ar X iv : m at h / 06 07 70 7 v 2 [ m at h . PR ] 2 9 Ju l 2 00 6 Stochastic Stokes ’ drift with inertia
نویسندگان
چکیده
We consider both the effect of particle inertia on stochastic Stokes’ drift, and also a related process which could be considered as a crude model of stochastic Stokes’ drift driven by an eddy diffusivity. In the latter, the stochastic forcing is a stable Ornstein–Uhlenbeck process rather than Brownian motion. We show that the eddy Stokes’ drift velocity has a peak at a non-zero value of the correlation time-scale for particles that have the same (limiting) diffusivity. For both of the models considered, this study shows that not only can stochastic Stokes’ drift be used to sort particles with different diffusivities, but also it can be used to sort particles of the same diffusivities but with different particle masses or correlation time-scales. This effect may be important in particle sorting applications.
منابع مشابه
ar X iv : m at h / 06 07 70 7 v 1 [ m at h . PR ] 2 7 Ju l 2 00 6 Stochastic Stokes ’ drift with inertia
We consider both the effect of particle inertia on stochastic Stokes’ drift, and also a related process which could be considered as a crude model of stochastic Stokes’ drift driven by an eddy diffusivity. In the latter, the stochastic forcing is a stable Ornstein–Uhlenbeck process rather than Brownian motion. We show that the eddy Stokes’ drift velocity has a peak at a non-zero value of the co...
متن کاملar X iv : m at h / 06 07 70 7 v 3 [ m at h . PR ] 6 S ep 2 00 6 Stochastic Stokes ’ drift with inertia
We consider both the effect of particle inertia on stochastic Stokes’ drift, and also a related process which could be considered as a crude model of stochastic Stokes’ drift driven by an eddy diffusivity. In the latter, the stochastic forcing is a stable Ornstein–Uhlenbeck process rather than Brownian motion. We show that the eddy Stokes’ drift velocity has a peak at a non-zero value of the co...
متن کاملar X iv : 0 90 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs
2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...
متن کاملar X iv : m at h / 06 07 20 6 v 2 [ m at h . PR ] 2 3 A ug 2 00 6 Dualities for Multi - State Probabilistic Cellular
The present work treats dualities for probabilistic cellular automata (PCA). A general result of duality is presented and is used to study two general classes of PCA: multi-opinion noisy voter models; and multi-state monotone biased models.
متن کاملar X iv : m at h / 06 11 72 1 v 1 [ m at h . PR ] 2 3 N ov 2 00 6 A LATTICE GAS MODEL FOR THE INCOMPRESSIBLE NAVIER - STOKES EQUATION
We recover the Navier-Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a meso-scopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier-Stokes equation in a fixed time interval. The proof does not use non-gradient methods or the multi-scale analysis due to the long range jumps.
متن کامل