Differential Fractal Dimension of Random Walk and Its Applications to Physical Systems

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概要

• 論文の詳細を見る

• In order to characterize the complexity of the patlt of any randomly walkingtest particle, we introduce the new conception, the differential fractal dimension(in short d.f.d.). This conception seems to have a special importance for theanalysis of turbulence, because it clearly represents the complexity of the pathobserved by a scale r (r is any given length), while the scales of the observationare particularly important for the theory of turbulence. It is shown that, as faras the diffusion and the kinetic energy are concerned, we can treat inclusivelyboth microscopic (or thermal) motions and macroscopic (or turbulent) motionsby means of the d.f.d. As an example, we obtain an analytical expression of thed.f.d. for an one-dimensional random walk with finite mean-free-path.

• 社団法人日本物理学会の論文
• 1982-09-15

著者

• Takayasu Hideki

  Department Of Earth Sciences Kobe University

関連論文

• Steady Distributions in Aggregation Process of Sticky Particles
• Stable Distribution and Levy Process in Fractal Turbulence
• Stable Distribution and Le^'vy Prosecc in Fractal Turbulence : Condensed Matter and Statistical Physics
• Differential Fractal Dimension of Random Walk and Its Applications to Physical Systems
• f^Power Spectrum and Stable Distribution
• Fractal Clusters and Stable Distribution
• Statistical Properties of a 3-Wave System
• A Deterministic Model of Fracture

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