Search results for "Mixing time"
showing 8 items of 8 documents
Convergence of Markov Chains
2020
We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of X n converges to π as n→∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces that the chain does not leave, or that are visited by the chain periodically; e.g., only for odd n or only for even n.
Income distribution dynamics: monotone Markov chains make light work
1995
This paper considers some aspects of the dynamics of income distributions by employing a simple Markov chain model of income mobility. The main motivation of the paper is to introduce the techniques of “monotone” Markov chains to this field. The transition matrix of a discrete Markov chain is called monotone if each row stochastically dominates the row above it. It will be shown that by embedding the dynamics of the income distribution in a monotone Markov chain, a number of interesting results may be obtained in a straightforward and intuitive fashion.
The pianigiani-yorke measure for topological markov chains
1997
We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.
QUANTITATIVE CONVERGENCE RATES FOR SUBGEOMETRIC MARKOV CHAINS
2015
We provide explicit expressions for the constants involved in the characterisation of ergodicity of subgeometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The results are fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our results accommodate also some classes of inhomogeneous chains.
Mixing dynamics in uncovered unbaffled stirred tanks
2014
Abstract The present work is aimed at providing experimental information on mixing rates in an unbaffled vessel under free surface vortexing conditions. The planar laser induced fluorescence (PLIF) technique was used for measuring the dispersion dynamics of a passive tracer over a vertical section of the vessel. In agreement with the quite scant literature information available for these systems, results confirm the existence of two well defined, partially segregated, zones that give rise to a double mixing dynamics behavior. A suitable mixing time definition is proposed and applied to a number of experimental runs with different stirrer geometries and agitation speeds. Results confirm that…
Unbaffled, Stirred Bioreactors for Animal Cell Cultivation
2017
One of the main features of animal cell bioreactors is that the cultured cells lack a strong membrane and are therefore more prone to shear damage. It is widely accepted that animal cell damage in aerated bioreactors is mainly related to burst bubbles at the air–liquid interface. A viable alternative to sparged bioreactors, aimed at minimizing cell damage, may be represented by uncovered, unbaffled, stirred tanks, which are able to provide sufficient mass transfer through the deep free surface vortex that takes place under agitation. As a consequence the need for bubble formation and subsequent bursting accompanied by cell damage is conveniently avoided. In this chapter, mass transfer perfo…
MIXING TIME IN UNBAFFLED STIRRED TANKS
2012
Unbaffled stirred tanks, despite their poorer mixing performance with respect to baffled vessels, are gaining a growing industrial interest as they provide significant advantages in selected applications, including a number of biochemical, food and pharmaceutical processes. There still is however a general lack of information on their mixing performance, that needs to be addressed in order to fully exploit their application potential. The present work is aimed at providing experimental information on mixing rates in an unbaffled vessel operated without top-cover (Uncovered Unbaffled Stirred Tank, UUST). The planar laser induced fluorescence (PLIF) technique was adopted for measuring the dis…
Statistics of transitions for Markov chains with periodic forcing
2013
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.