Related papers: Optical Diffraction from Fractals with a Structura…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
We describe a diffraction microscopy technique based on refractive optics to study structural variations in crystals. The X-ray beam diffracted by a crystal was magnified by beryllium parabolic refractive lenses on a 2D X-ray camera. The…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
This brief review of hard diffraction is focussed on the theory of the diffractive structure function F_2^D. Some aspects of diffractive vector meson production and of diffractive processes in hadron-hadron collisions are also discussed.
Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished…
Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale $\ell$, where the fragments are subsequently allowed to settle under…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
Colloidal systems offer unique opportunities for the study of phase formation and structure since their characteristic length scales are accessible to visible light. As a model system the two dimensional assembly of colloidal magnetic and…
This work proposes the development and study of a novel technique for the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal…
A theoretical approach for the interpretation of reflectance spectra of opal photonic crystals with fcc structure and (111) surface orientation is presented. It is based on the calculation of photonic bands and density of states…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
In the theory of optical gap solitons, slowly-moving finite-amplitude Lorentzian solutions are found to mediate the transition from bright to coexistent dark-antidark solitary wave pairs when the laser frequency is detuned out of the proper…
We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hillard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate…
We propose a new, efficient multi-scale method to decompose a map (or signal in general) into components maps that contain structures of different sizes. In the widely-used wave transform, artifacts containing negative values arise around…
The epitaxial growth of complex oxide thin films provide three avenues to generate unique properties: the ability to influence the 3-dimensional structure of the film, the presence of a surface, and the generation of an interface. In all…
A simple model of irreversible aggregation under differential sedimentation of particles in a fluid is presented. The structure of the aggregates produced by this process is found to feed back on the dynamics in such a way as to stabilise…