Density of states on fractals : « fractons »

  title={Density of states on fractals : « fractons »},
  author={Shlomo Alexander and Raymond L. Orbach},
  journal={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… 

Fractal geometry and anomalous diffusion in the backbone of percolation clusters

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

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

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

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.

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

Theory of self-avoiding walks on percolation fractals

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

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

Effective-medium approximation for density of states and the spectral dimension of percolation networks

The author uses the Green function formalism for the solution of the randomised master equation to calculate the density of states and the spectral dimension ds of percolation networks by an

On the relationship between the critical exponents of percolation conductivity and static exponents of percolation

The author argues that the critical exponent t of random conductance networks near the percolation threshold is given by t=(d-1) nu for low dimensionalities and t=1+ beta ' for high dimensionalities,



Fractal Form of Proteins

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

$^{57}\mathrm{Fe}$ $\ensuremath{\gamma}$-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

Excitation Dynamics in Random One-Dimensional Systems

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

Note added in proof.

  • A. Eddy
  • Mathematics
    The 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