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It is also possible to investigate such questions using molecular dynamics. This necessitates working in the full position-velocity phase space of the system; the computations are computationally intensive, but progress in this direction is possible. See for instance: Ortoleva, P.; Yip, S. J. Chem. Phys. 1976, 65, 2045.
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Gorecki, J.1
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Such models may also be used to explore fluctuation effects near equilibrium where the detailed balance condition guarantees decay to equilibrium; however, our focus is on systems maintained far from equilibrium by flows of reagents so that detailed balance no longer applies, and complex attracting states may be obtained.
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14
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For a review of reactive lattice-gas models see: Boon, J.-P.; Dab, D.; Kapral, R.; Lawniczak, A. Phys. Rep. 1996, 55, 273.
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Perdang, J., Lejeune, A., Eds.; World Scientific: Singapore
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Chopard, B.; Droz, M.; Cornell, S.; Frachebourg, L. In Cellular Automata for Astrophysics; Perdang, J., Lejeune, A., Eds.; World Scientific: Singapore, 1994.
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18
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85033065534
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-
note
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The restriction to regular lattices is not essential, and the dynamics on fractal lattices may be investigated.
-
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19
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85033046906
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note
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Typically, in simulations the average number of molecules at a node is selected to be less than the coordination number of the lattice, or the number of channels, so that multiple occupancy of a channel rarely occurs.
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23
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Bohr, T.; Grinstein, G.; He, Y.; Jayaprakash, C. Phys. Rev. Lett. 1987, 58, 2155.
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Wu, X.-G.; Kapral, R.; Wu, X.-G. Ann. N.Y. Acad. Sci. 1993, 706, 186;
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Phys. Rev. Lett. 1993, 70, 1940;
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Kapral, R.; Wu, X.-G. In Chemical Waves and Patterns; Kapral, R., Showalter, K., Eds.; Kluwer: Dordrecht, 1995; p 609.
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note
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For the Willamowski-Rössler model the period-2 structure is resolved with N = 300.
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The deterministic Kuramoto-Sivashinsky equation may be reduced in 1 + 1 dimensions to the KPZ equation by projecting onto the long wavelength modes. This procedure renormalizes v and gives rise to a noise term that accounts for the short wavelength structure [Yakhot, V. Phys. Rev. A 1981, 24, 642]. The source of noise in the present case arises from internal fluctuations in a region where there is no transverse instability.
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