Related papers: Wavy spirals and their fractal connection with chi…
The present paper introduces the notion of chiral gravitational elastic waves and explores their connections to equatorial and planetary waves. The analysis of the gravity-induced waveforms in gyroscopic systems composed of gyropendulums…
Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in fractal image compression but the results we obtained can be…
It is well known that the Minkowski dimension of spiral trajectories near a non-degenerate focus in analytic (smooth) systems is in one-to-one correspondence with the cyclicity of the focus in generic unfoldings. We give a complete fractal…
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the…
We study spiral waves in a mathematical model of a nonlinear optical system with a feedback loop. Starting from a delayed scalar diffusion equation in a thin annulus with oblique derivative boundary conditions, we shrink the annulus and…
The main aim in the current survey is to suggest models of the development of structures, such as vortices and spirals, in accretion white dwarf's binaries. Numerical methods and simulations are applied on the bases of hydrodynamic…
In this work, phase singularities embedded in a wavepacket are shown to act as sources of atypical localized oscillations when the packet interacts with a linear system. We refer to these oscillations as \textit{chirpons}, since they arise…
Spiral wave, whose rotation center can be regarded as a point defect, widely exists in various two dimensional excitable systems. In this paper, by making use of \emph{Duan's topological current theory}, we obtain the charge density of…
Spiral galaxies can be classified into the {\it Grand-designs} and {\it Flocculents} based on the nature of their spiral arms. The {\it Grand-designs} exhibit almost continuous and high contrast spiral arms and are believed to be driven by…
The tidally tilted pulsators are a new type of oscillating star in close binary systems that have their pulsation axis in the orbital plane because of the tidal distortion caused by their companion. We describe this group of stars on the…
We explore how the growth rate of spiral disks can be measured via analyses of the scatter in the Tully-Fisher (TF) relation of local and intermediate redshift galaxies. As an initial step, we show it is possible to construct a…
The phase spiral is a perturbation to the vertical phase-space distribution of stars in the Milky Way disk. We study the phase spiral's properties and how they vary with spatial position, in order to constrain its origin and evolution, as…
We introduce the notion of fractal index associated with the universal class $h$ of particles or quasiparticles, termed fractons, which obey specific fractal statistics. A connection between fractons and conformal field…
We present experimental measurements on the spontaneous formation of compact spiral structures in vertically-vibrated granular chains. Under weak vibration, when the chain is quasi two-dimensional and self-avoiding, spiral structures emerge…
We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly…
We present the results of hydrodynamical simulations of nonaxisymmetric gas flow past a gravitating compact object in two dimensions. Calculations were performed with uniform flow as well as with transverse velocity and density gradients.…
This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with…
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…