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A generalized Oseen theory of two-dimensional Brownian motion

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  • Varley, R.L.

Abstract

A generalization of the Oseen arguments to a quasi-two-dimensional system of a nonuniformly moving Brownian cylinder yields a remarkable “long time” behavior ø(t) ∼ {1 + 2t/τ}−32t−1 for the velocity autocorrelation function ø(t). The characteristic time τ = 16mbv/(kBT) is generally much greater than the initial relaxation time tR and “long times” means after a few tR. Previous theories have predicted ø(t) ∼ t−1 after a few tR and our result is consistent with this for times much less than τ. On a longer time scale ∼τ our result predicts an ususual behavior ø(t) ∼ t−52 which is sufficient to yield a finite diffusion coefficient from the Green-Kubo formula.

Suggested Citation

  • Varley, R.L., 1981. "A generalized Oseen theory of two-dimensional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 108(2), pages 417-440.
    • Handle: RePEc:eee:phsmap:v:108:y:1981:i:2:p:417-440
    DOI: 10.1016/0378-4371(81)90140-0
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