# Density of states on fractals : « fractons »

@article{Alexander1982DensityOS,
title={Density of states on fractals : « fractons »},
author={Shlomo Alexander and Raymond L. Orbach},
journal={Journal De Physique Lettres},
year={1982},
volume={43},
pages={625-631}
}
• Published 1982
• Physics
• Journal De Physique Lettres
The density of states on a fractal is calculated taking into account the scaling properties of both the volume and the connectivity. We use a Green's function method developed elsewhere which utilizes a relationship to the diffusion problem. It is found that proper mode counting requires a reciprocal space with new intrinsic fracton dimensionality d = 2 d/(2 + δ). Here, d is the effective dimensionality, and δ the exponent giving the dependence of the diffusion constant on distance. For example… Expand
1,335 Citations
Fractal geometry and anomalous diffusion in the backbone of percolation clusters
• Physics
• 1983
The backbone of the infinite percolation cluster is shown by Monte Carlo studies to be a fractal object, on short length scales. Its measured fractal dimensionality dB, at two dimensions, is found:Expand
Novel dimension-independent behaviour for diffusive annihilation on percolation fractals
• Physics
• 1984
The authors report the first studies of diffusive annihilation on fractal structures. They find super-universal (d-independent) behaviour for the time decay of the particle density; specifically, forExpand
The spectral dimension of aggregates of tunable fractal dimension
• Physics
• 1995
The dynamic properties of fractal aggregates with tunable fractal dimension are studied. The fractal dimensions are investigated in the range 1.0<or=D<or=2.5. The interactions are represented by theExpand
Percolation on infinitely ramified fractals
• Mathematics
• 1984
We present a family of exact fractals with a wide range of fractal and fracton dimensionalities. This includes the case of the fracton dimensionality of 2, which is critical for diffusion. This isExpand
Phonon-fracton crossover on fractal lattices.
• Physics
• 1985
Recently there has developed a growing interest in the dynamical properties of structures which have a fractal geometryl. Alexander and Orbach2 were the first to point out that three dimensionalitiesExpand
Percolation, fractals, and anomalous diffusion
Both the infinite cluster and its backbone are self-similar at the percolation threshold,pc. This self-similarity also holds at concentrationsp nearpc, for length scalesL which are smaller than theExpand
Metric properties of fractal lattices
• Physics
• 1984
The authors study the connectivity dimension d of fractal lattices viewed as networks (graphs) of sites and (constant length) bond. Two examples are investigated in detail: the 2D Sierpinski gasketExpand
Theory of self-avoiding walks on percolation fractals
• Mathematics
• 1990
A phenomenological approach which takes into account the basic geometry and topology of percolation fractal structures and of self-avoiding walks (SAW) is used to derive a new expression for theExpand
Connectivity and the fracton dimension of percolation clusters
• Physics
• 1990
The vibrational density of states of percolation clusters at threshold has been calculated for scalar models in two space dimensions. The effective fracton dimension is found to increaseExpand
Flicker (1/f) Noise in Percolation Networks
Statistical self-similarity is emerging as an important concept underlying the behavior of disordered systems. In percolation clusters, for example, the fractal dimension has been identified firstExpand

#### References

SHOWING 1-6 OF 6 REFERENCES
Scaling theory of percolation clusters
Abstract For beginners : This review tries to explain percolation through the cluster properties; it can also be used as an introduction to critical phenomena at other phase transitions for readersExpand
Fractal Form of Proteins
• Physics
• 1980
Electron spin relaxation measurements on low-spin ${\mathrm{Fe}}^{3+}$ in several proteins show that they occupy a space of fractal dimensionality $d=1.65\ifmmode\pm\else\textpm\fi{}0.04$, inExpand
Dynamics of the Iron-Containing Core in Crystals of the Iron-Storage Protein, Ferritin, through Mössbauer Spectroscopy
• Physics
• 1981
$^{57}\mathrm{Fe}$ $\ensuremath{\gamma}$-ray resonance-absorption spectra in crystals of the iron-storage protein, ferritin, display above 265\ifmmode^\circ\else\textdegree\fi{}K, in addition to aExpand
Excitation Dynamics in Random One-Dimensional Systems
• Physics
• 1981
In a number of recent publications, [1] – [5], we have discussed the asymptotic form of the dynamics of a general type of random one-dimensional chains. The equations we discuss are of the form Expand