Related papers: A procedure to Estimate the Fractal Dimension of W…
We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in…
We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to…
We present a comprehensive structural characterization of two different highly pure nuclear graphites that compasses all relevant length scales from nanometers to sub-mm. This has been achieved by combining several experiments and neutron…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude $\gamma = 10^{-5} \div 10^{-1}$. The accuracy of calculated numerical values of…
Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…
This paper serves as a complementary material to a poster presented at the XXXVI Dynamics Days Europe in Corfu, Greece, on June 6th-10th in 2016. In this study, fractal dimension ($D$) of two types of self-affine signals were estimated with…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation…
Measurements of the time of arrival of shock waves from explosions can serve as powerful markers of the evolution of the shock front for determining crucial parameters driving the blast. Using standard theoretical tools and a simple ansatz…
This paper modifies a box-counting method of estimating a fractal dimension of a graph, and applies it to estimate the roughness of a sample function of a stochastic process such as a Levy process or a Gaussian process with stationary…
An algorithm for computing eigenvalues and eigenfunctions of the angular spheroidal wave equation, based on a known but scarcely used method, is developed. By requiring the regularity of the wave function, represented by its series…
This report focuses on the dependencies for the center and radius of the confidence interval that arise when estimating the mass fractal dimensions of anisotropic sampling clusters in the site percolation model.
The problem of finding the convex hull of an IFS fractal is relevant in both theoretical and computational settings. Various methods exist that approximate it, but our aim is its exact determination. The finiteness of extremal points is…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
A new numerical algorithm for calculating isothermal wind accretion flows has been developed and is applied here to the analysis of the hydrodynamics of two-dimensional plane symmetric accretion flows in wind-fed sources. Polar coordinates…
In fractal geometry, the main objects of study have been geometric objects with a global dimension that need not be integer valued. More recently, locally fractal objects, ones in which the dimension is a local property rather than a global…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…