Radiative processes in external gravitational fields

Kinematically forbidden processes may be allowed in the presence of external gravitational fields. These ca be taken into account by introducing generalized particle momenta. The corresponding transition probabilities can then be calculated to all orders in the metric deviation from the field-free expressions by simply replacing the particle momenta with their generalized counterparts. The procedure applies to particles of any spin and to any gravitational fields. transition probabilities, emission power, and spectra are, to leading order, linear in the metric deviation. It is also shown how a small dissipation term in the particle wave equations can trigger a strong backreaction that introduces resonances in the radiative process and deeply affects the resulting gravitational background.Comment: 5 pages, 1 figur

Synchronization problems for unidirectional feedback coupled nonlinear systems

In this paper we consider three different synchronization problems consisting in designing a nonlinear feedback unidirectional coupling term for two (possibly chaotic) dynamical systems in order to drive the trajectories of one of them, the slave system, to a reference trajectory or to a prescribed neighborhood of the reference trajectory of the second dynamical system: the master system. If the slave system is chaotic then synchronization can be viewed as the control of chaos; namely the coupling term allows to suppress the chaotic motion by driving the chaotic system to a prescribed reference trajectory. Assuming that the entire vector field representing the velocity of the state can be modified, three different methods to define the nonlinear feedback synchronizing controller are proposed: one for each of the treated problems. These methods are based on results from the small parameter perturbation theory of autonomous systems having a limit cycle, from nonsmooth analysis and from the singular perturbation theory respectively. Simulations to illustrate the effectiveness of the obtained results are also presented.Comment: To appear in Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Ana

Can Gravity Distinguish Between Dirac and Majorana Neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavour system, as shown explicitly for SN1987A.Comment: 4 pages, 2 figures; minor changes of text; typo corrected; accepted in Physical Review Letter

Unbounded Solutions to Systems of Differential Equations at Resonance

We deal with a weakly coupled system of ODEs of the type xj\u2032\u2032+nj2xj+hj(x1,\u2026,xd)=pj(t),j=1,\u2026,d,with hj locally Lipschitz continuous and bounded, pj continuous and 2 \u3c0-periodic, nj 08 N (so that the system is at resonance). By means of a Lyapunov function approach for discrete dynamical systems, we prove the existence of unbounded solutions, when either global or asymptotic conditions on the coupling terms h1, \u2026 , hd are assumed

BANK EROSION AND INSTABILITY MONITORING WITH A LOW COST TERRESTRIAL LASER SCANNER

ABSTRACT: Among the dominant processes taking place in a river basin, especially mountain ones, sediments creation and transport play a key role in morphological processes. Studies usually focus on big mass movements, such as landslides and debris flows, or on wide spread slope erosion due to rainfalls, while bank erosion is neglected or not considered essential for sediment budget at basin scale. Nevertheless, authors consider bank erosion a process that deserve more careful studies; not only the sediment share from bank erosion is not negligible in steep mountain rivers, but also the process can threat structures on river sides due the possibility to have limited, but still significant, mass collapse of bank sections during intense events. The paper present an attempt to monitor bank erosion in a section of a river in Northern Italy Alps and to put it in relation with weather and water discharge. Survey campaign was set up at regular time intervals, or after particularly intense rainfalls, and uses a Terrestrial Laser Scanner (TLS) to acquire the bank surface. The tool was developed internally, at Politecnico di Milano, to meet requirements about low cost level and good accuracy. Successive acquisitions of point clouds were elaborated, via an ad-hoc MatLab code, to determine erosion, or deposition, volumes of sediments. These volumetric results have been evaluated in relation with rainfalls and freeze-thaw cycles looking for a relationship between environmental conditions and bank failures. Some interesting results are shown, such as a relation between erosion rates and temperature or water flow in the river. The path to a complete process understanding and modelling is long, however the results reported can be considered a first step towards objective

Coupling the Yoccoz-Birkeland population model with price dynamics: Chaotic livestock commodities market cycles

We propose a new model for the time evolution of livestock commodities prices which exhibits endogenous deterministic stochastic behaviour. The model is based on the Yoccoz\u2013Birkeland integral equation, a model first developed for studying the time-evolution of single species with high average fertility, a relatively short mating season and density-dependent reproduction rates. This equation is then coupled with a differential equation describing the price of a livestock commodity driven by the unbalance between its demand and supply. At its birth the cattle population is split into two parts: reproducing females and cattle for butchery. The relative amount of the two is determined by the spot price of the meat. We prove the existence of an attractor (theorem A) and of a non-trivial periodic solution (theorem B) and we investigate numerically the properties of the attractor: the strange attractor existing for the original Yoccoz\u2013Birkeland model is persistent but its chaotic behaviour depends also on the time evolution of the price in an essential way