arXiv subjects

Barbara Gutiérrez

Publications and source records attributed to Barbara Gutiérrez.

2 recordsLinked to original sources

arXiv2025

Revisiting the Longitudinal Development of Electromagnetic Air Showers: Analytical Improvements to the Greisen Formalism with Zenith Angle Dependence

We present a new analytical approach to the longitudinal development of electromagnetic air showers, offering improvements to the classical Greisen formalism. We introduce a novel profile for the slope function $λ_1(s)$ that achieves an agreement less than $0.75\%$ with the original $λ_1$ for shower age parameter $s$ between $0.3 < s < 1.4$, where $s$ represents the stage of shower development. Our new formalism provides an improved representation of shower evolution, particularly near and beyond the shower maximum. In addition, we derive a complete expression for the number of particles $N(t)$. Our implementation includes the zenithal angle dependence on the number of particles at the detector level at high altitudes, making it particularly useful for high-altitude observatories. This expression is suitable for implementing air shower simulation tool fitting procedures over a wide range of energies and geometries. Our analysis suggests that the proposed new formalism may provide better agreement with the expected evolution of particle numbers compared to the traditional Greisen formulation.

astro-ph.HE↗

arXiv2015

Motion planning in real flag manifolds

Starting from Borel's description of the mod-2 cohomology of real flag manifolds, we give a minimal presentation of the cohomology ring for semi complete flag manifolds $F_{k,m}:=F(1,\ldots,1,m)$ where $1$ is repeated $k$ times. The information is used in order to estimate Farber's topological complexity of these spaces when $m$ approaches (from below) a 2-power. In particular, we get almost sharp estimates for $F_{2,2^e-1}$ which resemble the known situation for the real projective spaces $F_{1,2^e}$. Our results indicate that the agreement between the topological complexity and the immersion dimension of real projective spaces no longer holds for other flag manifolds. More interestingly, we also get corresponding results for the $s$-th (higher) topological complexity of these spaces. Actually, we prove the surprising fact that, as $s$ increases, the estimates become stronger. Indeed, we get several full computations of the higher motion planning problem of these manifolds. This property is also shown to hold for surfaces: we get a complete computation of the higher topological complexity of all closed surfaces (orientable or not). A homotopy-obstruction explanation is included for the phenomenon of having a cohomologically accessible higher topological complexity even when the regular topological complexity is not so accessible.

math.AT↗