TY - CONF

T1 - Uni-directional diffusion flux, Brownian and Langevin simulations

AU - Singer, Amit

AU - Schuss, Zeev

AU - Nadler, Boaz

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Brownian simulations

KW - Diffusion

KW - Langevin

KW - Wiener's path integral

UR - http://www.scopus.com/inward/record.url?scp=84898830698&partnerID=8YFLogxK

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AN - SCOPUS:84898830698

T2 - 8th International Conference on Path Integrals: From Quantum Information to Cosmology, PI 2005

Y2 - 6 June 2005 through 10 June 2005

ER -