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Lattice gas simulations of dynamical geometry in two dimensions

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.

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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.

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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.
Funding AgencyGrant Number
Cottrell College Science Award Research Corporation for Science AdvancementUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Howard Hughes Medical InstituteUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 02.70.Ns, 05.20.Jj, 05.70.Ln
Record Number:CaltechAUTHORS:20101103-111730020
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20653
Deposited By: Jason Perez
Deposited On:03 Nov 2010 20:19
Last Modified:03 Oct 2019 02:13

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