Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent

Details Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent

2004-05-12

arxiv.org/abs/cond-mat/0405265v1

J. Phys. A 37, L361 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages

Scientific paper

10.1088/0305-4470/37/30/L01

We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We treat the class of models defined by f(y) = \pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). We show that the particle survives with probability Q(t) \sim t^{-\theta} with \theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-}, however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-}, and we determine this dependence.

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