We consider the mixing time of random walks on a graph G, using the eigenvalue gap to measure the mixing time. We attempt to bound the mixing time in terms of the diameter Diam of G. We show that, for the standard random walk, there exists a family of graphs with diameter 3 but mixing time Ω(n), and a family of trees with diameter 3 but mixing time Ω(n). The main result is a scheme for re-weigh...

in this paper, the present state of knowledge about axial mixing in gasliquid reactors is reviewed. a brief outline of the methods for measuring residence time distribution(rtd)of various phases in a multiphase reactor is presented. this is followed by a short description of differential and stage-wise models for characterizing back mixing from rtd measurments. backmixing characteristics of som...

  Objective: Evidence shows that the powder/liquid mixing ratio recommended by the manufacturers is often not respected when mixing the glass ionomer (GI) powder and liquid, yielding a GI cement with disproportionate powder/liquid ratio. Considering the confirmed effect of powder/liquid ratio on the GI properties, and more importantly, its fluoride release potential, this study aimed to assess ...

The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We introduce a new notion of mixing of a random walk on a (undirected) graph, called local mixing. Informally, the local mixing with respect to a given node s, is the mixing of a rando...

A numerical model for simulating Residence Time Distribution (RTD) of turbulent flows in helical static mixers is proposed and developed to improve the understanding of static mixers. The results of this model is presented in terms of different volumetric flow rate to illustrate the complicated flow patterns that drive the mixing process i...