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### Persistence properties of a system of coagulating and annihilating random walkers

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UNSPECIFIED.
(2003)
*Persistence properties of a system of coagulating and annihilating random walkers.*
PHYSICAL REVIEW E, 68
(4 Part 2).
-.
ISSN 1063-651X

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1103/PhysRevE.68.046103

## Abstract

We study a d-dimensional system of diffusing particles that on contact either annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1). In one dimension, the system models the zero-temperature Glauber dynamics of domain walls in the q-state Potts model. We calculate (P) over bar (m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly (m-1) coagulations. Using perturbative renormalization group analysis for d<2, we show that, if the number of coagulations m is much less than the typical number M(t), then (P) over bar (m,t)similar tom(zeta/d)t(-theta), with theta=dQ+Q(Q-1/2)epsilon+O(epsilon(2)), zeta=(2Q-1)epsilon+(2Q-1)(Q-1)(1/2+AQ)epsilon(2)+O(epsilon(3)), where Q=(q-1)/q, epsilon=2-d and A=-0.006.... M(t) is shown to scale as M(t)similar tot(d/2-delta), where delta=d(1-Q)+(Q-1)(Q-1/2)epsilon+O(epsilon(2)). In two dimensions, we show that (P) over bar (m,t)similar toln(t)(Q(3-2Q))ln(m)((2Q-1)2)t(-2Q) for m<t(2Q-1). We also derive an exact nonperturbative relation between the exponents: namely delta(Q)=theta(1-Q). The one-dimensional results corresponding to epsilon=1 are compared with results from Monte Carlo simulations.

Item Type: | Journal Article |
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Subjects: | Q Science > QC Physics |

Journal or Publication Title: | PHYSICAL REVIEW E |

Publisher: | AMERICAN PHYSICAL SOC |

ISSN: | 1063-651X |

Date: | October 2003 |

Volume: | 68 |

Number: | 4 Part 2 |

Number of Pages: | 12 |

Page Range: | - |

Identification Number: | 10.1103/PhysRevE.68.046103 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/9108 |

Data sourced from Thomson Reuters' Web of Knowledge

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