4 research outputs found
Limited Range Fractality of Randomly Adsorbed Rods
Multiple resolution analysis of two dimensional structures composed of
randomly adsorbed penetrable rods, for densities below the percolation
threshold, has been carried out using box-counting functions. It is found that
at relevant resolutions, for box-sizes, , between cutoffs given by the
average rod length and the average inter-rod distance $r_1$, these
systems exhibit apparent fractal behavior. It is shown that unlike the case of
randomly distributed isotropic objects, the upper cutoff $r_1$ is not only a
function of the coverage but also depends on the excluded volume, averaged over
the orientational distribution. Moreover, the apparent fractal dimension also
depends on the orientational distributions of the rods and decreases as it
becomes more anisotropic. For box sizes smaller than the box counting
function is determined by the internal structure of the rods, whether simple or
itself fractal. Two examples are considered - one of regular rods of one
dimensional structure and rods which are trimmed into a Cantor set structure
which are fractals themselves. The models examined are relevant to adsorption
of linear molecules and fibers, liquid crystals, stress induced fractures and
edge imperfections in metal catalysts. We thus obtain a distinction between two
ranges of length scales: where the internal structure of the
adsorbed objects is probed, and where their distribution is
probed, both of which may exhibit fractal behavior. This distinction is
relevant to the large class of systems which exhibit aggregation of a finite
density of fractal-like clusters, which includes surface growth in molecular
beam epitaxy and diffusion-limited-cluster-cluster-aggregation models.Comment: 10 pages, 7 figures. More info available at
http://www.fh.huji.ac.il/~dani/ or
http://www.fiz.huji.ac.il/staff/acc/faculty/biham or
http://chem.ch.huji.ac.il/employee/avnir/iavnir.htm . Accepted for
publication in J. Chem. Phy
Atom Scattering from Disordered Surfaces in the Sudden Approximation: Double Collisions Effects and Quantum Liquids
The Sudden Approximation (SA) for scattering of atoms from surfaces is
generalized to allow for double collision events and scattering from
time-dependent quantum liquid surfaces. The resulting new schemes retain the
simplicity of the original SA, while requiring little extra computational
effort. The results suggest that inert atom (and in particular He) scattering
can be used profitably to study hitherto unexplored forms of complex surface
disorder.Comment: 15 pages, 1 figure. Related papers available at
http://neon.cchem.berkeley.edu/~dan
Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data
The Sudden Approximation is applied to invert structural data on randomly
corrugated surfaces from inert atom scattering intensities. Several expressions
relating experimental observables to surface statistical features are derived.
The results suggest that atom (and in particular He) scattering can be used
profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at
http://neon.cchem.berkeley.edu/~dan
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