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Numerically Optimized Markovian Coupling and Mixing in One‐Dimensional Maps
Author(s) -
Jansons Kalvis M.,
Metcalfe Paul D.
Publication year - 2007
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000279
Subject(s) - mixing (physics) , mathematics , markov process , markov chain , coupling (piping) , statistical physics , state space , scale (ratio) , mathematical optimization , physics , quantum mechanics , mechanical engineering , statistics , engineering
Algorithms are introduced that produce optimal Markovian couplings for large finite‐state‐space discrete‐time Markov chains with sparse transition matrices; these algorithms are applied to some toy models motivated by fluid‐dynamical mixing problems at high Peclét number. An alternative definition of the time‐scale of a mixing process is suggested. Finally, these algorithms are applied to the problem of coupling diffusion processes in an acute‐angled triangle, and some of the simplifications that occur in continuum coupling problems are discussed.