Related papers: Dynamical fractalization of ring systems
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at…
We consider a particle that is subject to a constant force and scatters inelastically on a vibrating periodically corrugated floor. At small friction and small radius of the circular scatterers the dynamics is dominated by resonances…
It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for…
This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
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…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119,…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
This paper investigates quantized thin vortex rings with an internal structure. The quantization scheme of this dynamical system is based on an earlier the approach proposed by the author. Both energy spectrum and circulation spectrum are…
Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…
The analysis of the spatial distribution and kinematics of galaxies in clusters allows one to determine the cluster internal dynamics. In this paper, I review the state of the art of this topic. In particular, I summarize what we have…
The basic ingredients of models for the internal dynamics of globular clusters are reviewed, with an emphasis on the description of equilibrium configurations. The development of progressive complexity in the models is traced, concentrating…
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…
Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits…
The phenomena of radial and axial segregation in a horizontal rotating cylinder containing a mixture of granular particles of two different species have been modeled using discrete particle simulation. Space-time plots and detailed imagery…