Narrow Escape of Interacting Diffusing Particles

Abstract

The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism which allows us to evaluate the nonescape probability of a gas of diffusing particles that may interact with each other. In some cases the nonescape probability allows us to evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory. We also uncover an unexpected connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.

Salt parameterization can drastically affect the results from classical atomistic simulations of water desalination by MoS2 nanopores

“…At this point, is relevant to emphasize that the ionic passage trough small pores has two main events [47]: first the ion must hit the pore, secondly it need to have enough energy to overcome the energetic penalty related to leave the bulk, enter the pore with a distinct dielectric constant, and cross the pore to the bulk again. The first process is a classical problem from statistical mechanics, depending mainly in the system density and pore area [62,63]. In the second process the penalties can depend on the nanopore size, ion hydration, ion charge, pore chemical characteristics and pore geometry [57,47].…”

Occupation-time statistics of a gas of interacting diffusing particles

“…In many biologically relevant situations such as in crowded living cell, inter-particle interactions can be significant [29], and the single-particle approach breaks down. In this work we continue a previous line of research [30][31][32][33][34] and address this many-body problem by employing the Macroscopic Fluctuation Theory (MFT) [35]. The MFT proves to be useful also for non-interacting particles.…”

“…The extreme case ν = 1 corresponds to the so called survival problem, where all the particles are conditioned to stay inside the interval for the entire time T . This case has already been considered for a system of many non-interacting and interacting particles [31,33]. A natural next question concerns the complete distribution of the occupation fraction, 0 ≤ ν ≤ 1.…”

Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces

“…On the other hand, homogenization techniques were used to substitute piecewise constant reactivity κ(s) by an effective homogeneous reactivity [31][32][33][51][52][53][54][55][56][57][58]. More recent works investigated how the mean reaction time is affected by a finite lifetime of diffusing particles [59][60][61], by partial reactivity and interactions [63,64], by target aspect ratio [65], by reversible target-binding kinetics [66,67] and surface-mediated diffusion [68][69][70][71], by heterogeneous diffusivity [72], and by rapid re-arrangments of the medium [73][74][75]. Some of the related effects onto the whole distribution of reaction times were analyzed [76][77][78][79][80].…”