Fractal chemical kinetics: Reacting random walkers
type: Item
instance of: scholarly article
title: Fractal chemical kinetics: Reacting random walkers
zbMATH Open document ID: 0586.60064
DOI: 10.1007/BF01012924
author: L. W. Anacker
author: J. S. Newhouse
author: Raoul Kopelman
published in: Journal of Statistical Physics
publication date: 1984-01-01T00:00:00Z
review text: Computer simulations on binary reactions of random walkers \((A+A\to A)\) on fractal spaces bear out a recent conjecture: \((\rho^{-1}-\rho_ 0^{-1})\ltimes t^ f\), where \(\rho\) is the instantaneous walker density and \(\rho_ 0\) the initial one, and \(f=d_ s/2\), where \(d_ s\) is the spectral dimension. For the Sierpinski gaskets: \(d=2\), \(2f=1.38\) \((d_ s=1.365)\); \(d=3\), \(2f=1.56\) \((d_ s=1.547)\); biased initial random distributions are compared to unbiased ones. For site percolation: \(d=2\), \(p=0.60\), \(2f=1.35\) \((d_ s=1.35)\); \(d=3\), \(p=0.32\), \(2f=1.37\) \((d_ s=1.4)\); fractal-to-Euclidean crossovers are also observed. For energetically disordered lattices, the effective 2f (from reacting walkers) and \(d_ s\) (from single walkers) are in good agreement, in both two and three dimensions.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3940349
zbMATH Keywords: reacting random walkers
zbMATH Keywords: spectral dimension
zbMATH Keywords: percolation
zbMATH Keywords: Sierpinski gaskets
MaRDI profile type: Publication
cites work: On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling
cites work: Diffusion-limited reaction rate theory for two-dimensional systems
cites work: Single random walker on disordered lattices
full work available at URL: https://doi.org/10.1007/bf01012924
OpenAlex ID: W2087312149
description: scientific article; zbMATH DE number 3940349