We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [ 4 ]) from Boolean domain to general discrete domains. This property characterises distributions with limited correlations implies that corresponding Glauber dynamics is rapidly mixing. As a concrete application, we show for sampling proper q -colourings mixes in polynomial-time family triangle-free graph...

A device for rapid mixing of two solutions is presented. As the main mechanism for mixing is diffusional mass transport, the ̄ow has to be split into several laminae which are narrower than the capillary width. Complete mixing is achieved within a few seconds in a ̄ow-through device with a channel system that is 600mm wide at its narrowest spot.

We show that superpolynomial decay of correlations (rapid mixing) is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which Young proved exponential decay of correlations. The proof combines techniques of Dolgopyat and operator renewal theory. It follows from our results that planar periodic Lor...

We prove that the spectral gap of the Swendsen-Wang dynamics for the random-cluster model on arbitrary graphs with m edges is bounded above by 16m logm times the spectral gap of the single-bond (or heat-bath) dynamics. This and the corresponding lower bound (from [U12]) imply that rapid mixing of these two dynamics is equivalent. Using the known lower bound on the spectral gap of the Swendsen-W...

Abstract: Effective and rapid mixing is essential for various chemical and biological assays. The present work reports a simple and low-cost micromixer based on magnetofluidic actuation. The device takes advantage of magnetoconvective secondary flow, a bulk flow induced by an external magnetic field, for mixing. A paramagnetic stream of diluted ferrofluid and a non-magnetic stream are introduce...

In centrifugal microfluidics, dead volumes in valves downstream of mixing chambers can hardly be avoided. These dead volumes are excluded from mixing processes and hence cause a concentration gradient. Here we present a new bubble mixing concept which avoids such dead volumes. The mixing concept employs heating to create a temperature change rate (TCR) induced overpressure in the air volume dow...

Rapid freeze-quench (RFQ) trapping of short-lived reaction intermediates for spectroscopic study plays an important role in the characterization of biological reactions. Recently there has been considerable effort to achieve submillisecond reaction deadtimes. We present here a new, robust, high-velocity microfluidic mixer that enables such rapid freeze-quenching. It is a based on the mixing met...

This paper reviews work on a microfluidic system that relies on chaotic advection to rapidly mix multiple reagents isolated in droplets (plugs). Using a combination of turns and straight sections, winding microfluidic channels create unsteady fluid flows that rapidly mix the multiple reagents contained within plugs. The scaling of mixing for a range of channel widths, flow velocities and diffus...