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Mixing pp 145-162 | Cite as

Scale-Dependent Fractal Geometry

  • Haris J. Catrakis
  • Paul E. Dimotakis
Part of the NATO ASI Series book series (NSSB, volume 373)

Abstract

A generalization of fractal geometry that allows for scale-dependent behavior is described. The resulting framework, termed “scale-dependent fractal” (SDF) geometry, can be used to quantify and model various phenomena whose geometric complexity may depend on scale. Relations are derived between scale distributions and coverage dimensions in the SDF framework, for one-as well as multi-dimensional sets, and applied to level sets arising in turbulence and mixing.

Keywords

Fractal Dimension Spacing Scale Coverage Statistic Coverage Fraction Poisson Point Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Haris J. Catrakis
    • 1
  • Paul E. Dimotakis
    • 2
  1. 1.Mechanical and Aerospace EngineeringUniversity of CaliforniaIrvineUSA
  2. 2.Graduate Aeronautical LaboratoriesCalifornia Institute of TechnologyPasadenaUSA

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