The conserved Manna model with a planar absorbing boundary is studied in various space dimensions. We present a heuristic argument that allows one to compute the surface critical exponent in one dimension analytically. Moreover, we discuss the mean field limit that is expected to be valid in d > 4 space dimensions and demonstrate how the corresponding partial differential equations can be solve...

ion and Modular Veri cation of In nite-State Reactive Systems ? Zohar Manna, Michael A. Col on, Bernd Finkbeiner, Henny B. Sipma and Tom as E. Uribe Computer Science Department Stanford University Stanford, CA. 94305-9045 [email protected] Abstract. We review a number of temporal veri cation techniques for reactive systems using modularity and abstraction. Their use allows the veri cation o...

We study relaxation of long-wavelength density perturbations in a one-dimensional conserved Manna sandpile. Far from criticality where correlation length $\ensuremath{\xi}$ is finite, profiles having wave numbers $k\ensuremath{\rightarrow}0$ diffusive, with time ${\ensuremath{\tau}}_{R}\ensuremath{\sim}{k}^{\ensuremath{-}2}/D$ $D$ being the density-dependent bulk-diffusion coefficient. Near $k\...

Stochastic sandpiles self-organize to an absorbing-state critical point with scaling behavior different from directed percolation (DP) and characterized by the presence of an additional conservation law. This is usually called the C-DP or Manna universality class. There remains, however, an exception to this universality principle: a sandpile automaton introduced by Maslov and Zhang, which was ...

ion and Modular Verification of Infinite-State Reactive Systems ⋆ Zohar Manna, Michael A. Colón, Bernd Finkbeiner, Henny B. Sipma and Tomás E. Uribe Computer Science Department Stanford University Stanford, CA. 94305-9045 [email protected] Abstract. We review a number of temporal verification techniques for reactive systems using modularity and abstraction. Their use allows the verification...

Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the ab...