Mean first-passage time of an anisotropic diffusive searcher

Abstract

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 $⟨\mathbf{T}⟩\sim a^{-1/2}$ for $a\to 0$, in contrast with the classical logarithmic divergence obtained in the case of an isotropic $2D$ Brownian particle.

References in corpus (4)

• First-passage times in complex scale-invariant media
• Mean first-passage times of non-Markovian random walkers in confinement
• Non-Markovian polymer reaction kinetics
• Intermittent random walks for an optimal search strategy: One-dimensional case