Related papers: Filaments and voids in planar central configuratio…
Central configurations and relative equilibria are an important facet of the study of the $N$-body problem, but become very difficult to rigorously analyze for $N>3$. In this paper we focus on a particular but interesting class of…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…
The interstellar medium is characterised by an intricate filamentary network which exhibits complex structures. These show a variety of different shapes (e.g. junctions, rings, etc.) deviating strongly from the usually assumed cylindrical…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
We propose a simple geometrical mechanism for the flattening of galactic rotation curves, the local compression of field lines around their planes induced either by the presence of thin string-like objects at the centers of galaxies or by…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…
We offer an exact analytical equation for the void central region. We show that the central density is solely determined by the amplitude of the initial perturbation. Our results suggest that N-body simulations somewhat overestimate the…
We carry out a population study of magnetized radio filaments in the Galactic center using MeerKAT data by focusing on the spacing between the filaments that are grouped. The morphology of a sample of 43 groupings containing 174 magnetized…
We introduce a new self-consistent structure finding algorithm that parses large scale cosmological structure into clusters, filaments and voids. This structure finding algorithm probes the cosmological structure at multiple scales and…
A new class of geometric statistics for analyzing galaxy catalogs is presented. Filament statistics quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based…
Random planar graphs appear in a variety of context and it is important for many different applications to be able to characterize their structure. Local quantities fail to give interesting information and it seems that path-related…
We show that there exist an upper bound and a lower bound for the number of non-degenerate central configurations of the n-body problem in the plane with a homogeneous potential. In particular, both bounds are independent of the homogeneous…
We study the bias and scatter in mass measurements of galaxy clusters resulting from fitting a spherically-symmetric Navarro, Frenk & White model to the reduced tangential shear profile measured in weak lensing observations. The reduced…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.
We realized one dimensional disordered photonic structures by grouping high refractive index layers in clusters, randomly distributed in such structure. We have control on the maximum size of the cluster and on the ratio high-low refractive…
A previous work introduced pair space, which is spanned by the center of mass of a system and the relative positions (pair positions) of its constituent bodies. Here, I show that in the $N$-body Newtonian problem, a configuration that does…
We study the clustering of voids using $N$-body simulations and simple theoretical models. The excursion-set formalism describes fairly well the abundance of voids identified with the watershed algorithm, although the void formation…