Uni-directional diffusion flux, Brownian and Langevin simulations

Amit Singer, Zeev Schuss, Boaz Nadler

Research output: Contribution to conferencePaperpeer-review

Abstract

The Wiener path integral splits the net diffusion flux into infinite unidirectional fluxes, whose difference is the classical diffusion flux. The infinite unidirectional flux is an artifact of the diffusion approximation to Langevin's equation, an approximation that fails on time scales shorter than the relaxation time 1/γ. The probability of one-dimensional Brownian trajectories that cross a point in one direction per unit time Δt equals that of Langevin trajectories if γΔt = 2. This result is relevant to Brownian and Langevin dynamics simulation of particles in a finite volume inside a large bath. We describe the sources of new trajectories at the boundaries of the simulation that maintain fixed average concentrations and avoid the formation of spurious boundary layers.

Original languageEnglish
StatePublished - 2005
Event8th International Conference on Path Integrals: From Quantum Information to Cosmology, PI 2005 - Prague, Czech Republic
Duration: 6 Jun 200510 Jun 2005

Conference

Conference8th International Conference on Path Integrals: From Quantum Information to Cosmology, PI 2005
Country/TerritoryCzech Republic
CityPrague
Period6/06/0510/06/05

Funding

FundersFunder number
Defense Advanced Research Projects Agency
National Institutes of Health
National Science Foundation

    Keywords

    • Brownian simulations
    • Diffusion
    • Langevin
    • Wiener's path integral

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