Encounter-based model of a run-and-tumble particle

Abstract In this paper we extend the encounter-based model of diffusion-mediated surface absorption to case an unbiased run-and-tumble particle (RTP) confined a finite interval [0, L ] and switching between two constant velocity states ± v at rate α . The formalism is motivated by observation that various surface-based reactions are better modeled in terms reactivity function amount time spends neighborhood absorbing surface, which specified functional known as boundary local time. effects taken into account identifying first passage (FPT) for with event crosses some random threshold ℓ ^ Brownian particle, ℓ ( t ) continuous non-decreasing Taking ${\Psi}(\ell )\equiv \mathbb{P}[\hat{\ell } > \ell ]$?> Ψ stretchy="false">( stretchy="false">) ≡ mathvariant="double-struck">P stretchy="false">[ > stretchy="false">] be exponential distribution, ${\Psi}[\ell ]={\mathrm{e}}^{-{\kappa }_{0}\ell = mathvariant="normal">e − κ 0 , equivalent imposing Robin condition κ 0 One major difference RTP now discrete variable counts number collisions boundary. Given modification, show geometric distribution Ψ( = z 1/(1 + / ), recover analog condition. This allows us solve value problem (BVP) joint probability density position time, thus incorporate more general models based on non-geometric distributions ). We illustrate theory calculating mean FPT (MFPT) x given totally reflecting 0. also determine splitting when absorbing.