Multitemporal dendrogeomorphological analysis of slope instability in Upper Orcia Valley (Southern Tuscany, Italy)

The Upper Orcia Valley (Southern Tuscany, Italy) is a key site for the comprehension of denudation processes typically acting in Mediterranean badlands (calanchi) areas, thanks to the availability of long-lasting erosion monitoring datasets and the rapidity of erosion processes development. These features make the area suitable as an open air laboratory for the study of badlands dynamic and changes in geoheritage due to erosion (i.e. active geomorphosites). Decadal multitemporal investigations on the erosion rates and the geomorphological dynamics of the study area allowed to highlight a decrease in the average water erosion rates during the last 60 years. More in detail, a reduction of bare land and, consequently, of erosion processes effectiveness and a contemporary increasing frequency of mass wasting events were recorded. These trends can be partly related to the land cover changes occurred in the study area from the 1950s onwards, which consist of the significant increase of reforestation practices and important other forms of human impacts on slopes, mainly land levelling for agricultural exploitation. In order to better identify the most significant phases of geomorphological instability occurred in this area during the last decades, an integrated approach based on multitemporal geomorphological mapping and dendrogeomorphology analysis on specimen of Pinus nigra Arn. was used. In detail, trees colonizing a denudation slope located in the surrounding of the Radicofani town (Tuscany, Italy) and characterized by calanchi and shallow mass movements deposits, were analyzed for the 1985-2012 time period. The analysis of the growth anomaly indexes and of compression wood allowed to determine a spatio-temporal differentiation along the slope and respect to an undisturbed reference site. The negative anomaly index results to be more pronounced in the trees located on the investigated slope with respect to the ones sampled in a non-disturbed area. Compression wood characterizes trees on slope sectors mainly affected by runoff and/or mass movements with a different persistence. Erosion rates were finally calculated through dendrogeomorphological analysis on tree roots exposure (0.31-3 cm/y runoff prevailing; 5.86-27.5 cm/y, mass movements prevailing). Dendrogeomorphological results are in accordance with those obtained in the investigated areas with multitemporal photogrammetric and geomorphologic analyses

On the computation of reducible invariant tori on a parallel computer

We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections

Transport and invariant manifolds near L3 in the Earth-Moon Bicircular model

This paper focuses on the role of $\mathrm{L}_3$ to organise trajectories for a particle going from Earth to Moon and viceversa, and entering or leaving the Earth-Moon system. As a first model, we have considered the planar Bicircular problem to account for the gravitational effect of the Sun on the particle. The first step has been to compute a family of hyperbolic quasi-periodic orbits near $\mathrm{L}_3$. Then, the computation of their stable and unstable manifolds provides connections between Earth and Moon, and also generates trajectories that enter and leave the Earth-Moon system. Finally, by means of numerical simulations based on the JPL ephemeris we show that these connections can guide the journey of lunar ejecta towards the Earth

Noise-induced macroscopic bifurcations in globally-coupled chaotic units

Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.Comment: Phys. Rev. Lett., accepte

Using invariant manifolds to capture an asteroid near the L3 point of the Earth-Moon Bicircular model

This paper focuses on the capture of Near-Earth Asteroids (NEAs) in a neighbourhood of the $\mathrm{L}_{3}$ point of the Earth-Moon system. The dynamical model for the motion of the asteroid is the planar Earth-Moon-Sun Bicircular problem (BCP). It is known that the $\mathrm{L}_{3}$ point of the Restricted Three-Body Problem is replaced, in the BCP, by a periodic orbit of centre $\times$ saddle type, with a family of mildly hyperbolic tori that is born from the elliptic direction of this periodic orbit. It is remarkable that some pieces of the stable manifolds of these tori escape (backward in time) the Earth-Moon system and become nearly circular orbits around the Sun. In this work we compute this family of invariant tori and also high order approximations to their stable/unstable manifolds. We show how to use these manifolds to compute an impulsive transfer of a NEA to an invariant tori near $\mathrm{L}_{3}$. As an example, we study the capture of the asteroid $2006 \mathrm{RH} 120$ in its approach of 2006. We show that there are several opportunities for this capture, with different costs. It is remarkable that one of them requires a $\Delta v$ as low as 20 $\mathrm{m} / \mathrm{s}$

On the station keeping of a Solar sail in the Elliptic Sun-Earth system

In this work we focus on the dynamics of a solar sail in the Sun Earth Elliptic Restricted Three-Body Problem with solar radiation pressure. The considered situation is the motion of a sail close to the $L_{1}$ point, but displacing the equilibrium point with the sail so that it is possible to have continuous communication with the Earth. In previous works we derived a station keeping strategy for this situation but using the Circular RTBP as a model. In this paper we discuss the effect of the eccentricity in the region close to the sail-displaced $L_{1}$ point of the Circular RTBP. Then we show how to use the information on this dynamics to design a station keeping strategy. Finally, we apply these results to the GeoStorm mission, including errors in the sail orientation and on the estimation of the position of the sail in the simulations

Effective Reducibility of Quasi-Periodic Linear Equations close to Constant Coefficients

Let us consider the differential equation $$\dot{x}=(A+\varepsilon Q(t,\varepsilon))x, \;\;\;\; |\varepsilon|\le\varepsilon_0,$$ where A is an elliptic constant matrix and Q depends on time in a quasi-periodic (and analytic) way. It is also assumed that the eigenvalues of A and the basic frequencies of Q satisfy a diophantine condition. Then it is proved that this system can be reduced to $$\dot{y}=(A^{*}(\varepsilon)+\varepsilon R^{*}(t,\varepsilon))y, \;\;\;\; |\varepsilon|\le\varepsilon_0,$$ where $R^{*}$ is exponentially small in $\varepsilon$, and the linear change of variables that performs such a reduction is also quasi-periodic with the same basic frequencies as Q. The results are illustrated and discussed in a practical example

Theory of Materials and Finishes 1

Exam paper for second semester: Theory of Materials and Finishes