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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3933

Title: REACTION, TRAPPING, AND MULTIFRACTALITY IN ONE-DIMENSIONAL SYSTEMS
Authors: VAN DEN BROECK, Christian
Issue Date: 1991
Publisher: PLENUM PUBL CORP
Citation: JOURNAL OF STATISTICAL PHYSICS, 65(5-6). p. 971-990
Abstract: In the first part of this paper, we present two variants of the A + A --> A and A + A --> P reaction in one dimension that can be investigated analytically. In the first model, pairs of neighboring particles disappear reactively at a rate which is independent of their relative distance. It is shown that the probability density phi(x) for a nearest neighbor distance equal to x approaches the scaling form phi(x) approximately c exp(-cx/2)/(cx)1/2 in the long-time limit, with c being the concentration of particles. The second model is a ballistic analogue of the coagulation reaction A + A --> A. The model is solved by reducing it to a first-passage-time problem. The anomalous relaxation dynamics can be linked in a direct way to the fractal time properties of random walks. In the second part of this paper, we discuss the complications that arise in systems with disorder. We present a new approach that relates first-passage-time characteristics in a one-dimensional random walk to properties of random maps. In particular, we show that Sinai disorder is a borderline case for the appearance of multifractal properties. Finally, we apply a previously introduced renormalization technique to calculate the survival probability of particles moving on the line in the presence of a background of imperfect traps.
Notes: UNIV CATHOLIQUE LOUVAIN,B-3590 DIEPENBEEK,BELGIUM.VANDENBROECK, C, UNIV CALIF SAN DIEGO,DEPT CHEM,LA JOLLA,CA 92093.
URI: http://hdl.handle.net/1942/3933
DOI: 10.1007/BF01049593
ISI #: A1991GY07100011
ISSN: 0022-4715
Type: Journal Contribution
Appears in Collections: Research publications

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