Regensburg 2002 – scientific programme

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DY: Dynamik und Statistische Physik

DY 23: Brownsche Bewegung

DY 23.3: Talk

Tuesday, March 12, 2002, 12:15–12:30, H3

Diffusion Limited Reactions on Small-World Networks — •Florian Jasch and Alexander Blumen — Theoretische Polymerphysik, Universität Freiburg, 79104 Freiburg

As a simple example of a diffusion limited reaction we investigate the dynamics of the A+B->A Reaction on small-world networks (SWNs), disordered graphs of much recent interest [1]. SWNs are built starting from regular lattices through the insertion of additional links connecting distant pairs of sites [2]. In this way SWNs combine random and regular features. A quantity of central importance in reaction kinetics is the mean number of visited sites which obeys a scaling law on SWNs. On regular lattices the reaction leads for large times to a stretched exponential decay of B particles characterized by a universal exponent p depending on the dimension of the lattice. On a SWN additional features of the decay are revealed but it turns out that the universal exponent p is not changed by the existence of long range links [3]. [1] F. Jasch and A. Blumen, Phys. Rev. E 60, 7332 (1999). [2] D. J. Watts and S. H. Strogatz, Nature 393, 440 (1998). [3] F. Jasch and A. Blumen, to appear in Phys. Rev. E.