About this Journal Submit a Manuscript Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 981501, 4 pages
http://dx.doi.org/10.5402/2012/981501
Research Article

Stochastic Signatures of Phase Space Decomposition

1Depaul University, College of Digital Media and Computing, 243 South Wabash Avenue, Chicago, IL 60604-2301, USA
2Department of Chemistry and Seaver Chemistry Laboratory, Pomona College, Claremont, CA 91711, USA

Received 28 July 2011; Accepted 15 September 2011

Academic Editors: M.-B. Hu and O. Kuksenok

Copyright © 2012 John J. Kozak and Roberto A. Garza-López. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We explore the consequences of metrically decomposing a finite phase space, modeled as a d-dimensional lattice, into disjoint subspaces (lattices). Ergodic flows of a test particle undergoing an unbiased random walk are characterized by implementing the theory of finite Markov processes. Insights drawn from number theory are used to design the sublattices, the roles of lattice symmetry and system dimensionality are separately considered, and new lattice invariance relations are derived to corroborate the numerical accuracy of the calculated results. We find that the reaction efficiency in a finite system is strongly dependent not only on whether the system is compartmentalized, but also on whether the overall reaction space of the microreactor is further partitioned into separable reactors. We find that the reaction efficiency in a finite system is strongly dependent not only on whether the system is compartmentalized, but also on whether the overall reaction space of the microreactor is further partitioned into separable reactors. The sensitivity of kinetic processes in nanoassemblies to the dimensionality of compartmentalized reaction spaces is quantified.