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تسجيل مستخدم جديدDensity relaxation in conserved Manna sandpiles
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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.
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