Related papers: Sphractal: Estimating the Fractal Dimension of Sur…
We investigate the box dimensions of the horizon of a fractal surface defined by a function $f \in C[0,1]^2 $. In particular we show that a prevalent surface satisfies the `horizon property', namely that the box dimension of the horizon is…
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…
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…
Functional properties of nanomaterials strongly depend on their surface atomic structure, but they often become largely different from their bulk structure, exhibiting surface reconstructions and relaxations. However, most of the surface…
The degree of fractal substructure in molecular clouds can be quantified by comparing them with Fractional Brownian Motion (FBM) surfaces or volumes. These fields are self-similar over all length scales and characterised by a drift exponent…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $\alpha$. We investigate the fractal spatial structure of the visited lattice sites in a cubic…
We present PyXtal, a new package based on the Python programming language, used to generate structures with specific symmetry and chemical compositions for both atomic and molecular systems. This soft ware provides support for various…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
One way to recognise an object is to study how the echo has been shaped during the interaction with the target. Wideband sonar allows the study of the energy distribution for a large range of frequencies. The frequency distribution contains…
We present a newly developed approach for the calculation of interfacial stiffness and contact area evolution between two rough bodies exhibiting self affine surface structures. Using spline assisted discretization to define localised…
Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all deterministic bitwise operations on a finite alphabet. It is…
Fractal TRIDYN (F-TRIDYN) is a modified version of the widely used Monte Carlo, Binary Collision Approximation code TRIDYN that includes an explicit model of surface roughness and additional output modes for coupling to plasma edge and…
This study builds a bridge between two well-studied but distant topics: fractal dimension and Discrete Global Grid System (DGGS). DGGSs are used as covering sets for geospatial vector data to calculate the Minkowski-Bouligand dimension.…
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…
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…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
The surface morphology of metal influences its optical absorptivity. Recent experiments have demonstrated that the femtosecond laser induced surface structures on metals could be dynamically controlled by the fluence of laser and the number…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…
We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p_c of attractive sites. The percolation cluster is characterized by a…