Related papers: Phyllotaxis, disk packing and Fibonacci numbers
Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical…
The Galactic disk retains a vast amount of information about how it came to be, and how it evolved over cosmic time. However, we know very little about the secular processes associated with disk evolution. One major uncertainty is the…
The bar structure in disk galaxies models is formed by different families of orbits; however, it is not clear how these families of orbits support the bar throughout its secular evolution. Here, we analyze the orbital structure on three…
We present a comprehensive series of $N$-body as well as $N$-body + SPH simulations to study the secular evolution of the structure of disk galaxies. Our simulations are organized in a hierarchy of increasing complexity, ranging from…
Abstract Self-similar, fractal nature of turbulence is discussed in the context of two dimensional turbulence, by considering the fractal structure of the wave-number domain using spirals. In loose analogy with phyllotaxis in plants, each…
A collection of thin structures buckle, bend, and bump into each-other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will…
We study the growth of galactic disks in live triaxial DM halos. The halos have been assembled through constrained realizations method and evolved from the linear regime using cosmological simulations. The `seed' disks have been inserted at…
It is well established that stellar discs are destabilized by sharp features in their phase space, driving recurrent spiral modes. We explore the extent to which surface-density breaks in disc galaxies - which represent sharp changes in the…
Non-axisymmetric modes like spirals and bars are the main driver of the evolution of disks, in transferring angular momentum, and allowing mass accretion. This evolution proceeds through self-regulation and feedback mechanisms, such as bar…
The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth,…
The original problem of phyllotaxis was focused on the regular arrangements of leaves on mature stems represented by common fractions such as 1/2, 1/3, 2/5, 3/8, 5/13, etc. The phyllotaxis fraction is not fixed for each plant but it may…
From this vast subject, I will pick out and review three specific topics, namely the formation and evolution of bars, the formation of bulges, and the evolution during multiple major mergers. Bars form naturally in galactic discs. Their…
A simple model is presented which explains the occurrence of high order Fibonacci number parastichies in asteracae flowers by two distinct steps. First low order parastichies result from the fact that a new floret, at its appearance is…
Let ${\cal P}$ be the set of palindromes occurring in the Fibonacci sequence. In this note, we establish three structures of $\mathcal{P}$ and and discuss their properties: cylinder structure, chain structure and recursive structure. Using…
Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties…
We use a hybrid Monte Carlo algorithm to simulate the shaking of spheres at different vibrational amplitudes, and find that spontaneous crystallisation occurs in specific dynamical regimes. Several crystallising transitions are typically…
Leaves of vascular plants are arranged regularly around stems, a phenomenon known as phyllotaxis. A constant angle between two successive leaves is called divergence angle. On the one side, the divergence angle $\alpha_0$ of an initial…
Spiral density waves are known to exist in many astrophysical disks, potentially affecting disk structure and evolution. We conduct a numerical study of the effects produced by a density wave, evolving into a shock, on the characteristics…
Over the past 10 years abundant evidence has emerged that many (if not all) stars are born with circumstellar disks. Understanding the evolution of post-accretion disks can provide strong constraints on theories of planet formation and…
A new idea is proposed for the origin of bulges in spiral galaxies. Numerical simulations for the protogalactic collapse suggest strongly that galactic bulges have been assembled from massive clumps formed in the galactic disks in their…