Diffusion-limited aggregation on curved surfaces

被引:13
作者
Choi, J. [1 ]
Crowdy, D. [2 ]
Bazant, M. Z. [1 ,3 ]
机构
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England
[3] MIT, Dept Chem Engn, Cambridge, MA 02139 USA
基金
英国工程与自然科学研究理事会;
关键词
VISCOUS FLOWS; GROWTH;
D O I
10.1209/0295-5075/91/46005
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We develop a general theory of transport-limited aggregation phenomena occurring on curved surfaces, based on stochastic iterated conformal maps and conformal projections to the complex plane. To illustrate the theory, we use stereographic projections to simulate diffusion-limited aggregation (DLA) on surfaces of constant Gaussian curvature, including the sphere (K>0) and the pseudo-sphere (K<0), which approximate "bumps" and "saddles" in smooth surfaces, respectively. Although the curvature affects the global morphology of the aggregates, the fractal dimension (in the curved metric) is remarkably insensitive to curvature, as long as the particle size is much smaller than the radius of curvature. We conjecture that all aggregates grown by conformally invariant transport on curved surfaces have the same fractal dimension as DLA in the plane. Our simulations suggest, however, that the multifractal dimensions increase from hyperbolic (K<0) to elliptic (K>0) geometry, which we attribute to curvature-dependent screening of tip branching. Copyright (C) EPLA, 2010
引用
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页数:6
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