A note on confined diffusion
arXiv:cond-mat/0604133 · doi:10.1016/j.physa.2006.11.008
Abstract
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion operator. Unfortunately, the latter depend on space dimensionality and on the particular shape of the domain, and an analytical expression is in most circumstances not available. In this article, it is shown that the series may in some circumstances sum up exactly. Explicit calculations are performed for 2D diffusion restricted to a circular domain and 3D diffusion inside a sphere. In both cases, the short-time behaviour of the mean square displacement is obtained.
10 pages; Eq. (2) corrected
References in corpus (3)
Cited by in corpus (21)
- Membraneless organelles formed by liquid-liquid phase separation increase bacterial fitness
- Inferring diffusion in single live cells at the single molecule level
- Explicit calculation of nuclear magnetic resonance relaxation rates in small pores to elucidate molecular scale fluid dynamics
- Spreading dynamics of reactive surfactants driven by Marangoni convection
- Diffusive regimes in a two-dimensional chiral fluid
- Fractional Laplacians in bounded domains: Killed, reflected, censored and taboo Lévy flights
- Wave-particle interactions with parallel whistler waves: nonlinear and time-dependent effects revealed by Particle-in-Cell simulations
- Resetting mediated navigation of active Brownian searcher in a homogeneous topography
- Killing (absorption) versus survival in random motion
- Nanoconfined catalytic Ångström-size motors
- Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
- Water as a Levy rotor
- A Jump Distance-based Bayesian analysis method to unveil fine single molecule transport features
- Fluorescence correlation spectroscopy in thin films at reflecting substrates as a means to study nanoscale structure and dynamics at soft-matter interfaces
- Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories
- Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments
- Fractional Laplacians and Levy flights in bounded domains
- Characterizing pedestrian contact interaction trajectories to understand spreading risk in human crowds
- Ultrarelativistic bound states in the shallow spherical well
- Enhancing search efficiency through diffusive echo
- Superharmonic double-well systems with zero-energy ground states: Relevance for diffusive relaxation scenarios