Regensburg 2016 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 45: Brownian Motion and Transport
DY 45.4: Vortrag
Mittwoch, 9. März 2016, 17:15–17:30, H46
Large deviations in Taylor dispersion — •Marcel Kahlen1, Andreas Engel1, and Christian Van den Broeck2 — 1Institut für Physik, C. v. Ossietzky Universität, 26111 Oldenburg, Germany — 2Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium
Taylor dispersion plays an important role in our daily life. Addressing the dispersion of particles in shear flow, it is important for problems reaching from environmental pollution to the construction of water pipes.
A useful approach to analyze Taylor dispersion is to discretize the flow into N layers with different advection velocities. In this way it has been shown, that for sufficiently large time the distribution of particles is to leading order Gaussian. The theory of large deviations goes beyond this Gaussian approximation by quantifying the probability of exponentially rare realizations of particle distributions. The Gaussian result can be regained by a Taylor expansion of the large deviation function. Since the dispersion of particles is directly related to the sojourn times of the particles in the respective layers, the large deviation properties of the particle separations may be deduced from the large deviation behaviour of the empirical density.
In the talk, we apply the theory of large deviations to particle dispersion in an N-layer model. For N=2 we check our results against the exact analytic solution that exists for this case. Results for N>2 are compared to extensive numerical simulations. For N→∞, we show that our approach is in agreement with the Donsker-Varadhan result for the empirical density.