论文标题
一维Zhang砂泵模型中的能量波动
Energy fluctuations in one dimensional Zhang sandpile model
论文作者
论文摘要
我们考虑具有局部保守（或耗散）动力学的一维（1D）中的Zhang SandPile模型，并在外部驱动时间尺度上检查其总能量波动。批量驱动的系统导致Lorentzian Spectra，其截止时间$ t $随系统尺寸$ L $线性增长。波动显示边界驱动器的$ 1/f^α$行为，$α\ sim 1 $，截止时间差异无线。对于保守的局部动力学，截止时间显示了一个幂律增长$ t \ sim l^λ$，与指数形式$ \ sim \ exp（μl）$不同。我们建议，本地耗散不是1D以1D噪声的必要成分，而截止时间可以揭示局部动力学的独特性质。我们还讨论了随机耗散的局部非保守动力学的能量波动。
We consider the Zhang sandpile model in one-dimension (1D) with locally conservative (or dissipative) dynamics and examine its total energy fluctuations at the external drive time scale. The bulk-driven system leads to Lorentzian spectra, with a cutoff time $T$ growing linearly with the system size $L$. The fluctuations show $1/f^α$ behavior with $α\sim 1$ for the boundary drive, and the cutoff time varies non-linearly. For conservative local dynamics, the cutoff time shows a power-law growth $T \sim L^λ$ that differs from an exponential form $ \sim \exp(μL)$ observed for the nonconservative case. We suggest that the local dissipation is not a necessary ingredient of the system in 1D to get the $1/f$ noise, and the cutoff time can reveal the distinct nature of the local dynamics. We also discuss the energy fluctuations for locally nonconservative dynamics with random dissipation.
