Diffusive persistence and the "sign-time" distribution

T. J. Newman, Z. Toroczkai

    Research output: Contribution to journalArticle

    53 Citations (Scopus)

    Abstract

    We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of "sign times." With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.
    Original languageEnglish
    Pages (from-to)R2685-R2688
    Number of pages4
    JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
    Volume58
    Issue number3
    DOIs
    Publication statusPublished - 1 Sep 1998

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    Persistence
    Exact Results
    Diffusion equation
    Numerical Study
    Exponent
    exponents
    Arbitrary

    Cite this

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    abstract = "We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of {"}sign times.{"} With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.",
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    Diffusive persistence and the "sign-time" distribution. / Newman, T. J.; Toroczkai, Z.

    In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 58, No. 3 , 01.09.1998, p. R2685-R2688.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Diffusive persistence and the "sign-time" distribution

    AU - Newman, T. J.

    AU - Toroczkai, Z.

    PY - 1998/9/1

    Y1 - 1998/9/1

    N2 - We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of "sign times." With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.

    AB - We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of "sign times." With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.

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    U2 - 10.1103/PhysRevE.58.R2685

    DO - 10.1103/PhysRevE.58.R2685

    M3 - Article

    VL - 58

    SP - R2685-R2688

    JO - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

    JF - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

    SN - 1539-3755

    IS - 3

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