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Volumn 61, Issue 6, 2000, Pages 6448-6460

Spatiotemporal chaos and nonequilibrium transitions in a model excitable medium

Author keywords

[No Author keywords available]

Indexed keywords

BINARY MIXTURES; BOUNDARY CONDITIONS; CARBON DIOXIDE; CHAOS THEORY; MATHEMATICAL MODELS; OXIDATION; PHASE DIAGRAMS; PHASE TRANSITIONS; PLATINUM; POINT DEFECTS;

EID: 0034206357     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.6448     Document Type: Article
Times cited : (15)

References (30)
  • 12
    • 85036347513 scopus 로고    scopus 로고
    • 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)
    • 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).
  • 13
    • 85036298073 scopus 로고    scopus 로고
    • 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
    • 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.
  • 14
    • 85036198737 scopus 로고    scopus 로고
    • 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)
    • 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).
  • 18
    • 85036285770 scopus 로고    scopus 로고
    • W. H. Press et al. Numerical Recipies in C (Cambridge University, London, 1995), pp. 714–722
    • W. H. Press et al., Numerical Recipies in C (Cambridge University, London, 1995), pp. 714–722.
  • 19
    • 85036297601 scopus 로고    scopus 로고
    • 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
    • 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.
  • 20
    • 85036337369 scopus 로고    scopus 로고
    • e-printcond-mat/9903262
    • V. Hakim and A. Karma, e-print cond-mat/9903262.
    • Hakim, V.1    Karma, A.2
  • 24
    • 85036238878 scopus 로고    scopus 로고
    • 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
    • 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.
  • 27
    • 85036356468 scopus 로고    scopus 로고
    • 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
    • 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.
  • 28
    • 85036206150 scopus 로고    scopus 로고
    • We fit our data for each initial condition and use the standard deviation of the fitted parameters as the error
    • We fit our data for each initial condition and use the standard deviation of the fitted parameters as the error.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.