On Growth and Form: Fractal and Non-Fractal Patterns in Physics

Description

We have shown that simple power-law dynamics is expected for flexible fractal objects. Although the predicted behavior is well established for linear polymers, the situationm is considerably more complex for colloidal aggregates. In the latter case, the observed K-dependence of (r) can be explained either in terms of non-asymptotic hydrodynamics or in terms of weak power-law polydispersity. In the case of powders (alumina, in particular) apparent fractal behavior seen in static scattering is not found in the dynamics. ID. W. Schaefer, J. E. Martin, P. Wiitzius, and D. S. Cannell, Phys. Rev. Lett. 52,2371 (1984). 2 J. E. Martin and D. W. Schaefer, Phys. Rev. Lett. 5:1,2457 (1984). 3 D. W. Schaefer and C. C. Han in Dynamic Light Scattering, R. Pecora ed, Plenum, NY, 1985) p. 181. 4 P. Sen, this book. S J. E. Martin and B. J. Ackerson, Phys. Rev. A :11, 1180 (1985). 6 J. E. Martin, to be published. 7 D. A. Weitz, J. S. Huang, M. Y. Lin and J. Sung, Phys. Rev. Lett. 53,1657 (1984) . 8 J. E. Martin, D. W. Schaefer and A. J. Hurd, to be published; D. W. Schaefer, K. D. Keefer, J. E. Martin, and A. J. Hurd, in Physics of Finely Divided Matter, M. Daoud, Ed., Springer Verlag, NY, 1985. 9 D. W. Schaefer and A. J. Hurd, to be published. lOJ. E. Martin, J. Appl. Cryst. (to be published).;A. “The Course” -- Growth: An Introduction -- Form: An Introduction to Self-Similarity and Fractal Behavior -- Scale-Invariant Diffusive Growth -- DLA in the Real World -- Percolation and Cluster Size Distribution -- Scaling Properties of the Probability Distribution for Growth Sites -- Computer Simulation of Growth and Aggregation Processes -- Rate Equation Approach to Aggregation Phenomena -- Experimental Methods for Studying Fractal Aggregates -- On the Rheology of Random Matter -- Development, Growth, and Form in Living Systems -- B. “The Seminars” -- Aggregation of Colloidal Silica -- Dynamics of Fractals -- Fractal Viscous Fingers: Experimental Results -- Wetting Induced Aggregation -- Light Scattering from Aggregating Systems: Static, Dynamic (QELS) and Number Fluctuations -- Flocculation and Gelation in Cluster Aggregation -- Branched Polymers -- Dynamics of Aggregation Processes -- Fractal Properties of Clusters during Spinodal Decomposition -- Kinetic Gelation -- Dendritic Growth by Monte Carlo -- Flow through Porous Materials -- Crack Propagation and Onset of Failure -- The Theta Point -- Field Theories of Walks and Epidemics -- Transport Exponents in Percolation -- Non-Universal Critical Exponents for Transport in Percolating Systems -- Lévy Walks Versus Lévy Flights -- Growth Perimeters Generated by a Kinetic Walk: Butterflies, Ants and Caterpillars -- Asymptotic Shape of Eden Clusters -- Occupation Probability Scaling in DLA -- Fractal Singularities in a Measure and “How to Measure Singularities on a Fractal” -- List of Participants.