Elastic Scattering by Deterministic and Random Fractals: Self-Affinity of the Diffraction Spectrum

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the Cantor set and Sierpinski carpet as special cases. Also randomized versions of these fractals are treated. The general result is that the diffraction intensities obey a strict recursion relation, and become self-affine in the limit of large iteration number, with a self-affinity exponent related directly to the fractal dimension of the scattering object. Applications include neutron scattering, x-rays, optical diffraction, magnetic resonance imaging, electron diffraction, and He scattering, which all display the same universal scaling.Comment: 20 pages, 11 figures. Phys. Rev. E, in press. More info available at http://www.fh.huji.ac.il/~dani

Gravitational Field of Fractal Distribution of Particles

In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of the Gauss's law, we consider the simple examples of the fields of homogeneous fractal distribution. The examples of gravitational moments for fractal distribution are considered.Comment: 14 pages, LaTe

Review of experimental data and modeling of the viscosities of fully liquid slags in the Al2O3-CaO-'FeO'-SiO2 system

A general model based on the Urbain formalism has been developed, which enables the viscosities of liquid slags to be predicted for all compositions in the Al2O3-CaO-'FeO'-SiO2 system in equilibrium with metallic iron. Available experimental viscosity data have been analyzed and critically reviewed. The Urbain formalism has been modified to include compositional dependent model parameters. Experimental data in unaries, binaries, ternaries, and the quaternary system have been described by the model over the whole compositional and temperature ranges using one set of model parameters. This viscosity model can now be applied to various industrial slag systems