A new scientific approach to subgrid scale modeling is presented for chaotic problems involving a high degree of mixing over rapid time scales. RichtmyerMeshkov unstable flows are typical of such problems. Chemical reaction rates for turbulent mixtures are shown to converge with feasible grid resolution. The essential dependence of fluid mixing observables on transport phenomena is observed.

We have developed an instrument capable of freezing transient intermediates in rapid biochemical reactions for subsequent freeze-fracturing, replication, and viewing by transmission electron microscopy. The machine combines a rapid mixing unit similar to one widely used in chemical kinetics (Johnson, 1986) with a propane jet freezing unit previously used to prepare static samples for freeze-fra...

We consider the problem of uniformly sampling proper 3-colourings of an m × n rectangular region of Z. We show that the single-site “Glauber-dynamics” Markov chain is rapidly mixing. Our result complements an earlier result of Luby, Randall and Sinclair, which demonstrates rapid mixing when there is a fixed boundary (whose colour cannot be changed). c © John Wiley & Sons, Inc.

In this survey paper, we describe and characterize an extension to the classical path coupling method applied to statistical mechanical models, referred to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibi...

In this paper, we present a novel extension to the classical path coupling method to statistical mechanical models which we refer to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase t...

OBJECTIVE Mixing rapid acting insulin analogs with detemir insulin to minimize daily injections has been adopted as a common regimen, especially for some children with type 1 diabetes, despite the manufacturing company's caution against mixing these analogs in the same syringe. The effect of this practice on the pharmacodynamics (PD) of rapid-acting insulin has not been widely studied. This cro...

We consider proper 5-colourings of the kagome lattice. Proper q-colourings correspond to configurations in the zero-temperature q-state anti-ferromagnetic Potts model. Salas and Sokal have given a computer assisted proof of strong spatial mixing on the kagome lattice for q ≥ 6 under any temperature, including zero temperature. It is believed that there is strong spatial mixing for q ≥ 4. Here w...

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that the statistical criterion of posterior concentration need not imply the comput...

The Ising model is often referred to as the most studied model of statistical physics. It describes the behavior of ferromagnetic material at different temperatures. It is an interesting model also for mathematicians, because although the Boltzmann distribution is continuous in the temperature parameter, the behavior of the usual single-spin dynamics to sample from this measure varies extremely...

Random independent sets in graphs arise, for example, in statistical physics, in the hard-core model of a gas. In 1997, Luby and Vigoda described a rapidly mixing Markov chain for independent sets, which we refer to as the Luby–Vigoda chain. A new rapidly mixing Markov chain for independent sets is defined in this paper. Using path coupling, we obtain a polynomial upper bound for the mixing tim...