RADIALLY BIASED DIFFUSION-LIMITED AGGREGATION

被引:9
作者
MEAKIN, P [1 ]
FEDER, J [1 ]
JOSSANG, T [1 ]
机构
[1] UNIV OSLO, DEPT PHYS, N-0316 OSLO 3, NORWAY
来源
PHYSICAL REVIEW A | 1991年 / 43卷 / 04期
关键词
D O I
10.1103/PhysRevA.43.1952
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
A series of random growth models has been studied in which the growth probability at position r on the surface of the growing cluster is given by P(r) congruent-to mu-(r)l-phi, where mu-(r) is the harmonic measure at r and l is the distance from the seed or origin. The distance l can be either the Pythagorean distance or the minimum path distance measured on the growing cluster. The introduction of this scale-invariant perturbation of the usual diffusion-limited-aggregation (DLA) model (phi = 0) introduces a distance-dependent correlation length, xi = l /\phi\, that characterizes a geometrical crossover in the cluster structure. Although the structures generated by these models have an appearance that is quite different from that of DLA clusters (for \phi\ >> 0), the growth of their radii of gyration and the internal density profile rho(r) have simple power-law forms with the same exponents as those associated with DLA. The difference in scaling is manifest in the amplitudes of the power-law forms. These amplitudes exhibit a power-law dependence on the radial bias exponent-phi. For phi >> 1 the clusters become self-affine structures with the same exponents as those associated with DLA on length scales r << xi. These clusters exhibit a crossover to self-affine wedgelike linearly growing structures at r congruent-to R(x) congruent-to phi. For phi << - 1 the growth probability is enhanced in the core of the clusters. These clusters exhibit a dense core having radius R(x) approximately \phi\. For r congruent-to R(x), the structure crosses over to a structure having the same scaling behavior as DLA. For growth from a line in a strip of width L, the density-density correlation function in the lateral direction can be represented by the scaling form C(h)(x) approximately xi-(-a)g(x/xi-alpha/nu), where h is the distance from the line substrate (height) and exponents alpha and nu have values of about 1/3 and 1/2, respectively. The scaling function g(x) has the form g(x) congruent-to x-nu for x << 1 and g(x) approximately const for x >> 1.
引用
收藏
页码:1952 / 1964
页数:13
相关论文
共 49 条
[1]  
AHARONY A, 1989, FRACTALS PHYSICS ESS
[2]   CROSSOVER SCALING FROM MULTIFRACTAL THEORY - DIELECTRIC-BREAKDOWN WITH CUTOFFS [J].
ARIAN, E ;
ALSTROM, P ;
AHARONY, A ;
STANLEY, HE .
PHYSICAL REVIEW LETTERS, 1989, 63 (19) :2005-2009
[3]  
Avnir D., 1989, FRACTAL APPROACH HET
[4]  
BALL RC, 1989, P R SOC LONDON, V423, P1
[5]   FORMATION OF A DENSE BRANCHING MORPHOLOGY IN INTERFACIAL GROWTH [J].
BENJACOB, E ;
DEUTSCHER, G ;
GARIK, P ;
GOLDENFELD, ND ;
LAREAH, Y .
PHYSICAL REVIEW LETTERS, 1986, 57 (15) :1903-1906
[6]   STABILITY OF VISCOUS FINGERING PATTERNS IN LIQUID-CRYSTALS [J].
BUKA, A ;
PALFFYMUHORAY, P .
PHYSICAL REVIEW A, 1987, 36 (03) :1527-1529
[7]   SELF-AFFINE NATURE OF DIELECTRIC-BREAKDOWN MODEL CLUSTERS IN A CYLINDER [J].
EVERTSZ, C .
PHYSICAL REVIEW A, 1990, 41 (04) :1830-1842
[8]   DETERMINISTIC GROWTH-MODEL OF PATTERN-FORMATION IN DENDRITIC SOLIDIFICATION [J].
FAMILY, F ;
PLATT, DE ;
VICSEK, T .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1987, 20 (17) :L1177-L1183
[9]  
FEDER J, 1989, FRACTALS PHYSICS, P104
[10]  
FEDER J, 1988, FRACTALS