Gradual Diffusive Capture: Slow Death by Many Mosquito Bites

Abstract

We study the dynamics of a single diffusing particle (a "man") with diffusivity $D_M$ that is attacked by another diffusing particle (a "mosquito") with fixed diffusivity $D_m$. Each time the mosquito meets and bites the man, the diffusivity of the man is reduced by a fixed amount, while the diffusivity of the mosquito is unchanged. The mosquito is also displaced by a small distance $\pm a$ with respect to the man after each encounter. The man is defined as dead when $D_M$ reaches zero. At the moment when the man dies, his probability distribution of displacements $x$ is given by a Cauchy form, which asymptotically decays as $x^{-2}$, while the distribution of times $t$ when the man dies asymptotically decays as $t^{-3/2}$, which has the same form as the one-dimensional first-passage probability.

10 pages, 2 figure, IOP format, Version 2 contains minor corrections

References in corpus (9)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Inhomogeneous Systems with Unusual Critical Behaviour
• Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
• Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions
• Scaling limit of vicious walks and two-matrix model
• Life and Death in a Cage and at the Edge of a Cliff
• Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk
• Ordering of Random Walks: The Leader and the Laggard
• Non-Gaussianity and Dynamical Trapping in Locally Activated Random Walks

Cited by in corpus (1)

• Capture of a diffusive prey by multiple predators in confined space