Related papers: Dynamics of Fractal Solids
We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms…
We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
Using a generalization of vector calculus for the case of non-integer dimensional space we consider a Poiseuille flow of an incompressible viscous fractal fluid in the pipe. Fractal fluid is described as a continuum in non-integer…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Analytical models have been developed for fracture propagation over the last several decades and are now considered with renewed interest; the range of their applicability varies for different materials and different loading conditions.…
The scope of the paper is a theoretical analysis of the dynamical system, the model of which was reduced to Weierstrasse function. A fractal structure of the trajectory was proved and the entropy of the system information designated.
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns.…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
We use persistent homology in order to define a family of fractal dimensions, denoted $\mathrm{dim}_{\mathrm{PH}}^i(\mu)$ for each homological dimension $i\ge 0$, assigned to a probability measure $\mu$ on a metric space. The case of…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
We study the dynamics of an intruder moving through a fluidized granular medium in three dimensions ($d=3$). The intruder and grains have both translational and rotational degrees of freedom. The energy-dissipation mechanism is solid…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
The optical model is a fundamental tool to describe scattering processes in nuclear physics. The basic input is an optical model potential, which describes the refraction and absorption processes more or less schematically. Of special…
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…
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics (DPD) computer simulation for the thermal motion of monomers in the…
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the…