Related papers: Fractal Dimension of the Cantor Moire Structures
Context: During the first stages of dust coagulation in protoplanetary disks, the dust aggregates are expected to have a high degree of porosity. Most models of dust growth, however, do not take this into account. The reason for this is the…
The structure of the proton exhibits Fractal behavior at low \textit{x}, where \textit{x} is the fraction of the proton's momentum carried by the interacting partons. This Fractal behavior is characterized by self-similar properties at…
We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of…
We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the "dust"). In two dimensions, we…
The theory of complex dimensions of fractal strings developed by Lapidus and van Frankenhuijsen has proven to be a powerful tool for the study of Minkowski measurability of fractal subsets of the real line. In a very general setting, the…
Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid.…
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…
In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos {\it et al.} ({\it Proc. Natl. Acad. Sci. U.S.A.}, 2007, {\bf 104}: 7746). In this fractal network model, there is a…
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized correlation dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…
A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
During hydraulic fracturing, the injection of a pressurized fluid in a brittle elastic medium leads to the formation and growth of fluid-filled fractures. A disc-like or penny-shaped fracture grows radially from a point source during the…
The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the…
In this paper, we study the effective dimension of points in infinite fractal trees generated recursively by a finite tree over some alphabet. Using unequal costs coding, we associate a length function with each such fractal tree and show…
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…