Related papers: The scattering from generalized Cantor fractals
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
Small angle neutron and x-ray scattering methods are used to investigate the structure of dilute suspensions of two different ferrofluid systems dispersed in soft polyacrylamide hydrogels. It is found that the particles in the fluid are…
The fractal distribution of charged particles is considered. An example of this distribution is the charged particles that are distributed over fractal. The fractional integrals are used to describe fractal distribution. These integrals are…
We investigate the scattering phenomena in two dimensions produced by a general finite-range nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…
Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal…
Quantitative analysis of the structure of star clusters is crucial for understanding their formation and evolution. In this article, we explore the application of fractal dimension analysis to study the evolution of star clusters, also…
While the numerical methods which utilizes partitions of equal-size, including the box-counting method, remain the most popular choice for computing the generalized dimension of multifractal sets, two mass- oriented methods are investigated…
The fragmentation of a two-dimensional circular disc by lateral impact is investigated using a cell model of brittle solid. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic…
A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…
For the paradigmatic three-disk scattering system, we confirm a recent conjecture for open chaotic systems, which claims that resonance states are composed of two factors. In particular, we demonstrate that one factor is given by universal…
For each $k\ge 3$, we determine the dimensional threshold for planar fractal percolation to contain $k$ collinear points. In the critical case of dimension $1$, the largest linear slice of fractal percolation is a Cantor set of zero…
The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be…
We study various aspects of the scattering of generalized compact oscillons in the signum-Gordon model in (1+1) dimensions. Using covariance of the model we construct traveling oscillons and study their interactions and the dependence of…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
Using Monte Carlo simulations we study the distributions of the 3-block mass $N_3$ in 4d, 5d, and 6d percolation systems. Because the probability of creating large 3-blocks in these dimensions is very small, we use a ``go with the winners''…
Propagation of waves through Cantor-set media is investigated by renormalization-group analysis. For specific values of wave numbers, transmission coefficients are shown to be governed by the logistic map, and in the chaotic region, they…
A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…