Diffusion-limited growth
The diffusion limited growth ( diffusion limited aggregation , DLA) comes by random attachment of particles about. The basis for this is the Brownian molecular movement , according to the laws of which particles in gases or liquids move thermally. They are one of the simplest mechanisms for creating fractals .
The particles are more likely to attach to the existing tips. The resulting heavily branched structures ("Brownian trees") are in the limit of infinitely small particles fractals .
The diffusion-limited growth was described in 1981 by Leonard M. Sander and Thomas Witten . Their attention was drawn to the observation of such structures in deposits of iron colloids, reminiscent of Mandelbrot's fractals, and they tried to simulate their formation in a simple computer model. In the Witten-Sander model, a particle moves mainly under the influence of diffusion (Brownian movement) until it comes close to a “cluster” of particles that have already been deposited. If it falls below a minimum distance, it attaches to the cluster. To the surprise of Sander and Witten, the simulation revealed ramified, fractal structures.
Examples of this:
- Accumulation of soot particles: particles accumulate on the walls of a chimney and cause the pipe to grow in size
- Precipitations in electrolytic solutions, e.g. B. Copper sulphate solution, which can be precipitated to pure copper using suitable cathodes (see picture, copper refining ).
- Tree-like structures in biology, such as the formation of fur markings in zebra , tiger , leopard , tapir
- Lichtenberg figures
- Snowflakes , see also Koch curve
literature
- Thomas Witten, Leonard Sander: Diffusion limited aggregation - a kinetic critical phenomenon , Physical Review Letters, Vol. 47, 1981, pp. 1400-1403
- Witten, Sander: diffusion limited aggregation Archived from the original on March 14, 2014. In: Physical Review B . 27, 1983, p. 5686. doi : 10.1103 / PhysRevB.27.5686 .
- Witten, Sander: Fractal Growth , Scientific American, Vol. 256, 1987, pp. 94-100
Web links
- Applet simulates diffusion-limited growth
- Witten on the article by Witten, Sander "DLA", 1981, at Science Citation Classics, PDF file (PDF; 152 kB)
photos
A brownish tree that was created by electrolytic deposition in a copper sulphate solution
Brownian tree in the scanning electron microscope, magnified 4,850 times
Brownian tree, enlarged 8,470 times
Brownian tree (134,980x magnification)
