Peleg A, Conti M, Meerson B
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036127. doi: 10.1103/PhysRevE.64.036127. Epub 2001 Aug 30.
We find that globally conserved interface-controlled coarsening of diffusion-limited aggregates exhibits dynamic scale invariance (DSI) and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The general sharp-interface limit of this equation is introduced and reduced to volume preserving motion by mean curvature. A simple example of globally conserved interface-controlled coarsening system: the sublimation/deposition dynamics of a solid and its vapor in a small closed vessel, is presented in detail. The results of the numerical simulations show that the scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal dynamic scaling. A decrease of the cluster radius with time, predicted by DSI, is observed. The difference between global and local conservation is discussed.
我们发现，扩散限制聚集体的全局守恒界面控制粗化表现出动态尺度不变性（DSI）和正常标度。这通过具有全局守恒律的金兹堡-朗道方程的数值解得到了证明。引入了该方程的一般尖锐界面极限，并通过平均曲率将其简化为体积守恒运动。详细给出了一个全局守恒界面控制粗化系统的简单示例：固体及其蒸汽在小型封闭容器中的升华/沉积动力学。数值模拟结果表明，相关函数的标度形式具有幂律尾部，适应分形初始条件。粗化长度表现出正常的动态标度。观察到了DSI预测的团簇半径随时间的减小。讨论了全局守恒和局部守恒之间的差异。
