The power of two: Assessing the impact of a second measurement of the weak-charge form factor of 208Pb

[Background] Besides its intrinsic value as a fundamental nuclear-structure observable, the weak-charge density of 208Pb - a quantity that is closely related to its neutron distribution - is of fundamental importance in constraining the equation of state of neutron-rich matter. [Purpose] To assess the impact that a second electroweak measurement of the weak-charge form factor of 208Pb may have on the determination of its overall weak-charge density. [Methods] Using the two putative experimental values of the form factor, together with a simple implementation of Bayes' theorem, we calibrate a theoretically sound - yet surprisingly little known - symmetrized Fermi function, that is characterized by a density and form factor that are both known exactly in closed form. [Results] Using the charge form factor of 208Pb as a proxy for its weak-charge form factor, we demonstrate that using only two experimental points to calibrate the symmetrized Fermi function is sufficient to accurately reproduce the experimental charge form factor over a significant range of momentum transfers. [Conclusions] It is demonstrated that a second measurement of the weak-charge form factor of 208Pb supplemented by a robust theoretical input in the form of the symmetrized Fermi function, would place significant constraints on the neutron distribution of 208Pb and, ultimately, on the equation of state of neutron-rich matter.Comment: 14 pages, 3 tables, and 6 figure

A statistical model of fracture for a 2D hexagonal mesh: the Cell Network Model of Fracture for the bamboo Guadua angustifolia

A 2D, hexagonal in geometry, statistical model of fracture is proposed. The model is based on the drying fracture process of the bamboo Guadua angustifolia. A network of flexible cells are joined by brittle junctures of different Young moduli that break at a fixed threshold in tensile force. The system is solved by means of the Finite Element Method (FEM). The distribution of avalanche breakings exhibits a power law with exponent -2.93(9), in agreement with the random fuse model

Size distribution and waiting times for the avalanches of the Cell Network Model of Fracture

The Cell Network Model is a fracture model recently introduced that resembles the microscopical structure and drying process of the parenchymatous tissue of the Bamboo Guadua angustifolia. The model exhibits a power-law distribution of avalanche sizes, with exponent -3.0 when the breaking thresholds are randomly distributed with uniform probability density. Hereby we show that the same exponent also holds when the breaking thresholds obey a broad set of Weibull distributions, and that the humidity decrements between successive avalanches (the equivalent to waiting times for this model) follow in all cases an exponential distribution. Moreover, the fraction of remaining junctures shows an exponential decay in time. In addition, introducing partial breakings and cumulative damages induces a crossover behavior between two power-laws in the avalanche size histograms. This results support the idea that the Cell Network Model may be in the same universality class as the Random Fuse Model

La resolución numérica de ecuaciones de Viète y su difusión en el curso matemático de Hérigone

Postprint (published version

Algunos resultados sobre periodicidad global de ecuaciones en diferencias de orden dos y tres

En esta nota repasamos algunos resultados sobre periodicidad global en ecuaciones (autónomas) en diferencias finitas de órdenes dos y tres, y aportamos algún modesto avance en el tema