Effects of surface size on minimalistic stochastic models for the catalytic CO oxidation

authored by: M. Pineda, R. Imbihl, L. Schimansky-Geier
Abstract: The impact of surface size on two minimalistic models for the bistable CO oxidation is analytically studied. A simple model for the catalytic CO oxidation on nanoscale surfaces is analyzed by the chemical master equation. The analytical results predict a shift of the bistable region and cusp point in the global bifurcation diagram as a function of surface size. A reaction-diffusion stochastic model consisting of a collection of reactive subdomains locally coupled by CO diffusion is also considered. A local description of fluctuations can be obtained after applying a Weiss-type mean-field approximation. This approximation predicts, for infinitely many subdomains, a break of ergodicity and a bifurcation behavior like in first-order phase transitions as a function of surface size and coupling parameter. Analytical results are compared with Gillespie-type Monte Carlo simulations.
Organisation(s): Institute of Physical Chemistry and Electrochemistry
External Organisation(s): IFISC Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB)
Humboldt-Universität zu Berlin (HU Berlin)
Type: Article
Journal: Physica A: Statistical Mechanics and its Applications
Volume: 389
Pages: 1178-1188
No. of pages: 11
ISSN: 0378-4371
Publication date: 15.03.2010
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistics and Probability, Condensed Matter Physics
Electronic version(s): https://doi.org/10.1016/j.physa.2009.11.024 (Access: Closed)

BibTeX

@article{3eec729959c64e52a23a28ed9d709d81,
title = "Effects of surface size on minimalistic stochastic models for the catalytic CO oxidation",
abstract = "The impact of surface size on two minimalistic models for the bistable CO oxidation is analytically studied. A simple model for the catalytic CO oxidation on nanoscale surfaces is analyzed by the chemical master equation. The analytical results predict a shift of the bistable region and cusp point in the global bifurcation diagram as a function of surface size. A reaction-diffusion stochastic model consisting of a collection of reactive subdomains locally coupled by CO diffusion is also considered. A local description of fluctuations can be obtained after applying a Weiss-type mean-field approximation. This approximation predicts, for infinitely many subdomains, a break of ergodicity and a bifurcation behavior like in first-order phase transitions as a function of surface size and coupling parameter. Analytical results are compared with Gillespie-type Monte Carlo simulations.",
keywords = "CO oxidation, Master equation, Monte Carlo simulations",
author = "M. Pineda and R. Imbihl and L. Schimansky-Geier",
note = "Funding Information: M.P acknowledges the financial support of project FIS2007-60327 from MICINN (Spain) and FEDER (EU). LSG acknowledges support by DFG through Sfb555.",
year = "2010",
month = mar,
day = "15",
doi = "10.1016/j.physa.2009.11.024",
language = "English",
volume = "389",
pages = "1178--1188",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "6",
}