Approximate analytical calculations of photon geodesics in the Schwarzschild metric

We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime. Based on this, we derive the approximate equations for light bending and propagation delay that have been introduced empirically. We then derive for the first time an approximate analytical equation for the solid angle. We discuss the accuracy and range of applicability of the new equations and present a few simple applications of them to known astrophysical problems.Comment: 8 pages, 10 Figures; Received: 08 June 2016 / Accepted: 04 August 2016and accepted from A&

integrating capacity and logistics of large additive manufacturing networks

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Negotiating and Sharing Capacities of Large Additive Manufacturing Networks

This paper focuses on dynamics of productive and demanding nodes for Scattered Manufacturing Networks within 3D Printings contexts. The various nodes issue orders or sell production slots in order to achieve their own aims. An orchestrator coordinates the dynamics along the network according to principles of sustainability, equated shared resources and transparency by managing communication activities among nodes. In particular, suitable tradeoffs occur by a unique framework that, with the aim of optimizing the overall costs, suggests either logistics paths along the network or negotiation policies among nodes in order to reallocate resources. Numerical examples present the proposed approach. Keywords: Industry 4.0, Additive Manufacturing, Sharing Capacities, Operation Models, Optimization of networks JEL Codes:  C02; O21 and P4

Challenges and new trends in power electronic devices reliability

Power electronic devices are expected to play an ever more fundamental role in unlocking the potentialities of smart power systems and in developing more electric ground and air transportation systems. The reliability of power electronic devices at different hierarchical levels (single component, single device, installation and system) becomes a crucial point in this framework, as failures may determine technical, economical and safety issues that should be carefully addressed at the design and maintenance stages. Power electronic devices are subject to thermal, electrical and mechanical stresses, which can be assessed through consolidated, traditional techniques [1,2,3,4]. However, today these devices are expected to operate under challenging environmental conditions (e.g., high altitudes in more electric aircrafts or high temperatures on photovoltaic (PV) installations), undermining the effectiveness of traditional approaches that are typically based on historical failure data, fault rates or past observed scenarios. In fact, the rapid evolution of power electronic technologies and the ever more challenging operating frameworks pose severe limitations on the trustworthiness of available reliability data, as they are typically related to incoherent operating conditions [1,2,3,4]

Geomorphological Evolution of Volcanic Cliffs in Coastal Areas: The Case of Maronti Bay (Ischia Island)

The morphoevolution of coastal areas is due to the interactions of multiple continental and marine processes that define a highly dynamic environment. These processes can occur as rapid catastrophic events (e.g., landslides, storms, and coastal land use) or as slower continuous processes (i.e., wave, tidal, and current actions), creating a multi-hazard scenario. Maronti Bay (Ischia Island, Southern Italy) can be classified as a pocket beach that represents an important tourist and environmental area for the island, although it has been historically affected by slope instability, sea cliff recession, and coastal erosion. In this study, the historical morphoevolution of the shoreline was analysed by means of a dataset of aerial photographs and cartographic information available in the literature over a 25-year period. Furthermore, the role of cliff recession and its impact on the beach was also explored, as in recent years, the stability condition of the area was worsened by the occurrence of a remarkable landslide in 2019. The latter was reactivated following a cloudburst on the 26th of November 2022 that affected the whole Island and was analysed with the Dem of Difference technique. It provided an estimate of the mobilised volumes and showed how the erosion and deposition areas were distributed and modified by wave action. The insights from this research can be valuable in developing mitigation strategies and protective measures to safeguard the surrounding environment and ensure the safety of residents and tourists in this multi-hazard environment

Neutron Star Radius-to-mass Ratio from Partial Accretion Disc Occultation as Measured through Fe Kα\alpha Line Profiles

We present a new method to measure the radius-to-mass ratio (R/M) of weakly magnetic, disc-accreting neutron stars by exploiting the occultation of parts of the inner disc by the star itself. This occultation imprints characteristic features on the X-ray line profile that are unique and are expected to be present in low mass X-ray binary systems seen under inclinations higher than ~65 degrees. We analyse a NuSTAR observation of a good candidate system, 4U 1636-53, and find that X-ray spectra from current instrumentation are unlikely to single out the occultation features owing to insufficient signal-to-noise. Based on an extensive set of simulations we show that large-area X-ray detectors of the future generation could measure R/M to ~2{\div}3% precision over a range of inclinations. Such is the precision in radius determination required to derive tight constraints on the equation of state of ultradense matter and it represents the goal that other methods too aim to achieve in the future.Comment: 17 pages, 8 figures; this is a pre-print edition of an article that has been accepted for publication in the Astrophysical Journa

The three-dimensional general relativistic Poynting-Robertson effect I: radial radiation field

In this paper we investigate the three-dimensional (3D) motion of a test particle in a stationary, axially symmetric spacetime around a central compact object, under the influence of a radiation field. To this aim we extend the two-dimensional (2D) version of the Poynting-Robertson effect in General Relativity (GR) that was developed in previous studies. The radiation flux is modeled by photons which travel along null geodesics in the 3D space of a Kerr background and are purely radial with respect to the zero angular momentum observer (ZAMO) frames. The 3D general relativistic equations of motion that we derive are consistent with the classical (i.e. non-GR) description of the Poynting-Robertson effect in 3D. The resulting dynamical system admits a critical hypersurface, on which radiation force balances gravity. Selected test particle orbits are calculated and displayed, and their properties described. It is found that test particles approaching the critical hypersurface at a finite latitude and with non-zero angular moment are subject to a latitudinal drift and asymptotically reach a circular orbit on the equator of the critical hypersurface, where they remain at rest with respect to the ZAMO. On the contrary, test particles that have lost all their angular momentum by the time they reach the critical hypersurface do not experience this latitudinal drift and stay at rest with respects to the ZAMO at fixed non-zero latitude.Comment: 17 pages, 19 figures, accepted for publication on Physical Review D the 3rd of January 201