First-encounter time of two diffusing particles in confinement

Abstract

We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we focus on two one-dimensional settings: a half-line and an interval. We first consider the case with equal particle diffusivities, for which exact results can be obtained for the survival probability and the associated first-encounter time density over the full time domain. We also evaluate the moments of the first-encounter time when they exist. We then turn to the case when the diffusivities are not equal, and focus on the long-time behavior of the survival probability. Our results highlight the great impact of boundary effects in diffusion-controlled kinetics even for simple one-dimensional settings, as well as the difficulty of obtaining analytic results as soon as translational invariance of such systems is broken.

References in corpus (46)

• Intermittent search strategies
• First-passage times in complex scale-invariant media
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Geometry-controlled kinetics
• Geometrical structure of Laplacian eigenfunctions
• Diffusion-limited reactions in dynamic heterogeneous media
• First passages in bounded domains: When is the mean first passage time meaningful?
• Mean first-passage times of non-Markovian random walkers in confinement
• Anomalous, non-Gaussian tracer diffusion in heterogeneously crowded environments
• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Optimal reaction time for surface-mediated diffusion
• Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
• Paradigm shift in diffusion-mediated surface phenomena
• Survival of an evasive prey
• Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
• Vicious walkers, friendly walkers and Young tableaux II: With a wall
• Diffusive escape through a narrow opening: new insights into a classic problem
• Towards a full quantitative description of single-molecule reaction kinetics in biological cells
• Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps
• Pascal Principle for Diffusion-Controlled Trapping Reactions
• Non-crossing run-and-tumble particles on a line
• Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps
• Survival probability of a particle in a sea of mobile traps: A tale of tails
• Tracer diffusion in a sea of polymers with binding zones: mobile vs frozen traps
• Lattice theory of trapping reactions with mobile species
• Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces
• The subdiffusive target problem: Survival probability
• Computation of the Mean First-Encounter Time Between the Ends of a Polymer Chain
• Exit time distribution in spherically symmetric two-dimensional domains
• Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials
• Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents
• Theory of diffusion-influenced reactions in complex geometries
• Semi-analytical computation of Laplacian Green functions in three-dimensional domains with disconnected spherical boundaries
• Survival probability of an immobile target in a sea of evanescent diffusive or subdiffusive traps: a fractional equation approach
• Encounter times in overlapping domains: application to epidemic spread in a population of territorial animals
• Some exact results for the trapping of subdiffusive particles in one dimension
• The two-particle problem in comb-like structures
• Slow Encounters of Particle Pairs in Branched Structures
• Vicious Walkers in a Potential
• The target problem with evanescent subdiffusive traps
• Survival probability of a Brownian motion in a planar wedge of arbitrary angle
• Influence of atomic kinetics on inverse Bremsstrahlung heating and non-local thermal transport
• Multiparticle trapping problem in the half-line
• Slow Kinetics of Brownian Maxima
• Survival probability and order statistics of diffusion on disordered media
• Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers

Cited by in corpus (15)

• Statistics of boundary encounters by a particle diffusing outside a compact planar domain
• Statistics of diffusive encounters with a small target: Three complementary approaches
• First-passage times to anisotropic partially reactive targets
• First-passage times of multiple diffusing particles with reversible target-binding kinetics
• Distribution of first-reaction times with target regions on boundaries of shell-like domains
• A physicist's guide to explicit summation formulas involving zeros of Bessel functions and related spectral sums
• Resonance scattering in a waveguide with identical thick barriers
• Efficiency of random search with space-dependent diffusivity
• Capture of a diffusive prey by multiple predators in confined space
• First-encounter time of two diffusing particles in two- and three-dimensional confinement
• A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
• The microscopic mechanism of bulk melting of ice
• Contact statistics in populations of noninteracting random walkers in two dimensions
• First-passage times to a fractal boundary: local persistence exponent and its log-periodic oscillations
• Conditioning two diffusion processes with respect to their first-encounter properties