Hentschel H G E, Popescu M N, Family F
Department of Physics, Emory University, Atlanta, Georgia 30322, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):036141. doi: 10.1103/PhysRevE.65.036141. Epub 2002 Mar 6.
In Laplacian growth processes pinning may be expected due to a nonlinear response of a material during dielectric breakdown, or due to stick-slip boundary conditions in two-fluid flow in a porous medium, while thermal noise will lead to depinning. Using a method recently proposed by Hastings and Levitov, the size R(max) approximately E(-alpha)(c) of the pinned pattern is shown to scale with the critical field E(c) (electric field for dielectric breakdown, pressure gradient for fluid flow). These pinned patterns have a lower effective fractal dimension d(f) than diffusion-limited aggregation due to the enhancement of growth at the hot tips of the developing pattern. At finite temperature, thermal noise leads to depinning and growth of patterns with a shape and dimensionality dependent on both E(c) and the thermal noise. Using multifractal analysis, scaling expressions are established for this dependency.
在拉普拉斯生长过程中，由于材料在介电击穿期间的非线性响应，或者由于多孔介质中双流体流动中的粘滑边界条件，可能会出现钉扎现象，而热噪声会导致去钉扎。使用黑斯廷斯和列维托夫最近提出的一种方法，已表明钉扎图案的大小(R_{(max)})近似为(E^{(-\alpha)}{(c)})，它与临界场(E{(c)})（介电击穿的电场、流体流动的压力梯度）成比例。由于发展图案热尖端处生长的增强，这些钉扎图案的有效分形维数(d_{(f)})比扩散限制聚集的要低。在有限温度下，热噪声导致去钉扎以及具有取决于(E_{(c)})和热噪声的形状和维度的图案生长。使用多重分形分析，建立了这种依赖性的标度表达式。
