Theory of diffusion-limited growth
- 1 December 1993
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 48 (6) , R4207-R4210
- https://doi.org/10.1103/physreve.48.r4207
Abstract
We review and extend the field-theoretic approach to diffusion-limited growth at a finite background walker density. This approach leads to an Ito-type stochastic evolution equation with a multiplicative noise term. We show that a consistent mean-field (i.e., deterministic) reduction of this problem contains an unexpected low-density cutoff induced by the net probability drift due to the aforementioned noise. At the conclusion, implications of these findings for a first-principles theory of diffusion-limited-aggregation fractals are discussed.Keywords
This publication has 26 references indexed in Scilit:
- Adaptive self-organization during growth of bacterial coloniesPhysica A: Statistical Mechanics and its Applications, 1992
- Kinetic Phase Diagram and Scaling Relations for Stationary Diffusional GrowthEurophysics Letters, 1992
- Bacterial Fractal Growth in the Concentration Field of NutrientJournal of the Physics Society Japan, 1991
- The formation of patterns in non-equilibrium growthNature, 1990
- Pattern selection in fingered growth phenomenaAdvances in Physics, 1988
- Viscous flows in two dimensionsReviews of Modern Physics, 1986
- Morphology and Microstructure in Electrochemical Deposition of ZincPhysical Review Letters, 1986
- Dendritic and Fractal Patterns in Electrolytic Metal DepositsPhysical Review Letters, 1986
- Diffusion-limited aggregationPhysical Review B, 1983
- Diffusion-Limited Aggregation, a Kinetic Critical PhenomenonPhysical Review Letters, 1981