Zentralblatt für Geologie und Paläontologie, Teil I 11/12, 1035 (1997)
submitted on
Friday, May 24, 1996
This contribution gives a brief introduction to local porosity theory. It is shown that fractal porosity fluctuations may arise for macroscopic media in a suitable upscaling limit.
Physical Review A 37, 578 (1988)
10.1103/PhysRevA.37.578
submitted on
Monday, June 8, 1987
We present a probabilistic picture for the Einstein relation which holds for arbitrarily connected structures. The diffusivity is related to mean first-passage times, while the conductance is given as a direct-passage probability. The fractal Einstein relation is an immediate consequence of our result. In addition, we derive a star-triangle transformation for Markov chains and calculate the exact values of the fracton (spectral) dimension for treelike structures. We point to the relevance of the probabilistic interpretation for simulation and experiment.
For more information see
Physical Review Letters 60, 1514 (1988)
10.1103/PhysRevLett.60.1514
submitted on
Tuesday, May 26, 1987
We present a theory for a new mode of phase separation discovered recently in thin layers of amorphous Al-Ge alloys. Phase separation and crystallization occurs in colonies developing from Al nuclei. Their growth is controlled by diffusion of atomic Ge inside crystalline Al, and by the nucleation and growth of Ge crystallites on the Al-Ge interface. We find that the growth velocity is constant as a consequence of the interaction between the ramified Al-Ge interface and the smooth boundary of the colony with the amorphous phase. Diffusion occurs only in a narrow strip controlled by a length scale related to the width of the Ge dendrites. Solution of the growth equations leads to a velocity selection mechanism as long as the Ge concentration is above a critical threshold. The basic length scale is argued to be controlled by a competition between nucleation and growth of the Ge crystallites.
For more information see
in: Fractals in Physics
edited by: L. Pietronero and E. Tosatti
Elsevier Publishing Co., Amsterdam, 33 (1986)
submitted on
Thursday, July 11, 1985
We construct deterministic fractal lattices using generators with tetrahedral symmetry. From the corresponding master equation we determine the spectral dimension d and prove that d<2. Furthermore we extend our set of fractals (with d dense in [1,2]) by direct multiplication, thus obtaining fractals whose d are dense for all real numbers larger than or equal to 1 .
For more information see
J.Phys.A: Math. Gen. 17, L783 (1984)
https://doi.org/10.1088/0305-4470/17/14/011
submitted on
Monday, July 9, 1984
We introduce and investigate new classes of Sierpinski-type fractals. We determine their fractal and spectral dimensions using renormalisation procedures and, for particular classes, we give these dimensions in closed form. The spectral dimensions densely fill the interval [1,2], allowing us to choose flexibly models for applications.
For more information see
Journal of Physics A: Mathematical and General 17, L573-L545 (1984)
10.1088/0305-4470/17/10/004
submitted on
Friday, April 13, 1984
We present a family of deterministic fractals which generalise the d-dimensional Sierpinski gaskets and we establish their order of ramification and their fractal and spectral dimensions. Random walks on these fractals are renormalisable and lead to rational, not necessarily polynomial, mappings.
For more information see
