Fractal chemical kinetics: Reacting random walkers
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.
scientific article; zbMATH DE number 3940349