Related papers: Phyllotaxis, disk packing and Fibonacci numbers
Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set $[n]=\{1,2,\dots,n\}$, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define…
This work studies combinatorics and geometry of the Yoccoz puzzle for quadratic polynomials. It is proven that the moduli of the ``principal nest'' of annuli grow at linear rate. As a corollary we obtain complex a priori bounds and local…
The vertical evolution of galactic discs is governed by the sub-structures within them. We examine the diversity of kinematic sub-structure present in the first 12 galaxies observed from the GECKOS survey, a VLT/MUSE large programme…
We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
We analyze the spiral structure that results in a numerical simulation of a galactic disk with stellar and gaseous components evolving in a potential that includes an axisymmetric halo and bulge. We perform a second simulation without the…
We examined the gravitational contraction of isothermal molecular cloud cores with slow rotation by means of two-dimensional numerical simulations. Applying a sink-cell method, we followed the evolution of the cloud cores up to the stages…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
We present our recent results on the properties of the outskirts of disk galaxies. In particular, we focus on spiral galaxies with stellar disk truncations in their radial surface brightness profiles. Using SDSS, UDF and GOODS data we show…
The stellar disc kinematics in a sample of fifteen intermediate- to late-type edge-on spiral galaxies are studied using a dynamical modeling technique. The sample covers a substantial range in maximum rotation velocity and deprojected…
We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic, cylindrical granular material, using high-resolution capacitive monitoring. In these experiments, the particle configurations…
I discuss results from the COSMOS survey, showing that the fraction of disc galaxies that is barred decreases considerably with look-back time from z ~ 0.2 to z ~ 0.8. This decrease is more important for small mass and low luminosity…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…
In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree.…
I follow a bar from its formation, via its evolution, to its destruction and, perhaps, regeneration. I discuss the main features at each stage and particularly the role of the halo. Bars can form even in sub-maximum discs. In fact, such…
We use numerical simulation to investigate and analyze the way that rigid disks and spheres arrange themselves when compressed next to incommensurate substrates. For disks, a movable set is pressed into a jammed state against an ordered…
We experimentally study the crystallization of a monolayer of vibrated discs with a built-in polar asymmetry, a model system of active liquids, and contrast it with that of vibrated isotropic discs. Increasing the packing fraction $\phi$,…
The selection of stacking order in a broad range of close-packed polymorphic materials remains a challenging enigma. Using in situ cryogenic transmission electron microscopy, we uncover the atomistic mechanisms governing the vapour…
Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational as well as translational order. The study of these structures is important…
We investigate permutations in terms of their cycle structure and descent set. To do this, we generalize the classical bijection of Gessel and Reutenauer to deal with permutations that have some ascending and some descending blocks. We then…