Related papers: The structure factor of fat deterministic Vicsek f…
In this paper, we construct a three-phase model (that is, a system consisting of three homogeneous regions with various scattering length densities), which illustrate the behavior of small-angle scattering (SAS) scattering curves. Here two…
We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In…
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…
We explored the fractal and multifractal characteristics of breast mammogram micrographs to identify quantitative biomarkers associated with breast cancer progression. In addition to conventional fractal and multifractal analyses, we…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis…
We outline a strategy for quantitatively evaluating the conformational characteristics of self-assembled structures using the techniques of contrast variation small angle neutron scattering. By means of basis function expansion, a case…
We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the F\"oppl-von K\'arm\'an…
Scalar curvature constraints can be studied by means of splitting procedures. The success of this strategy depends on the control we can get on its splitting factors. We introduce canonical so-called minimal splitting factors. They have…
We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction,…
The effects of periodic and aperiodic distortions on the structure factor and radial distribution function of single-component lattices are investigated. To this end, different kinds of distortions are applied to the otherwise perfect…
The multifractal structure underlying a self-similar measure stems directly from the weighted self-similar system (or weighted iterated function system) which is used to construct the measure. This follows much in the way that the dimension…
We study theoretically the scattering imprint of a number of branched supramacromolecular architectures, namely, polydisperse stars and dendrimeric, hyperbranched structures. We show that polydispersity and nature of branching highly…
We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a…
Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. For such random fractals we consider mean values of the Lipschitz-Killing curvatures of their…
Brittle fracturing of materials is common in natural and industrial processes over a variety of length scales. Knowledge of individual particle dynamics is vital to obtain deeper insight into the atomistic processes governing crack…
Preliminary results of extensive numerical experiments on a simple model specified by the smooth canonical strongly chaotic 2D-map with global virtual invariant curves (VICs) are presented and discussed. We focus on the statistics of the…
In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…