An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown that this formula describes the increase of the pendulum period with amplitude better than other simple formulas found in literature. A good agreement with experimental data for a low air-resistance pendulum is also verified and it suggests, together with the current availability/precision of timers and detectors, that the proposed formula is useful for extending the pendulum experiment beyond the usual small-angle oscillations.Comment: 15 pages and 4 figures. to appear in American Journal of Physic

Awaking the vacuum with spheroidal shells

It has been shown that well-behaved spacetimes may induce the vacuum fluctuations of some nonminimally coupled free scalar fields to go through a phase of exponential growth. Here, we discuss this mechanism in the context of spheroidal thin shells emphasizing the consequences of deviations from spherical symmetry.Comment: 10 pages, 7 figures. Minor changes, version published on Phys. Rev.

Explainable Metamodels for ATM Performance Assessment

Fast-time simulation constitutes a well-known and long-established technique within the Air Traffic Management (ATM) community. However, it is often the case that simulation input and output spaces are underutilized, limiting the full understandability, transparency, and interpretability of the obtained results. In this paper, we propose a methodology that combines simulation metamodeling and SHapley Additive exPlanations (SHAP) values, aimed at uncovering the intricate hidden relationships among the input and output variables of a simulated ATM system in a rather practical way. Whereas metamodeling provides explicit functional approximations mimicking the behavior of the simulators, the SHAP-based analysis delivers a systematic framework for improving their explainability. We illustrate our approach using a state-of-the-art ATM simulator across two case studies in which two delay-centered performance metrics are analyzed. The results show that the proposed methodology can effectively make simulation and its results more explainable, facilitating the interpretation of the obtained emergent behavior, and additionally opening new opportunities towards novel performance assessment processes within the ATM research field

Avaliação da ferrugem da videira em variedades uvas de vinho.

O objetivo deste trabalho foi avaliar a ocorrência da ferrugem da videira em variedades de uva para vinho