Projection Operators and Fractal Dispersion

  • J. H. Cushman
  • M. Moroni
  • T. R. Ginn
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 94)



It is common in statistical physics to upscale phenomena via projection operators. Specifically one tries to isolate fast variables and to selectively project them out of the dynamics at higher scales. Here we show how this method may be used to obtain constitutive theories for. dispersive processes in geophysical problems with evolving spatial/temporal heterogeneity. The resultant constitutive model is space-time nonlocal and it reduces to an α-stable (Levy) law with an appropriate choice of the kernel in the integro-differential flux. We examine the role of long range correlations and study conditions under which such processes may be renormalized. Two examples are presented involving nanofilm dispersion and Darcy-scale dispersion.


Porous Medium Projection Operator Stochastic Differential Equation Constitutive Theory Conservative Tracer 
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • J. H. Cushman
    • 1
  • M. Moroni
    • 2
  • T. R. Ginn
    • 3
  1. 1.Center for Applied Math, Math Science BuildingPurdue UniversityW. LafayetteUSA
  2. 2.Department of Hydraulics, Transportation and RoadsUniversity of Rome “La Sapienza”RomeItaly
  3. 3.Department of Civil EngineeringUniv. of CaliforniaDavisUSA

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