First integrals for the Kepler problem with linear drag

In this work we consider the Kepler problem with linear drag, and prove the existence of a continuous vector-valued first integral, obtained taking the limit as \(t\rightarrow +\infty \) of the Runge–Lenz vector. The norm of this first integral can be interpreted as an asymptotic eccentricity \(e_{\infty }\) with \(0\le e_{\infty } \le 1\). The orbits satisfying \(e_{\infty } <1\) approach the singularity by an elliptic spiral and the corresponding solutions \(x(t)=r(t)e^{i\theta (t)}\) have a norm r(t) that goes to zero like a negative exponential and an argument \(\theta (t)\) that goes to infinity like a positive exponential. In particular, the difference between consecutive times of passage through the pericenter, say \(T_{n+1} -T_n\), goes to zero as \(\frac{1}{n}\).     

Real-time assimilation of streamflow observations into a hydrological routing model: effects of model structures and updating methods

This paper comparatively assesses the performance of five data assimilation techniques for three-parameter Muskingum routing with a spatially lumped or distributed model structure. The assimilation techniques used include direct insertion (DI), nudging scheme (NS), Kalman filter (KF), ensemble Kalman filter (EnKF) and asynchronous ensemble Kalman filter (AEnKF), which are applied to river reaches in Texas and Louisiana, USA. For both lumped and distributed routing, results from KF, EnKF and AEnKF are sensitive to the error specification. As expected, DI outperformed the other models in the case of lumped modelling, while in distributed routing, KF approaches, particularly AEnKF and EnKF, performed better than DI or nudging, reflecting the benefit of updating distributed states through error covariance modelling in KF approaches. The results of this work would be useful in setting up data assimilation systems that employ increasingly abundant real-time observations using distributed hydrological routing models.     

Integrated Electrical Resistivity Tomography and Ground Penetrating Radar Measurements Applied to Tomb Detection

The integrated use of electrical resistivity tomography (ERT) and ground penetrating radar (GPR) measurements, and in particular the joint analysis of 2D and 3D data, can represent a valid solution for target identification at complex archaeological sites. A good example, in this respect, is given by the case study of a Phoenician–Punic necropolis in the archaeological site of Nora, in southern Sardinia (Italy), where GPR and ERT measurements were collected before site excavation. In this specific case, the mix of soil and air in the buried chambers, as well as the orientation and the complex spatial distribution of these structures into the sandstone bedrock, generated a number of anomalies difficult to interpret only using 2D results. Only the integration of all GPR and ERT data in a 3D view, and the comparison with archaeological evidence after the excavation, allowed a solid interpretation of geophysical anomalies visible in the 2D sections. Overall, this case study demonstrates the efficiency of the combined use of GPR and ERT acquisitions and shows how, in general, only the joint analysis of 2D data and in a 3D view can help the interpretation of the real distribution of the buried archaeological remains at similar archaeological complex sites.     

Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity

Earthquakes are one of the most destructive natural disasters and the spatial distribution of their epicentres generally shows diverse interaction structures at different spatial scales. In this paper, we use a multi-scale point pattern model to describe the main seismicity in the Hellenic area over the last 10 years. We analyze the interaction between events and the relationship with geological information of the study area, using hybrid models as proposed by Baddeley et al. (2013). In our analysis, we find two competing suitable hybrid models, one with a full parametric structure and the other one based on nonparametric kernel estimators for the spatial inhomogeneity.     

ASPHAA: A GIS‐Based Algorithm to Calculate Cell Area on a Latitude‐Longitude (Geographic) Regular Grid

One characteristic of a Geographic Information System (GIS) is that it addresses the necessity to handle a large amount of data at multiple scales. Lands span over an area greater than 15 million km² all over the globe and information types are highly variable. In addition, multi‐scale analyses involve both spatial and temporal integration of datasets deriving from different sources. The currently worldwide used system of latitude and longitude coordinates could avoid limitations in data use due to biases and approximations. In this article a fast and reliable algorithm implemented in Arc Macro Language (AML) is presented to provide an automatic computation of the surface area of the cells in a regularly spaced longitude‐latitude (geographic) grid at different resolutions. The approach is based on the well‐known approximation of the spheroidal Earth's surface to the authalic (i.e. equal‐area) sphere. After verifying the algorithm's strength by comparison with a numerical solution for the reference spheroidal model, specific case studies are introduced to evaluate the differences when switching from geographic to projected coordinate systems. This is done at different resolutions and using different formulations to calculate cell areas. Even if the percentage differences are low, they become relevant when reported in absolute terms (hectares).     

