example, for systems of size ≤ 12, and also study the density profile in the steady state.
منابع مشابه
Characteristics of deterministic and stochastic sandpile models in a rotational sandpile model.
Rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in an out-of-equilibrium situation like self-organized criticality, a two state "quasideterministic" rotational sandpile model is developed here imposing rotational con...
متن کاملLongest Path in Networks of Queues in the Steady-State
Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Fu...
متن کاملQuenched noise and over-active sites in sandpile dynamics
– The dynamics of sandpile models are mapped to discrete interface equations. We study in detail the Bak-Tang-Wiesenfeld model, a stochastic model with random thresholds, and the Manna model. These sandpile models are, respectively, discretizations of the Edwards-Wilkinson equation with columnar, point-like and correlated quenched noise, with the constraint that the interface velocity is either...
متن کاملNonuniversal exponents in sandpiles with stochastic par - ticle number transfer
– We study fixed density sandpiles in which the number of particles transferred to a neighbor on relaxing an active site is determined stochastically by a parameter p. Using an argument, the critical density at which an active-absorbing transition occurs is found exactly. We study the critical behavior numerically and find that the exponents associated with both static and time-dependent quanti...
متن کاملAbsorbing-State Phase Transition for Driven-Dissipative Stochastic Dynamics on Z
We study the long-time behavior of conservative interacting particle systems in Z: the activated random walk model for reaction-diffusion systems and the stochastic sandpile. We prove that both systems undergo an absorbing-state phase transition. This preprint has the same numbering for sections, theorems, equations and figures as the published article “Invent. Math. 188 (2012): 127–150.”
متن کامل