THE MARKOFF AUTOMATON: A NEW ALGORITHM FOR SIMULATING THE TIME-EVOLUTION OF LARGE STOCHASTIC DYNAMIC SYSTEMS

Thomas Fricke () and Dietmar Wendt ()
Additional contact information
Thomas Fricke: Institut für Physik, Humboldt-Universität, Invalidenstr. 110, D-100 99 Berlin, Germany
Dietmar Wendt: Institut für Theoretische Physik, Rheinisch Westfälische Technische Hochschule Aachen, Sommerfeldstraβe, D-52 056 Aachen, Germany

International Journal of Modern Physics C (IJMPC), 1995, vol. 06, issue 02, 277-306

Abstract: We describe a new algorithm for simulating complex Markoff processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or configurations not being related to any spatial geometry. The events within a single cell are managed by an event handler which has been implemented independently of the system studied. The method is exact on the Markoff level including the correct treatment of finite numbers of molecules.To demonstrate its properties, we apply it on a very simple reaction-diffusion-systems (RDS). The chemical equations$A+A\to\emptyset$and$A+B\to\emptyset$in 1 to 4 dimensions serve as models for systems whose dynamics on an intermediate time scale are governed by fluctuations. We compare our results to the analytic approach by the scaling ansatz. The simulations confirm the exponents of theA+Bsystem within statistical errors, including the logarithmic corrections in the dimensiond=2.The method is able to simulate the crossover from the reaction to diffusion limited regime, which is defined be a crossover time depending on the system size.

Date: 1995
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183195000216
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:06:y:1995:i:02:n:s0129183195000216

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183195000216

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().