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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-LN 2002-11
August 2002

Lectures on Multiscale and Multiplicative Processes in Fluid Flows


Ed Waymire et al


These lecture notes were prepared for the Instructional and Research Workshop on Multiplicative Processes and Fluid Flows at MaPhySto, Aarhus University, 23-28 August 2001. Much of this is based upon collaborations within the Focussed Research Group on Navier-Stokes equations at Oregon State University/Indiana University on the one hand and the turbulence research group around Max-Planck Institute for Physics of Complex Systems, Dresden, on the other. In particular, the treatment of multiplicative Fourier cascade solutions to diffusion, fractional diffusion, reaction-diffusion, Burgers, and Navier-Stokes are largely un-published results due to the OSU/Indiana Focussed Research Group. Also included are results of long time collaborations with Vijay Gupta at University of Colorado on problems concerning hydrologic flows in ungauged river basins.

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This paper has now been published in Trans. Amer. Math. Soc. (2003) and in: Probability, Statistics and their Applications, Papers in honor of Rabi Bhattacharya, eds K. Athreya, M. Majumdar, M. Puri, E. Waymire, IMS Lecture Notes-Monograph Series, 65-80 (2002)