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Title: | REACTION, TRAPPING, AND MULTIFRACTALITY IN ONE-DIMENSIONAL SYSTEMS | Authors: | VAN DEN BROECK, Christian | Issue Date: | 1991 | Publisher: | PLENUM PUBL CORP | Source: | 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. | Keywords: | TRAPPING, MULTIFRACTALITY; ONE-DIMENSIONAL SYSTEMS | Document URI: | http://hdl.handle.net/1942/3933 | DOI: | 10.1007/BF01049593 | ISI #: | A1991GY07100011 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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