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Projection of Compact Fractal Sets: Application to Diffusion-limited and Cluster-cluster Aggregates : Volume 15, Issue 4 (26/08/2008)

By Maggi, F.

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Book Id: WPLBN0003985600
Format Type: PDF Article :
File Size: Pages 5
Reproduction Date: 2015

Title: Projection of Compact Fractal Sets: Application to Diffusion-limited and Cluster-cluster Aggregates : Volume 15, Issue 4 (26/08/2008)  
Author: Maggi, F.
Volume: Vol. 15, Issue 4
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2008
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Maggi, F. (2008). Projection of Compact Fractal Sets: Application to Diffusion-limited and Cluster-cluster Aggregates : Volume 15, Issue 4 (26/08/2008). Retrieved from http://hawaiilibrary.net/


Description
Description: Berkeley Water Center, Civil and Environmental Engineering, 413 O'Brien Hall, University of California, Berkeley, CA 94720-1710, USA. The need to assess the three-dimensional fractal dimension of fractal aggregates from the fractal dimension of two-dimensional projections is very frequent in geophysics, soil, and atmospheric sciences. However, a generally valid approach to relate the two- and three-dimensional fractal dimensions is missing, thus questioning the accuracy of the method used until now in practical applications. A mathematical approach developed for application to suspended aggregates made of cohesive sediment is investigated and applied here more generally to Diffusion-Limited Aggregates (DLA) and Cluster-Cluster Aggregates (CCA), showing higher accuracy in determining the three-dimensional fractal dimension compared to the method currently used.

Summary
Projection of compact fractal sets: application to diffusion-limited and cluster-cluster aggregates

Excerpt
Coleman P. and Pietronero L.: The fractal structure of the Universe, Phys. Rep. 213, 311–389, 1992.; Friedlander S. K.: Smoke, Dust and Haze, fundamentals of aerosol behavior. Wiler, New York, 1977.; Grassberger H. G. E. and Procaccia I.: Characterization of strange attractors, Phys. Rev. Lett. 50(5), 346–349, 1983.; Hunt B. R. and Kaloshin V. Y.: How projections affect the dimension spectrum of fractal measures, Nonlinearity 10, 1031–1046, 1997.; Kranenburg C.: On the fractal structure of cohesive sediment aggregates, Continental and Shelf Science, 39, 451–460, 1994.; %Maggi F.: Flocculation dynamics of cohesive sediments, %Ph.D. Thesis, Delft Universitiy of Technology, The Netherlands, %2005.; Maggi F. and Winterwerp J. C.: Method for computing the three-dimensional capacity dimension from two-dimensional projections of fractal aggregates, Phys. Rev. E, 69, 011405, doi:10.1103/PhysRevE.69.011405, 2004. %; Maggi F.: Variable fractal dimension: a major control for floc structure and flocculation kinematics of suspended cohesive sediment, J. Geophys. Res., 112, C07012, doi:10.1029/2006JC003951, 2007.; Meakin P.: Fractal aggregates in geophysics, Reviews of Geophysics, 29, 317–354, 1991.; Meakin P.: Fractals, Scaling and Growth far from Equilibrium, Cambridge University Press, Cambridge, England, 1998.; Perrier E., Rieu M., Sposito G., and de Marsily G.: Models of the water retention curve for soils with a fractal pore size distribution, Wat. Res. Res., 32(10), 3025–3031, 2002.; Shaw R. A.: Particle-turbulence interactions in atmospheric clouds, Annu. Rev. Fluid Mech. 35, 183–227, 2003.; Thieberger R. and Spiegel E. A.: Luminosity effects in projected fractals, Bull. of Astron. Soc. India 30, 461, 2000.; Vicsek T.: Fractal growth phenomena, World Scientific, Singapore, 1992.; Winterwerp J. C.: On the dynamics of high-concentrateed mud suspensions, Ph.D. Thesis, Delft University of Technology, 1999. %; %Winterwerp J.C.: On the flocculation and settling velocity of %estuarine mud. Cont. Shelf Res. 22, 1339-1360, 2002.

 

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