## Abstract

We investigate the average time for the earliest particle to hit a spherical absorber when a homogeneous gas of freely diffusing particles with density ρ and diffusivity D is prepared in a deterministic state and is initially separated by a minimum distance l from this absorber. In the high-density limit, this first absorption time scales as l^{2}/D 1/lnρl in one dimension; a similar scaling behavior occurs in greater than one dimension. In one dimension, we also determine the probability that the kth-closest particle is the first one to hit the absorber. At large k, this probability decays as k^{1/3}exp(-Ak^{2/3}), with A = 1.932 99... analytically calculable. As a corollary, the characteristic hitting time T_{k} for the kth-closest particle scales as k^{4/3}; this corresponds to superdiffusive but still subballistic motion.

Original language | American English |
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Article number | P06019 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2014 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jun 2014 |

## Keywords

- diffusion
- large deviations in non-equilibrium systems
- transport processes/heat transfer (theory)