论文标题
保守的甘露砂岩中的密度松弛
Density relaxation in conserved Manna sandpiles
论文作者
论文摘要
我们研究了在一维甘露砂岩中的长波长密度扰动的松弛。相关长度$ξ$是有限的远非关键，而是具有波数$ k \ rightarrow 0 $的密度曲线的放松是扩散的，放松时间$τ_r\ sim k^{ - 2}/d $与$ d $是密度依赖的体积 - 散热器 - 散布 - 散布式 - 散装系数。几乎具有$k吻\ gsim 1 $的临界性，散装扩散率分歧，传输变得异常；因此，放松时间的变化为$τ_r\ sim k^{ - z} $，具有动态指数$ z = 2-（1-β）/ν_ {\ perp} <2 $，其中$β$是关键的订单 - 参数仪 - 参数仪的关键订单 - 参数指数和$ν_ {\ perp} $是关键的correLation-lentement。在无限临界背景上最初局部密度曲线的放松表现出自相似的结构。在这种情况下，通过分析计算时间相关密度曲线的渐近缩放形式：我们发现，在长期$ t $中，密度扰动的宽度$σ$异常增长，即$σ\ sim t^{w} $，具有增长指数$ω= 1/（1+β）> 1+β）> 1-2 $ 1-2 $ 1-2 $ 1-2 $ 1-2 $ 1-2 $ 1-2 $ 1-2 $ 1-2 $ 1-2 $ 1-2。在所有情况下，理论预测与模拟都相当良好。
We study relaxation of long-wavelength density perturbations in one dimensional conserved Manna sandpile. Far from criticality where correlation length $ξ$ is finite, relaxation of density profiles having wave numbers $k \rightarrow 0$ is diffusive, with relaxation time $τ_R \sim k^{-2}/D$ with $D$ being the density-dependent bulk-diffusion coefficient. Near criticality with $k ξ\gsim 1$, the bulk diffusivity diverges and the transport becomes anomalous; accordingly, the relaxation time varies as $τ_R \sim k^{-z}$, with the dynamical exponent $z=2-(1-β)/ν_{\perp} < 2$, where $β$ is the critical order-parameter exponent and and $ν_{\perp}$ 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 $σ$ of the density perturbation grows anomalously, i.e., $σ\sim t^{w}$, with the growth exponent $ω=1/(1+β) > 1/2$. In all cases, theoretical predictions are in reasonably good agreement with simulations.
