Klales, Anna and Cianci, Donato and Needell, Zachary and Meyer, David A. and Love, Peter J. (2010) Lattice gas simulations of dynamical geometry in two dimensions. Physical Review E, 82 (4). 046705. ISSN 1539-3755 http://resolver.caltech.edu/CaltechAUTHORS:20101103-111730020
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We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch et al. [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian et al. [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as t^(1/3), in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.
|Additional Information:||© 2010 American Physical Society. Received 11 February 2010; revised 30 June 2010; published 12 October 2010. This work received financial support from Research Corporation for Science Advancement through a Cottrell College Science Award, and from the Sherman Fairchild Foundation and Howard Hughes Medical Institute. P.J.L. thanks Bruce Boghosian, Gianluca Caterina, Suzanne Amador-Kane, and Stephon Alexander for stimulating discussions, and the Department of Mathematics at UCSD and the Institute for Quantum Information at Caltech for hosting visits during which parts of this work were completed.|
|Classification Code:||PACS: 02.70.Ns, 05.20.Jj, 05.70.Ln|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||03 Nov 2010 20:19|
|Last Modified:||26 Dec 2012 12:35|
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