gas mixing in a t-shape micro mixer has been simulated using the direct simulation monte carlo (dsmc) method. it is considered that the adequate mixing occurs when the mass composition of the species, co or n2, deviates below 1 % from their equilibrium composition. the mixing coefficient is defined as the ratio of the mixing length to the main channel’s height. as the inlet kn increases, while ...

In the past decade many proofs of tractability have involved showing that some Markov chain ”mixes rapidly”. We will do a fast tour of the highlights of Markov chain mixing, with a view toward answering—or at least addressing—the following questions: What is rapid mixing? How do you prove it, and why would you want to? Does it really have anything to do with computational complexity? And, most ...

A preformed T-microchannel imprinted in polycarbonate was postmodified with a pulsed UV excimer laser (KrF, 248 nm) to create a series of slanted wells at the junction. The presence of the wells leads to a high degree of lateral transport within the channel and rapid mixing of two confluent streams undergoing electroosmotic flow. Several mixer designs were fabricated and investigated. All desig...

We obtain general results on the stability of mixing and rapid mixing (superpolynomial decay of correlations) for hyperbolic flows. Amongst Cr Axiom A flows, r ≥ 2, we show that there is a C2-open, Cr-dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing. This is the first general result on the stability of rapid mixing (or even mixing) for Axiom A flows that holds i...

We prove comparison results for the Swendsen-Wang (SW) dynamics, the heat-bath (HB) dynamics for the Potts model and the single-bond (SB) dynamics for the randomcluster model on arbitrary graphs. In particular, we prove that rapid (i.e. polynomial) mixing of HB implies rapid mixing of SW on graphs with bounded maximum degree and that rapid mixing of SW and rapid mixing of SB are equivalent. Add...

Computing, or at least estimating, the volume of a body is one of the oldest questions in mathematics, studied already in Egypt and continued by Euclid and Archimedes. Here we are mostly concerned with the computational complexity of estimating volumes of convex bodies in R , with n large. The problems and results to be discussed are all rather recent, most of them less than ten years old, and ...