Abstract
In this work it is investigated how the proper choice of the underlying grid for computer simulations in complex systems can increase its observed isotropy; thus increasing dependability of the obtained results. The square lattice with both the von Neumann and the Moore neighborhood as well as the hexagonal lattice are being considered. The average speed isotropy is examined with regard to different length scales. The concept of the borrowed time is reintroduced and expanded for the square lattice with the Moore neighborhood. It is shown that such treatment can decrease the anisotropy of the average speed without increasing complexity of the calculations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Alea-Saclay (2005)
Wolfram, S.: Cellular automaton fluids 1: Basic theory. J. Stat. Phys. 45(3/4) (1986)
Schonfisch, B.: Propagation of fronts in cellular automata. Physica D: Nonlinear Phenomena 80(4), 433–450 (1995)
Schonfisch, B.: Anisotropy in cellular automata. BioSystems (41), 29–41 (1997)
Kurrer, C., Schulten, K.: Propagation of chemical waves in discrete excitable media: anisotropic and isotropic wave fronts. In: Holden, M.M., Othmer, A.V., Othmer, H.G. (eds.) Nonlinear Wave Processes in Excitable Media. Plenum Press (1991)
Markus, M.: Dynamics of a cellular automaton with randomly distributed elements. In: Arino, A.D.E., Kimmel, O., Kimmel, M. (eds.) Mathematical Population Dynamics. Marcel Dekker (1991)
Nishiyama, A., Tokihiro, T.: Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk. J. Phys. Soc. Jpn. 80, 054003 (2010)
Frish, U., Hasslacher, B., Pomeau, Y.: Lattice-gas automata for the navier-stokes equation. Physical Review Letters 56(14), 1505–1508 (1986)
Kirchner, A., Klupfel, H., Nishinari, K., Schadschneider, A., Schreckenberg, M.: Discretization effects and the influence of walking speed in cellular automata models for pedestrian dynamics. J. Stat. Mech. (2004)
Klupfel, H.: A Cellular Automaton Model for Crowd Movement and Egress Simulation. Dissertation, University Duisburg-Essen (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Mycek, M. (2013). An Expanded Concept of the Borrowed Time as a Mean of Increasing the Average Speed Isotropy on Regular Grids. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) New Results in Dependability and Computer Systems. Advances in Intelligent Systems and Computing, vol 224. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00945-2_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-00945-2_28
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00944-5
Online ISBN: 978-3-319-00945-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)