TY - JOUR

T1 - First invader dynamics in diffusion-controlled absorption

AU - Redner, S.

AU - Meerson, Baruch

PY - 2014/6/1

Y1 - 2014/6/1

N2 - 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 l2/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 k1/3exp(-Ak2/3), with A = 1.932 99... analytically calculable. As a corollary, the characteristic hitting time Tk for the kth-closest particle scales as k4/3; this corresponds to superdiffusive but still subballistic motion.

AB - 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 l2/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 k1/3exp(-Ak2/3), with A = 1.932 99... analytically calculable. As a corollary, the characteristic hitting time Tk for the kth-closest particle scales as k4/3; this corresponds to superdiffusive but still subballistic motion.

KW - diffusion

KW - large deviations in non-equilibrium systems

KW - transport processes/heat transfer (theory)

UR - http://www.scopus.com/inward/record.url?scp=84905171741&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2014/06/P06019

DO - 10.1088/1742-5468/2014/06/P06019

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AN - SCOPUS:84905171741

SN - 1742-5468

VL - 2014

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 6

M1 - P06019

ER -