Surface thickness in the Eden model.
Surface thickness in the Eden model.
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Eden 模型中的表面厚度。
DOI：
10.1103/physrevlett.54.2055
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发表时间：
1985
影响因子：
8.6
通讯作者：
Botet
中科院分区：
文献类型：
--
作者：
Jullien;Botet
我们已经通过tr= Xt（z，-z）/n n n计算了表面的厚度，其中z= g; z/n n n，其中总和覆盖表面的n个位置。在模型A中，我们还计算了a。通过在邻近表面的未被占用的位置上执行求和（如PR所做的）。包括孔的表面（如果有）。α取决于两个参数，宽度l和有效高度h= N/l，N是粒子数。对于大的I和h，我们恢复缩放a。（i，h）-l f（h/l ′），其中y）1，且f（x）对于x~ 1为常数，且f（x）-l ′ r对于x ~ 0为常数，使得a.（~，h）-h l}'，a（l，~）-i f.或h））1（稳态）。当与PR几何比较时，我们的n/y变成了a-与半径a-Rl”相关的指数。n/y= v/v，用PR符号表示。我们在这里报告一些结果的指数n。对于给定的i，我们精确地确定了da。（l，~）（直到h= 20 i）。结果如图1所示。而版本C曲线（a）
We have calculated the thickness of the surface, by tr= Xt (z,—z)/n „with z= g; z/n „where the sum covers the n, sites of the surface. In model A, we have also calculateda.', by performing instead the sum over the unoccupied sites adjacent to the surface (as PR did). The surface of holes (if any) is included. a-depends on two parameters, the width l and an effec-tive height h= N/l, N being the number of particles. For large I and h, we recover the scaling a.(i, h)—l f (h/l}'), with y) 1 and with f (x) const for x~ and f (x)—x l'r for x 0, so that a.(~, h)—h l}'for h && l and a (l,~)—i f. or h)) l (steady state). When comparing with the PR geometry, our n/y becomes the exponent relating a-to the radius, a-—R l". n/y= v/v, with PR notations. We report here on some results for the exponent n. For given i, we have precisely determineda.(l,~)(going up to h= 20i) by averaging over 1000 trials. Results are givenin Fig. 1. While the version-C curve (a)