Generalized Fibonacci Description of Fractal aggregates

ORAL

Abstract

We present a theory for calculating the fractal dimension of Diffusion Limited Cluster Aggregates (DLCA) based on cluster shape preservation. The shape is described by a d-dimensional Golden Mean, which is the ratio of consecutive d-dimensional Fibonacci numbers. For d =2 the canonical Fibonacci series is found with the Golden Mean value known since antiquity, phi = 1.618{\ldots} to yield a fractal dimension of 1.44, in agreement with simulations and experiment. Generalizations to other dimensions are equally successful. Recent computer simulations also yield accurate values for the fractal aggregate prefactor, thus completing the theory.

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Authors

  • Chris Sorensen

    Kansas State University, Kansas State Univ.

  • John Poate

    Brigham Young University, Los Alamos National Laboratory, Department of Physics and Astronomy, University of Utah, USA, MV Systems, Inc., USA, Helmholtz-Zentrum Berlin fuer Materialien und Energie, Abteilung Silizium-Photovoltaik, Germany, Colorado School of Mines, Department of Physics, USA, Georgia Institute of Technology, Arizona State University, Physics Department of Babolsar University, Iran, Physics Department, New Mexico State University, Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ, 85287-1604, USA, Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701, USA, Department of Physics, Arizona State University, Tempe, AZ, 85287-1504, USA, Colorado State University, University of Wisconsin, NSF ERC for Extreme Ultraviolet Science and Technology, Colorado State University, BYU-Provo, Michigan Technical University and Pierre Auger Collaboration, University of Colorado, Colorado School of Mines, Department of Physics, Colorado State University, Department of Physics, Cornell University, NASA, University of Massachusetts at Amherst, University of Massachusetss at Amherst, APS President, Harvard University, Society of Physics Students, Duke University, Computer Science, Brigham Young University, Chemistry \& Biochemistry, Brigham Young University, University of Arizona, University of Utah, Kansas State Univ., Bethel University, University of New Mexico, Stanford University, JILA, University of Colorado at Boulder, NIST, JILA, University of Colorado at Boulder, National Renewable Energy Laboratory, University of Denver, University of Colorado, Boulder, NREL, Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ, 85287- 1604, USA, DU, ERI, Eleanor Roosevelt Institute (ERI), Cerro Tololo Interamerican Observatory, Utah State University, Center for Atmospheric and Space Sciences, Sciprint.org, University of Colorado at Boulder, JILA and University of Colorado, Kirchhoff Institute for Physics, University of Heidelberg, Utah Valley University, University of New South Wales, San Francisco State University, Weber State University, Cambridge University, Department of Physics and Astronomy, University of Utah, Kansas State University, Columbia University, NY, University of Colorado/JILA, Vice-President for Research and Technology Transfer, Colorado School of Mines

  • John Poate

    Brigham Young University, Los Alamos National Laboratory, Department of Physics and Astronomy, University of Utah, USA, MV Systems, Inc., USA, Helmholtz-Zentrum Berlin fuer Materialien und Energie, Abteilung Silizium-Photovoltaik, Germany, Colorado School of Mines, Department of Physics, USA, Georgia Institute of Technology, Arizona State University, Physics Department of Babolsar University, Iran, Physics Department, New Mexico State University, Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ, 85287-1604, USA, Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701, USA, Department of Physics, Arizona State University, Tempe, AZ, 85287-1504, USA, Colorado State University, University of Wisconsin, NSF ERC for Extreme Ultraviolet Science and Technology, Colorado State University, BYU-Provo, Michigan Technical University and Pierre Auger Collaboration, University of Colorado, Colorado School of Mines, Department of Physics, Colorado State University, Department of Physics, Cornell University, NASA, University of Massachusetts at Amherst, University of Massachusetss at Amherst, APS President, Harvard University, Society of Physics Students, Duke University, Computer Science, Brigham Young University, Chemistry \& Biochemistry, Brigham Young University, University of Arizona, University of Utah, Kansas State Univ., Bethel University, University of New Mexico, Stanford University, JILA, University of Colorado at Boulder, NIST, JILA, University of Colorado at Boulder, National Renewable Energy Laboratory, University of Denver, University of Colorado, Boulder, NREL, Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ, 85287- 1604, USA, DU, ERI, Eleanor Roosevelt Institute (ERI), Cerro Tololo Interamerican Observatory, Utah State University, Center for Atmospheric and Space Sciences, Sciprint.org, University of Colorado at Boulder, JILA and University of Colorado, Kirchhoff Institute for Physics, University of Heidelberg, Utah Valley University, University of New South Wales, San Francisco State University, Weber State University, Cambridge University, Department of Physics and Astronomy, University of Utah, Kansas State University, Columbia University, NY, University of Colorado/JILA, Vice-President for Research and Technology Transfer, Colorado School of Mines