Related papers: Filaments and voids in planar central configuratio…
We consider the finiteness problem for central configurations of the $n-$body problem. We prove that, for $n\geq4$, there exists a (Zariski) closed subset $B$ in the mass space $\mathbb{R}^{n}$, such that if $(m_1,...,m_n) \in…
Scale invariance has received very little attention in physics. Nevertheless, it provides a natural conceptual foundation for a relational understanding of the universe, where absolute size loses meaning and only dimensionless ratios retain…
We consider the space of all configurations of finitely many (potentially nested) circles in the plane. We prove that this space is aspherical, and compute the fundamental group of each of its connected components. It turns out these…
A new class of geometric statistics for analyzing galaxy catalogs is presented. {\it Filament statistics} quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are…
Finitely many hypersurfaces are removed from unordered configuration spaces of $n$ points in $\mathbb{C}$ to obtain a fibration over unordered configuration spaces of $n-1$ complex points. Fundamental groups of these restricted…
In this paper,we study spatial central configurations where N bodies are at the vertices of a regular N-gon $T$ and the other 4 bodies are symmetrically located on the straight line that is perpendicular to the plane that contains $T$ and…
The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific…
We present a new method to identify large scale filaments and apply it to a cosmological simulation. Using positions of haloes above a given mass as node tracers, we look for filaments between them using the positions and masses of all the…
In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The…
For the power-law potential $n$-body problem, we study a special kind of central configurations where all the masses lie on a circle and the center of mass coincides with the center of the circle. It is also called the centered co-circular…
An algorithm to compute the six distances between particles of a planar Four-Body central configuration is presented according to the following schema. An orthocentric tetrahedron is computed as a function of given masses. Each mass is…
A $configuration$ of a linkage $\Gamma$ is a possible positioning of $\Gamma$ in $\mathbb{R}^d$ and the collection of all such forms the configuration space $\mathcal{C}(\Gamma)$ of $\Gamma$. We here introduce the notion of the $symmetric…
In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of…
In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…
The formation, inner properties, and spatial distribution of galaxy groups and clusters are closely related to the background cosmological model. We use numerical simulations of variants of the CDM model with different cosmological…
There is abundant observational evidence for the hierarchical, interconnected nature of filaments in the interstellar medium (ISM) extending from galactic down to sub-parsec scales. New JWST images of NGC 628 in particular, show clusters…
This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and finite covers of those complements, focusing on homological and enumerative…
Hierarchical theories of structure formation predict that clusters of galaxies should be embedded in a web like structure, with filaments emanating from them to large distances. The amount of mass contained within such filaments near a…