Mean first-passage time of an anisotropic diffusive searcher
Résumé
We consider an anisotropic needle-like Brownian particle with nematic symmetry confined in a 2D domain. For this system, the coupling of translational and rotational diffusion makes the process \mathbf{x}(t) of the positions of the particle non Markovian. Using scaling arguments, a Gaussian approximation and numerical methods, we determine the mean first passage time < \mathbf{T}> of the particle to a target of radius a and show in particular that < \mathbf{T}> ∼ {{a}-1/2} for a\to 0 , in contrast with the classical logarithmic divergence obtained in the case of an isotropic 2D Brownian particle.