# 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} }

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

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## 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…

### Note added in proof.

- MathematicsThe EMBO journal
- 1984

Copeland,T.D., Oroszlan,S., Kalyanaraman,V.S., Sarngadharan,M.G. and Gallo,R.C. (1983b) FEBS Lett., 162, 390-395. Crouch,R.J. and Dirksen,M.L. (1982) in Linn,S. and Roberts,R. (eds.), Nucleases, Cold…

### Excitation Dynamics in Random One-Dimensional Systems

- Mathematics
- 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
…