Paczuski M, Bassler KE
Department of Mathematics, Huxley Building, Imperial College of Science, Technology, and Medicine, London SW7 2BZ, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Oct;62(4 Pt B):5347-52. doi: 10.1103/physreve.62.5347.
We study a directed stochastic sandpile model of self-organized criticality, which exhibits multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the steady-state all stable states are equally likely. Using this fact, we explicitly derive a discrete dynamical equation for avalanches on the lattice. By coarse graining we arrive at a continuous Langevin equation for the propagation of avalanches and calculate all the critical exponents characterizing avalanches. The avalanche equation is similar to the Edwards-Wilkinson equation, but with a noise amplitude that is a threshold function of the local avalanche activity, or interface height, leading to a stable absorbing state when the avalanche dies.
我们研究了一个自组织临界性的有向随机沙堆模型，该模型呈现出多次崩塌，使其处于与Dhar和Ramaswamy的精确求解模型不同的普适类中。我们表明，在稳态下，所有稳定状态的可能性相同。利用这一事实，我们明确推导了晶格上雪崩的离散动力学方程。通过粗粒化，我们得到了雪崩传播的连续朗之万方程，并计算了表征雪崩的所有临界指数。雪崩方程类似于Edwards-Wilkinson方程，但噪声幅度是局部雪崩活动或界面高度的阈值函数，当雪崩停止时会导致一个稳定的吸收态。
