On Taylor dispersion in oscillatory channel flows

We revisit Taylor dispersion in oscillatory flows at zero Reynolds number, giving an alternative method of calculating the Taylor dispersivity that is easier to use with computer algebra packages to obtain exact expressions. We consider the effect of out-of-phase oscillatory shear and Poiseuille flow, and show that the resulting Taylor dispersivity is independent of the phase difference. We also determine exact expressions for several examples of oscillatory power-law fluid flows

Stochastic Stokes' drift of a flexible dumbbell

We consider the stochastic Stokes drift of a flexible dumbbell. The dumbbell consists of two isotropic Brownian particles connected by a linear spring with zero natural length, and is advected by a sinusoidal wave. We find an asymptotic approximation for the Stokes drift in the limit of a weak wave, and find good agreement with the results of a Monte Carlo simulation. We show that it is possible to use this effect to sort particles by their flexibility even when all the particles have the same diffusivity.Comment: 12 pages, 1 figur

The general drift decomposition for diffusion with advection

A general class of advection-diffusion equations is considered for which a new kind of decomposition theorem exists. The systems studied have nonuniform and nonconstant advection terms, but their solution can be written as a position- and time-dependent average of the solutions of diffusion equations with uniform and constant drift terms. The types of advection possible resemble stagnation-point flows, and may have practical applications in that area. However, a much more important possibility is that this type of decomposition may be a first example of a much more general result. 1

Excursions into a New Duality Relation for Diffusion Processes

This work was motivated by the recent work by H. Dette, J. Pitman and W.J. Studden on a new duality relation for random walks [1]. In this note we consider the diffusion process limit of their result, and use the alternative approach of Ito excursion theory. This leads to a duality for Ito excursion rates. 1 A Duality for Excursion Rates of a Brownian Motion with Non-Uniform Drift In a recent paper [1] a new duality relation for random walks was introduced, and at the end of that paper a brief mention was made of a corresponding result conjectured for diffusion processes. In this note we show how the diffusion process limit of the random walk result is very much easier to prove directly. This leads to a duality for Ito excursion rates. For a good review of Ito excursion theory see the book by Rogers and Williams [2], or for the bare bones of excursion theory, which is sufficient for the current work see Dean and Jansons [3], who use it to consider polymer solutions in straining flows...

ELECTRONIC COMMUNICATIONS in PROBABILITY EXCURSIONS INTO A NEW DUALITY RELATION FOR DIFFUSION PROCESSES

This work was motivated by the recent work by H. Dette, J. Pitman and W.J. Studden on a new duality relation for random walks [1]. In this note we consider the diffusion process limit of their result, and use the alternative approach of Itô excursion theory. This leads to a duality for Itô excursion rates. 1 A Duality for Excursion Rates of a Brownian Motion with Non-Uniform Drift In a recent paper [1] a new duality relation for random walks was introduced, and at the end of that paper a brief mention was made of a corresponding result conjectured for diffusion processes. In this note we show how the diffusion process limit of the random walk result is very much easier to prove directly. This leads to a duality for Itô excursion rates. For a good review of Itô excursion theory see the book by Rogers and Williams [2], or for the bare bones of excursion theory, which is sufficient for the current work see Dean and Jansons [3], who use it to consider polymer solutions in straining flows. Let u:IR↦ → IR be locally integrable, and let u ∗ (x) =−u(x). Fixing a<band λ>0unti