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3
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4243965830
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M. Bär, M. Hildebrand, M. Eiswirth, M. Falcke, H. Engel, and M. Neufeld, Chaos 4, 499 (1994).
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(1994)
Chaos
, vol.4
, pp. 499
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Bär, M.1
Hildebrand, M.2
Eiswirth, M.3
Falcke, M.4
Engel, H.5
Neufeld, M.6
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11
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36449000398
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M. Bär, N. Gottschalk, M. Eiswirth, and G. Ertl, J. Chem. Phys. 100, 1202 (1994).
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(1994)
J. Chem. Phys.
, vol.100
, pp. 1202
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Bär, M.1
Gottschalk, N.2
Eiswirth, M.3
Ertl, G.4
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12
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85036347513
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A. Pande and R. Pandit, in Structure and Dynamics of Materials in the Mesoscopic Domain, edited by B. D. Kulkarni and Moti Lal (Imperial College Press-The Royal Society, London, 1999)
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A. Pande and R. Pandit, in Structure and Dynamics of Materials in the Mesoscopic Domain, edited by B. D. Kulkarni and Moti Lal (Imperial College Press-The Royal Society, London, 1999).
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13
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85036298073
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This is analogous to using the Fourier components (Formula presented) of the density (Formula presented) as the order parameters for the transition from a liquid to a crystalline solid. Visual observations show that on larger system sizes, there is a density of large spirals. Thus we conjecture that the peak in the structure factor will scale with system size giving a valid order parameter in the thermodynamic limit
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This is analogous to using the Fourier components (Formula presented) of the density (Formula presented) as the order parameters for the transition from a liquid to a crystalline solid. Visual observations show that on larger system sizes, there is a density of large spirals. Thus we conjecture that the peak in the structure factor will scale with system size giving a valid order parameter in the thermodynamic limit.
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14
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85036198737
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For a given system size L, there is a time (Formula presented) after which large spiral patches aggregate. This time diverges with system size since large spiral patches nucleate at random on the grid and have to “find” each other. After this time, for a time (Formula presented), observations obtained at any point in the large-spiral region will see quasiperiodic behavior and those from the pointlike defect region will see irregular behavior; (Formula presented) is the mean time over which the large spiral region drifts across any observation point. This time will diverge with system size. Thus, while averaging data for the inhomogeneous state MP, averaging times should be (Formula presented)
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For a given system size L, there is a time (Formula presented) after which large spiral patches aggregate. This time diverges with system size since large spiral patches nucleate at random on the grid and have to “find” each other. After this time, for a time (Formula presented), observations obtained at any point in the large-spiral region will see quasiperiodic behavior and those from the pointlike defect region will see irregular behavior; (Formula presented) is the mean time over which the large spiral region drifts across any observation point. This time will diverge with system size. Thus, while averaging data for the inhomogeneous state MP, averaging times should be (Formula presented).
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18
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85036285770
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W. H. Press et al. Numerical Recipies in C (Cambridge University, London, 1995), pp. 714–722
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W. H. Press et al., Numerical Recipies in C (Cambridge University, London, 1995), pp. 714–722.
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19
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85036297601
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It is possible that (Formula presented) with PBC is different from (Formula presented) with NBC, i.e., the S-MP and S-MN boundaries are different; however, given our numerical resolution, we cannot distinguish the two. Our value is consistent with that in Ref. 1
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It is possible that (Formula presented) with PBC is different from (Formula presented) with NBC, i.e., the S-MP and S-MN boundaries are different; however, given our numerical resolution, we cannot distinguish the two. Our value is consistent with that in Ref. 1.
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20
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85036337369
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e-printcond-mat/9903262
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V. Hakim and A. Karma, e-print cond-mat/9903262.
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Hakim, V.1
Karma, A.2
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21
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0000058225
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D. T. Kaplan, J. R. Clay, T. Manning, L. Glass, M. R. Guevara, and A. Shrier, Phys. Rev. Lett. 76, 4074 (1996).
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(1996)
Phys. Rev. Lett.
, vol.76
, pp. 4074
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Kaplan, D.T.1
Clay, J.R.2
Manning, T.3
Glass, L.4
Guevara, M.R.5
Shrier, A.6
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24
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85036238878
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many equilibrium two-phase regimes the sizes of such domains grow as a power of time in the wake of a quench; however, slower growth laws, especially in disordered systems, are not unknown
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In many equilibrium two-phase regimes the sizes of such domains grow as a power of time in the wake of a quench; however, slower growth laws, especially in disordered systems, are not unknown.
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27
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85036356468
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It is not quite clear whether PBC’s or NBC’s have been used to determine the stability diagram of Ref. 1. Some quantities (e.g., the spatial autocorrelation function of the defect density) are computed with PBC and others (e.g., the M-T1 boundary) are computed with NBC. Reference 1 also does not make the MP-MN distinction, which we elucidate here
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It is not quite clear whether PBC’s or NBC’s have been used to determine the stability diagram of Ref. 1. Some quantities (e.g., the spatial autocorrelation function of the defect density) are computed with PBC and others (e.g., the M-T1 boundary) are computed with NBC. Reference 1 also does not make the MP-MN distinction, which we elucidate here.
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28
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85036206150
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We fit our data for each initial condition and use the standard deviation of the fitted parameters as the error
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We fit our data for each initial condition and use the standard deviation of the fitted parameters as the error.
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29
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0003493232
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C. Domb, J. L. Lebowitz, Academic Press, New York
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B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1995), Vol. 17.
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(1995)
Phase Transitions and Critical Phenomena
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Schmittmann, B.1
Zia, R.K.P.2
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