## Abstract

There have been a number of recent investigations of statistical properties of the nearest-neighbor distance of the closest diffusing particle in the presence of a trap. These have been shown to be useful characterizations of self-organizing properties of simple binary reactions of the form A+A A or A+A 0. In this paper we extend our results to diffusion in the presence of an imperfect trap in one and three dimensions. The imperfect trap is modeled in terms of a radiation boundary condition. Our exact solution permits one to follow the transition in the shape of the probability density for the nearest-neighbor distance from the exponential in one dimension corresponding to total reflection, to the skewed Gaussian form for perfect reaction. Similar results are given for the case of a reactive sphere in the presence of mobile particles in three dimensions.

Original language | English |
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Pages (from-to) | 3116-3120 |

Number of pages | 5 |

Journal | Physical Review A |

Volume | 41 |

Issue number | 6 |

DOIs | |

State | Published - 1990 |