ISSN:
1572-9613
Keywords:
Kolmogorov system
;
Markov chain
;
rate laws
;
correlation function decay
;
relaxation process
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0⩽c⩽1. The resulting dynamical system is Kolmogorov for anyc≠0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2−n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01010428
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