RADIALLY BIASED DIFFUSION-LIMITED AGGREGATION

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.