V. Hernández Mederos

arXiv2025

ConicCurv: A curvature estimation algorithm for planar polygons

ConicCurv is a new derivative-free algorithm to estimate the curvature of a plane curve from a sample of data points. It is based on a known tangent estimator method grounded on classic results of Projective Geometry and Bézier rational conic curves. The curvature values estimated by ConicCurv are invariant to Euclidean changes of coordinates and reproduce the exact curvature values if the data are sampled from a conic. We show that ConicCurv< has convergence order $3$ and, if the sample points are uniformly arc-length distributed, the convergence order is $4$. The performance of ConicCurv is compared with some of the most frequently used algorithms to estimate curvatures and its performance is illustrated in the calculation of the elastic energy of subdivision curves and the location of L-curves corners.

math.NA↗

arXiv2019

Modeling anisotropic magnetized White Dwarfs with $γ$ metric

The effect of magnetic fields in the Equations of State (EoS) of compact objects is the splitting of the pressure in two components, one parallel and the other perpendicular to the magnetic field. This anisotropy suggests the necessity of using structure equations considering the axial symmetry of the magnetized system. In this work, we consider an axially symmetric metric in spherical coordinates, the $γ$-metric, and construct a system of equations to describe the structure of spheroidal compact objects. In addition, we connect the geometrical parameter $γ$ linked to the spheroid's radii, with the source of the anisotropy. So, the model relates the shape of the compact object to the physics that determines the properties of the composing matter. To illustrate how our structure equations work, we obtain the mass-radii solutions for magnetized White Dwarfs. Our results show that the main effect of the magnetic field anisotropy in White Dwarfs structure is to cause a deformation of these objects. Since this effect is only relevant at low densities, it does not affect the maximum values of magnetized White Dwarf's masses, which remain under Chandrasekhar limit.

astro-ph.HE↗