Continuous manufacturing is an important element of future solutions enabling for both high product quality and streamlined development process. The increasing possibilities with computer simulations allow innovating novel mixing principles applicable continuous manufacturing. However, these innovative ideas based on need experimental validation. use rapid prototyping additive opens a possibili...

We consider Glauber dynamics on finite spin systems. The mixing time of Glauber dynamics can be bounded in terms of the influences of sites on each other. We consider three parameters bounding these influences — α, the total influence on a site, as studied by Dobrushin; α′, the total influence of a site, as studied by Dobrushin and Shlosman; and α′′, the total influence of a site in any given c...

We prove that the spectral gap of the Swendsen-Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single-spin dynamics. This implies rapid mixing for the two-dimensional Potts model at all temperatures above the critical one, as well as rapid mixing at the critical temperature for the Ising model. After this we int...

In this paper, we study a biased version of the nearest-neighbor transposition Markov chain on the set of permutations where neighboring elements i and j are placed in order (i, j) with probability pi,j . Our goal is to identify the class of parameter sets P = {pi,j} for which this Markov chain is rapidly mixing. Specifically, we consider the open conjecture of Jim Fill that all monotone, posit...

The material covered in this volume is the text of a series of papers presented at a colloquium on rapid mixing and sampling techniques held in 1964. This reviewer cannot comment on the value of this book for the expert but it is quite certain that it is of limited value to the biochemist not highly trained in the field of instrumentation. Little effort has been made by the editors to make this...

Graph dynamics arise naturally in many contexts. For instance in peer-to-peer networks, a participating peer may replace an existing connection with one neighbour by a new connection with a neighbour’s neighbour. Several such local rewiring rules have been proposed to ensure that peer-to-peer networks achieve good connectivity properties (e.g. high expansion) in equilibrium. However it has rema...