Fig. 3: Distribution of reaction times for diffusive processes in various confining domains, for sink and surface reactivity.
From: Universal kinetics of imperfect reactions in confinement
(a) Geometry of the confining domains (called A and B) that are considered for stochastic simulations. In 2D, these domains are defined in polar coordinates by r(θ) = Rf(θ) with \(f=1.6(1+0.5{\cos }^{2}\theta )\) for domain A and \(f=1.6(1+0.1\sin \theta +0.3\sin 3\theta )\) for domain B. Domains in 3D are obtained by considering revolution of 2D surfaces around the vertical dashed line. The geometry of the target (red sphere) and initial position of the random walker are indicated. In the figure, we have used R = 6a. (b)–(e) Results of stochastic simulations for the mean reaction time in 2D/3D, for surface/sink reactivity, compared to our theoretical expressions. (f) and (g) Rescaled survival probabilities for 2D/3D simulations, all parameters are in legend except for R/a = 6 and ka2/D = 1 (for sink reactivity) and κa/D = 1 (for surface reactivity). In 3D we evaluated 〈T〉G = Vϕ(∞). In 2D, we used 〈T〉G = Vϕ(1) + 〈τ〉G where 〈τ〉G was evaluated numerically for each domain. In all simulations we used a time step Δt = 10−4a2/D. For surface reactivity we implemented our simulation algorithm by using ref. 49. Error bars (95% confidence intervals) are smaller than symbols.
