Anomalous Time Scaling of the Mean Square Distance in On-Off Diffusion : General Physics

概要

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The mean square distance σ^2(t) of the diffusion induced by on-off intermittency is derived based on the continuous-time random walk theory. It obeys a scaling law σ^(t) = 2Dtφ(t/τ) with diffusion constant D and characteristic time τ, which is confirmed by the use of numerical iterations of a specific periodic map. The scaling function φ and the power spectrum of the on-off intermittency variable I(ω) are analytically obtained from the distribution function of the laminar duration. Normal diffusion (φ(z) 〜 1) and slow diffusion (φ(z) ∝ 1/√z) are observed, respectively, for t ≫ τ and t ≪ τ. The former and latter correspond to the flat part (I(ω) 〜const) and the power law (I(ω) ∝ 1/√ω), respectively, for the power spectrum.
社団法人日本物理学会の論文
2000-09-15