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
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

Show full item record

SCOPUSTM   
Citations

7
checked on Sep 2, 2020

WEB OF SCIENCETM
Citations

6
checked on May 13, 2022

Page view(s)

44
checked on May 17, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.