Related papers: Phyllotaxis, disk packing and Fibonacci numbers
We show that every irreducible integral Apollonian packing can be set in the Euclidean space so that all of its tangency spinors and all reduced coordinates and co-curvatures are integral. As a byproduct, we prove that in any integral…
The text of lectures to the 2011 Tenerife Winter School. The School's theme was "Secular Evolution of Galaxies" and my task was to present the underlying stellar-dynamical theory. Other lecturers were speaking on the role of bars and…
In many growth processes particles are highly mobile in an active layer at the surface, but are relatively immobile once incorporated in the bulk. We study models in which atoms are allowed to interact, equilibrate, and order on the…
Based on VLT/FORS spectroscopy and HST/ACS imaging, we have constructed a sample of ~200 field spiral galaxies that cover redshifts up to z~1. Such a large data set allows to study the evolution of fundamental galaxy parameters like…
Phylogenetic methods, traditionally used in biology to trace the evolutionary relationships among species, are emerging as a powerful framework to reconstruct evolutionary processes in galaxies from chemical information. We apply galactic…
We study particle dynamics in local two-dimensional simulations of self-gravitating accretion discs with a simple cooling law. It is well known that the structure which arises in the gaseous component of the disc due to a gravitational…
We consider transport exponents associated with the dynamics of a wavepacket in a discrete one-dimensional quantum system and develop a general method for proving upper bounds for these exponents in terms of the norms of transfer matrices…
Recent observations have shown that star-forming galaxies like our own Milky Way evolve kinematically into ordered thin disks over the last ~8 billion years since z=1.2, undergoing a process of "disk settling." For the first time, we study…
The evolution of galaxies is driven strongly by dynamical processes including internal instabilities, tidal interactions and mergers. The cluster environment is a useful laboratory for studying these effects. I present recent results on…
Detection of bending waves is a highly challenging task even in nearby disc galaxies due to their sub-kpc bending amplitudes. However, simulations show that the harmonic bending of a Milky Way like disc galaxy is associated with a harmonic…
A spiral in $\mathbb{R}^{d+1}$ is defined as a set of the form $\left\{\sqrt[d+1]{n}\cdot\boldsymbol{u}_n\right\}_{n\ge 1},$ where $\left(\boldsymbol{u}_n\right)_{n\ge 1}$ is a spherical sequence. Such point sets have been extensively…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
We performed a series of 3D N-body simulations where the initial conditions were chosen to get two sets of models; unbarred and barred ones. In this work, we analyze the growth of spirals and bar structures using 1D, and 2D Fourier…
We present a simple resonant Hamiltonian model for the vertical response of a stellar disk to the growth of a bar perturbation. As a bar perturbation grows stars become trapped in vertical Inner Lindblad resonances and are lifted into…
Newly formed stars are often observed to possess circumstellar disks, from which mass continues to be accreted onto the star and fed into outflowing jets, and which eventually may evolve into dusty debris disks and planetary systems. Recent…
The depth function of three numbers representing curvatures of three mutually tangent circles is introduced. Its 2D plot leads to a partition of the moduli space of the triples of mutually tangent circles/disks that is unexpectedly a…
The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second…
Natural numbers divisible by the same prime factor lie on defined spiral graphs which are running through the Square Root Spiral (also named as the Spiral of Theodorus or Wurzel Spirale or Einstein Spiral). Prime Numbers also clearly…
We present a novel interpretation of the previously puzzling different behaviours of stellar populations of the Milky Way's bulge. We first show, by means of pure N-body simulations, that initially co-spatial stellar populations with…
A model of a galactic disk is presented which extends the homogeneous one zone models by incorporating propagation of material and energy in the disk. For reasonable values of the parameters the homogeneous steady state is unstable to the…