# 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 1 September 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…
1,366 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:

### 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, for

### 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 the

### Percolation on infinitely ramified fractals

• Physics, 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 is

### Phonon-fracton crossover on fractal lattices.

• Physics, Medicine
Physical review letters
• 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 dimensionalities

### 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 the

### 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 gasket

### Theory of self-avoiding walks on percolation fractals

• Physics
• 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 the

### 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 increase

### 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 first

## References

SHOWING 1-5 OF 5 REFERENCES

### 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 $d=1.65\ifmmode\pm\else\textpm\fi{}0.04$, in

### Dynamics of the Iron-Containing Core in Crystals of the Iron-Storage Protein, Ferritin, through Mössbauer Spectroscopy

• Materials Science
• 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 a