Unidirectional flux in Brownian and Langevin simulations of diffusion

Amit Singer, Z. Schuss, B. Nadler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Brownian and Langevin simulations of ions in solution require the maintenance of average fixed concentrations at the interface between the simulation volume and the surrounding continuum. This requires the injection of new trajectories into the simulation, which creates a unidirectional flux at the interface. The Wiener path integral splits the net diffusion flux into infinite unidirectional fluxes, whose difference is finite, as in classical diffusion theory. The infinite unidirectional flux is an artifact of the diffusion approximation to Langevin's equation, which fails on time scales shorter than the relaxation time 1/γ. The probability of 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 dynamics simulation of particles in a finite volume inside a large bath.

Original languageEnglish (US)
Title of host publicationUNSOLVED PROBLEMS OF NOISE AND FLUCTUATIONS
Subtitle of host publicationUPoN 2005: Fourth International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology, and High Technology
Pages400-406
Number of pages7
DOIs
StatePublished - Nov 14 2005
Externally publishedYes
EventUPoN 2005: 4th International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology and High Technology - Gallipoli, Lecce, Italy
Duration: Jun 6 2005Jun 10 2005

Publication series

NameAIP Conference Proceedings
Volume800
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherUPoN 2005: 4th International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology and High Technology
CountryItaly
CityGallipoli, Lecce
Period6/6/056/10/05

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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    Singer, A., Schuss, Z., & Nadler, B. (2005). Unidirectional flux in Brownian and Langevin simulations of diffusion. In UNSOLVED PROBLEMS OF NOISE AND FLUCTUATIONS: UPoN 2005: Fourth International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology, and High Technology (pp. 400-406). (AIP Conference Proceedings; Vol. 800). https://doi.org/10.1063/1.2138644