The role of structural inheritance in continental break-up and exhumation of Alpine Tethyan mantle(Canavese Zone,Western Alps)

The Canavese Zone(CZ)in the Western Alps represents the remnant of the distal passive margin of the Adria microplate,which was stretched and thinned during the Jurassic opening of the Alpine Tethys.Through detailed geological mapping,stratigraphic and structural analyses,we document that the continental break-up of Pangea and tectonic dismemberment of the Adria distal margin,up to mantle rocks exhumation and oceanization,did not simply result from the syn-rift Jurassic extension but was strongly favored by older structu ral inheritances(the Proto-Canavese Shear Zone),which controlled earlier lithospheric weakness.Our findings allowed to redefine in detail(i)the tectono-stratigraphic setting of the Variscan metamorphic basement and the Late Carbonife rous to Early Cretaceous CZ succession,(ii)the role played by inherited Late Carboniferous to Early Triassic structures and(iii)the significance of the CZ in the geodynamic evolution of the Alpine Tethys.The large amount of extensional displacement and crustal thinning occurred during different pulses of Late Carbonife rous-Early Triassic strike-slip tectonics is wellconsistent with the role played by long-lived regional-scale wrench faults(e.g.,the East-Variscan Shear Zone),suggesting a re-discussion of models of mantle exhumation driven by low-angle detachment faults as unique efficient mechanism in stretching and thinning continental crust.     

Channel mobility drives a diverse stratigraphic architecture in the dryland Mojave River (California,USA)

The links between flood frequency and rates of channel migration are poorly defined in the ephemeral rivers typical of arid regions. Exploring these links in desert fluvial landscapes would augment our understanding of watershed biogeochemistry and river morphogenesis on early Earth (i.e. prior to the greening of landmasses). Accordingly, we analyse the Mojave River (California), one of the largest watercourses in the Great Basin of the western United States. We integrate discharge records with channel-migration rates derived from dynamic time-warping analysis and chronologically calibrated subsidence rates, thereby constraining the river's formative conditions. Our results reveal a slight downstream decrease in bankfull discharge on the Mojave River, rather than the downstream increase typically exhibited by perennial streams. Yet, the number of days per year during which the channel experiences bankfull or higher stages is roughly maintained along the river's length. Analysis of historical peak flood records suggests that the incidence of channel-formative events responds to modulation in watershed runoff due to the precipitation in the river's headwaters over decades to centuries. Our integrated analysis finally suggests that, while maintaining hydraulic geometries that are fully comparable with many other rivers worldwide, ephemeral desert rivers akin to the Mojave are capable of generating a surprisingly wide range of depositional geometries in the stratigraphic record. © 2020 John Wiley & Sons, Ltd.     

Sar Interferometry And Its Applications

Satellite mounted Synthetic Aperture Radars (SAR) provide informationof the amplitude of the backscatterer its phase. This corresponds to the totaltravel time (source receiver and back), plus the phase of the scatterer itself.SAR interferometry yields the image of the differences of the phases takenin two successive passes. Or in the same pass if two receivers are availableon board; these images give a good digital elevation model of the terrain,with a vertical resolution that could be in the meter range. Millimetric motionof large areas of the terrain or of corner reflectors can also be measured withgood reliability; the system then measures subsidence, co-seismic motions andsmall motions of buildings and constructions. The coherence of t e interferometric pair, i.e., the permanence of the scattering characteristics of the terrain from one pass to the next combined with the more usual backscatterer amplitude, leads to high quality image segmentation. The possibilities and the limits of this technique are summarized.     

Proper elements for highly inclined asteroidal orbits

Based on Williams' work and rewritten in action angle variables, a method for the calculation of proper elements is here presented. The averaging over the long periodic terms is performed by the semi numerical method developed by Henrard (1990); no series expansion in eccentricity or inclination of the asteroid is used which allows calculating proper elements for highly inclined orbits. Conversely, the theory is truncated at the first degree in the eccentricity and the inclination of the perturbing planets. A few tests about accuracy and consistency are presented.     

On the dynamics in the asteroids belt. Part I : General theory

The classical problem of the dynamics in the asteroids belt is revisited in the light of recently developed perturbation methods. We consider the spatial problem of three bodies both in the circular and in the elliptic case, looking for families of periodic or quasi periodic orbits. Some criteria for deciding the stability of these families are also indicated.