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We study relaxation of long-wavelength density perturbations in one dimensional conserved Manna sandpile. Far from criticality where correlation length $xi$ is finite, relaxation of density profiles having wave numbers $k rightarrow 0$ is diffusive, with relaxation time $tau_R sim k^{-2}/D$ with $D$ being the density-dependent bulk-diffusion coefficient. Near criticality with $k xi gsim 1$, the bulk diffusivity diverges and the transport becomes anomalous; accordingly, the relaxation time varies as $tau_R sim k^{-z}$, with the dynamical exponent $z=2-(1-beta)/ u_{perp} < 2$, where $beta$ is the critical order-parameter exponent and and $ u_{perp}$ is the critical correlation-length exponent. Relaxation of initially localized density profiles on infinite critical background exhibits a self-similar structure. In this case, the asymptotic scaling form of the time-dependent density profile is analytically calculated: we find that, at long times $t$, the width $sigma$ of the density perturbation grows anomalously, i.e., $sigma sim t^{w}$, with the growth exponent $omega=1/(1+beta) > 1/2$. In all cases, theoretical predictions are in reasonably good agreement with simulations.
Adding grains at a single site on a flat substrate in the Abelian sandpile models produce beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each site has two
We study the sandpile model on three-dimensional spanning Ising clusters with the temperature $T$ treated as the control parameter. By analyzing the three dimensional avalanches and their two-dimensional projections (which show scale-invariant behavi
We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the small drive
We propose a modified voter model with locally conserved magnetization and investigate its phase ordering dynamics in two dimensions in numerical simulations. Imposing a local constraint on the dynamics has the surprising effect of speeding up the ph
We consider the isotropic spin-1/2 Heisenberg spin chain weakly perturbed by a local translationally- and SU(2)-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-cons