Lin Chai-Yu, Chen Chien-Fu, Chen Chi-Ning, Yang Chao-Shun, Jiang I-Min
Department of Physics, National Chung Cheng University, Chia-Yi 66117, Taiwan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 1):031304. doi: 10.1103/PhysRevE.74.031304. Epub 2006 Sep 18.
Bulk dissipation of a sandpile on a square lattice with the periodic boundary condition is investigated through a dissipating probability f during each toppling process. We find that the power-law behavior is broken for f>10(-1) and not evident for 10(-1)}>f>10(-2). In the range 10(-2)>or=f>or=10(-5), numerical simulations for the toppling size exponents of all, dissipative, and last waves have been studied. Two kinds of definitions for exponents are considered: the exponents obtained from the direct fitting of data and the exponents defined by the simple scaling. Our result shows that the exponents from these two definitions may be different. Furthermore, we propose analytic expressions of the exponents for the direct fitting, and it is consistent with the numerical result. Finally, we point out that small dissipation drives the behavior of this model toward the simple scaling.
通过在每次倾倒过程中的耗散概率f，研究了具有周期性边界条件的方形晶格上沙堆的大量耗散。我们发现，当f>10^(-1)时，幂律行为被打破，而当10^(-1)>f>10^(-2)时则不明显。在10^(-2)≥f≥10^(-5)范围内，研究了所有波、耗散波和最后一波的倾倒尺寸指数的数值模拟。考虑了两种指数定义：从数据直接拟合得到的指数和由简单标度定义的指数。我们的结果表明，这两种定义的指数可能不同。此外，我们提出了直接拟合指数的解析表达式，它与数值结果一致。最后，我们指出小耗散驱动该模型的行为趋向于简单标度。
