2014-15 UNOPA Annual Report

Revue de press

Elation KM-arcs

In this paper, we study KM-arcs in PG(2, q), the Desarguesian projective plane of order q. A KM-arc A of type t is a natural generalisation of a hyperoval: it is a set of q+t points in PG(2, q) such that every line of PG(2, q) meets A in 0, 2 or t points. We study a particular class of KM-arcs, namely, elation KM-arcs. These KM-arcs are highly symmetrical and moreover, many of the known examples are elation KM-arcs. We provide an algebraic framework and show that all elation KM-arcs of type q/4 in PG(2, q) are translation KM-arcs. Using a result of [2], this concludes the classification problem for elation KM-arcs of type q=4. Furthermore, we construct for all q = 2(h), h > 3, an infinite family of elation KM-arcs of type q/8, and for q=2(h), where 4, 6, 7 | h an infinite family of KM-arcs of type q/16. Both families contain new examples of KM-arcs

Extending small arcs to large arcs

This is a post-peer-review, pre-copyedit version of an article published in European Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s40879-017-0193-xAn arc is a set of vectors of the k-dimensional vector space over the finite field with q elements Fq , in which every subset of size k is a basis of the space, i.e. every k-subset is a set of linearly independent vectors. Given an arc G in a space of odd characteristic, we prove that there is an upper bound on the largest arc containing G. The bound is not an explicit bound but is obtained by computing properties of a matrix constructed from G. In some cases we can also determine the largest arc containing G, or at least determine the hyperplanes which contain exactly k-2 vectors of the large arc. The theorems contained in this article may provide new tools in the computational classification and construction of large arcs.Postprint (author's final draft

A linear set view on KM-arcs

In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting from a particular F2-linear set, called an i-club, we reconstruct the projective triads, the translation hyperovals as well as the translation arcs constructed by Korchmaros-Mazzocca, Gacs-Weiner and Limbupasiriporn. We show the KM-arcs of type q/4 recently constructed by Vandendriessche are translation arcs and fit in this family. Finally, we construct a family of KM-arcs of type q/4. We show that this family, apart from new examples that are not translation KM-arcs, contains all translation KM-arcs of type q/4

Effects of immersed moonlets in the ring arc particles of Saturn

Ring arcs are the result of particles in corotation resonances with nearby satellites. Arcs are present in Saturn and Neptune systems, in Saturn they are also associated with small satellites immersed on them. The satellite Aegaeon is immersed in the G~ring arc, and the satellites Anthe and Methone are embedded in arcs named after them. Since most of the population of the arcs is formed by $\mu$m-sized particles the dissipative effects, such as the plasma drag and the solar radiation force, decrease the lifetime of the arcs. We analysed the effects of the immersed satellites on these arcs by computing the mass production rate and the perturbation caused by them in the arc particles. By comparing the lifetime of the particles and the mass production rate we concluded that Aegaeon, Anthe and Methone did not act as sources for their arcs. We took a step further by analysing a hypothetical scenario formed by an immersed moonlet of different sizes. As a result we found that regardless the size of the hypothetical moonlet (from about 0.10 km to 4.0 km) these moonlets will not act as a source. These arcs are temporary structures and they will disappear in a very short period of time

A simple prescription for simulating and characterizing gravitational arcs

Simple models of gravitational arcs are crucial to simulate large samples of these objects with full control of the input parameters. These models also provide crude and automated estimates of the shape and structure of the arcs, which are necessary when trying to detect and characterize these objects on massive wide area imaging surveys. We here present and explore the ArcEllipse, a simple prescription to create objects with shape similar to gravitational arcs. We also present PaintArcs, which is a code that couples this geometrical form with a brightness distribution and adds the resulting object to images. Finally, we introduce ArcFitting, which is a tool that fits ArcEllipses to images of real gravitational arcs. We validate this fitting technique using simulated arcs and apply it to CFHTLS and HST images of tangential arcs around clusters of galaxies. Our simple ArcEllipse model for the arc, associated to a S\'ersic profile for the source, recovers the total signal in real images typically within 10%-30%. The ArcEllipse+S\'ersic models also automatically recover visual estimates of length-to-width ratios of real arcs. Residual maps between data and model images reveal the incidence of arc substructure. They may thus be used as a diagnostic for arcs formed by the merging of multiple images. The incidence of these substructures is the main factor preventing ArcEllipse models from accurately describing real lensed systems.Comment: 12 pages, 11 figures, accepted for publication in A&