Many microfluidic applications require the mixing of reagents, but efficient mixing in these laminar (i.e., low Reynolds number) systems is typically difficult. Instead of using external fields, miniature stirrers, complex geometries, and/or relatively long channels, we demonstrate the merits of flow rate time dependency mixing in a simple “--II-” channel confluence. By means of computational f...

Since the seminal work of Sinai one studies chaotic properties of planar billiards tables. Among them is the study of decay of correlations for these tables. There are examples in the literature of tables with exponential and even polynomial decay. However, until now nothing is known about mixing properties for billiard tables with non-compact cusps. There is no consensual definition of mixing ...

We consider the problem of diffusion on temporal networks, where the dynamics of each edge is modelled by an independent renewal process. Despite the apparent simplicity of the model, the trajectories of a random walker exhibit non-trivial properties. Here, we quantify the walker’s tendency to backtrack at each step (return where he/she comes from), as well as the resulting effect on the mixing...

We consider small random perturbations of a large class of nonuniformly hy-perbolic unimodal maps and prove stochastic stability in the strong sense (L 1-convergence of invariant densities) and uniform bounds for the exponential rate of decay of correlations. Our method is based on an analysis of the spectrum of a modiied Perron-Frobenius operator for a tower extension of the Markov chain.

Let Tn denote the set of triangulations of a convex polygon K with n sides We study the random walk on Tn whose transitions are ips of one of the n internal diagonals of the current triangulation the choice of diagonal being random By bounding the conductance of this graph we show that the walk mixes rapidly namely in time O n A direct argument is given for the fact that the mixing rate is at l...

Convective mixing in porous media is triggered by a Rayleigh-Bénard-type hydrodynamic instability as a result of an unstable density stratification of fluids. While convective mixing has been studied extensively, the fundamental behavior of the dissolution flux and its dependence on the system parameters are not yet well understood. Here, we show that the dissolution flux and the rate of fluid ...