Related Experiment Videos
Anisotropic diffusion limited aggregation in three dimensions: universality and nonuniversality.
Nicholas R Goold1, Ellák Somfai, Robin C Ball
1Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom. N.R.Goold@warwick.ac.uk
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
Lattice anisotropy in three-dimensional diffusion limited aggregation (DLA) creates anisotropic dendrites. Noise reduction accelerates the approach to universal states, with hexagonal lattices resembling snowflake structures.
Area of Science:
- Computational Physics
- Materials Science
- Complex Systems
Background:
- Diffusion Limited Aggregation (DLA) is a fundamental model for pattern formation in nature.
- Understanding the influence of underlying lattice structures on DLA is crucial for predicting growth morphologies.
- Previous studies have explored DLA in various dimensions, but the impact of lattice anisotropy requires further investigation.
Purpose of the Study:
- To investigate the macroscopic consequences of lattice anisotropy on three-dimensional DLA.
- To characterize the asymptotic states and their approach for different lattice types (simple cubic, bcc, fcc, hexagonal).
- To introduce and evaluate a new, dimension-independent DLA model implementation.
Main Methods:
- Development of a novel, dimension-independent DLA model utilizing sphere coverings and spherical moves for efficient random walks.
- Simulation of DLA growth on simple cubic, body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal lattices.
- Introduction of anisotropy by restricting growth to preferred directions within the simulated lattices.
Main Results:
- Simple cubic and bcc lattice growths exhibit anisotropic dendrites, approaching universal asymptotic states, with noise reduction accelerating this convergence.
- Fcc lattice growth suggests at least two stable anisotropy fixed points, one aligning with the bcc case.
- Hexagonal growths display a line of asymptotic states with tunable polar anisotropy, with planar growths visually mimicking snowflake structures.
Conclusions:
- Lattice anisotropy significantly influences DLA morphology, leading to distinct anisotropic dendrites and tunable structures.
- The developed DLA model provides an efficient and dimension-independent approach for studying anisotropic growth phenomena.
- The findings offer insights into the formation of complex natural patterns, such as snowflakes, through anisotropic aggregation processes.