Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-11-05
Eur. Phys. J. B 78, 139 (2010)
Physics
Condensed Matter
Statistical Mechanics
Revised version (20/5/2010) accepted for publication in EPJB
Scientific paper
We study the motion of N=2 overdamped Brownian particles in gravitational interaction in a space of dimension d=2. This is equivalent to the simplified motion of two biological entities interacting via chemotaxis when time delay and degradation of the chemical are ignored. This problem also bears some similarities with the stochastic motion of two point vortices in viscous hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We analytically obtain the density probability of finding the particles at a distance r from each other at time t. We also determine the probability that the particles have coalesced and formed a Dirac peak at time t (i.e. the probability that the reduced particle has reached r=0 at time t). Finally, we investigate the variance of the distribution
Chavanis Pierre-Henri
Mannella Riccardo
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