Dynamics of Fractal Networks

Random structures often exhibit fractal geometry, defined in terms of the mass scaling exponent, D, the fractal dimension. The vibrational dynamics of fractal networks are expressed in terms of the exponent ̿d, the fracton dimensionality. The eigenstates on a fractal network are spatially localized...

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Published inScience (American Association for the Advancement of Science) Vol. 231; no. 4740; pp. 814 - 819
Main Author Orbach, R.
Format Journal Article
LanguageEnglish
Published United States The American Association for the Advancement of Science 21.02.1986
American Association for the Advancement of Science
Subjects
Amorphous materials
Amorphous substances
Crystallography, Mathematical
Energy
Fractal dimensions
Fractals
Geometry
Glass & glassware industry
Mathematical crystallography
Phonons
Physics
Temperature dependence
Thermal conductivity
Time dependence
Vibrational states
Wave functions
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Summary:Random structures often exhibit fractal geometry, defined in terms of the mass scaling exponent, D, the fractal dimension. The vibrational dynamics of fractal networks are expressed in terms of the exponent ̿d, the fracton dimensionality. The eigenstates on a fractal network are spatially localized for ̿d less than or equal to 2. The implications of fractal geometry are discussed for thermal transport on fractal networks. The electron-fracton interaction is developed, with a brief outline given for the time dependence of the electronic relaxation on fractal networks. It is suggested that amorphous or glassy materials may exhibit fractal properties at short length scales or, equivalently, at high energies. The calculations of physical properties can be used to test the fractal character of the vibrational excitations in these materials.
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ISSN:0036-8075
1095-9203
DOI:10.1126/science.231.4740.814