The correct characterization of wall pressure fluctuations (WPF) and of the response of an elastic structure subjected to turbulent boundary layer (TBL) represents one of the most challenging problems in the fluid structure interaction field. This kind of excitation for an elastic structure is encountered on a number of different engineering applications: in naval field WPF acting along the ship hull impinge on comfort on board high speed vessels and they are also responsible for strong vibrations of the sonar dome, which can degrade the correct functioning of the sensors mounted inside the dome itself. Moreover, the sound pressure levels produced by TBL load acting along the aircraft fuselage can be intense enough to result in an unacceptable cabin noise and can cause a reduction of the lifetime of fuselage panels due to structural fatigue. The study of WPF induced by TBL load in the naval and aeronautical fields are characterized by important differences in terms of both flow and structural characteristics, which provide highly different dynamical responses of a typical naval and aeronautic panel. Nevertheless, the characterization of the TBL load using model scale tests of a ship and an aircraft or sections of them have also strong similarities and for a great number of problems can be analysed using parallel experimental approaches in towing tanks, water channels and wind tunnels. The base of this approach is given by the identification of the most appropriate scaling laws for wall pressure fluctuation spectra and spatial models in the frequency domain, which allow to obtain in principle the full scale spectra from the sole knowledge of few mean flow parameters. Unfortunately, these models are based on very restrictive hypotheses on the nature of the flow and the structure, basically canonical flat boundary layer. Aim of this work is to show how some of the typical perturbations from the canonical flat plate boundary layer, encountered when studying a real structure in naval and aeronautical fields, can interfere in the modelling of this load and to show possible solutions to these specific problems. To examine these features for complex boundary layer, the results of three different experimental campaigns performed at CNR-INSEAN towing tank and CIRA PT-1 transonic wind tunnel are here discussed.

We give a Sobolev inequality with the weight K(x) belonging to the class A_2\cap G_n for the function |u|^t and the weight K(x)^{-1} for |u|^2. The constant in the relevant inequality is seen to depend on the G_n and A_2 constants of the weight.

Motion of test particles in the gravitational field associated with an electromagnetic plane wave is investigated. The interaction with the radiation field is modeled by a force term entering the equations of motion given by the 4-momentum density of radiation observed in the particle's rest frame with a multiplicative constant factor expressing the strength of the interaction itself. Explicit analytical solutions are obtained. Scattering of fields by the electromagnetic wave, i.e., scalar (spin 0), electromagnetic (spin 1) and and massless spin $\frac12$ fields, is studied too.

The motion of matter immersed in a radiation field is affected by radiation drag, as a result of scattering or absorption and re-emission. The resulting friction-like drag, also known as Poynting-Robertson effect, has been recently studied in the general relativistic background of the Schwarzschild and Kerr metric, under the assumption that all photons in the radiation field possess the same angular momentum. We calculate here the signal produced by an emitting point-like specific source moving in a Schwarzschild spacetime under the influence of such a radiation field. We derive the flux, redshift factor and solid angle of the hot spot as a function of (coordinate) time, as well as the time-integrated image of the hot spot as seen by an observer at infinity. The results are then compared with those for a spot moving on a circular geodesic in a Schwarzschild metric.

The motion of a massive test particle inside a thermal (test) photon gas is studied near a Schwarzschild black hole, leading to a novel description of the effect of radiation scattering on the particle trajectory, responsible for half of the Poynting-Robertson effect: the azimuthal radiation drag. Lacking the outward directed radiation pressure of the latter effect, gravitationally bound orbits always decay, leading to capture by the black hole or the central object generating the exterior Schwarzschild field in which this discussion takes place.

The motion of a massive test particle in a Schwarzschild spacetime surrounded by a perfect fluid with equation of state $p_0= w \rho_0$ is investigated. Deviations from geodesic motion are analyzed as a function of the parameter $w$, ranging from $w=1$ which corresponds to the case of massive free scalar fields, down into the so-called ``phantom" energy, with $w<-1$. It is found that the interaction with the fluid leads to capture (escape) of the particle trajectory in the case $1+w>0$ ($<0$), respectively. Based on this result, it is argued that inspection of the trajectories of test particles in the vicinity of a Schwarzschild black hole with matter around may offer a new means of gaining insights into the nature of cosmic matter.

The observer-dependent tidal effects associated with the electric and magnetic parts of the Riemann tensor with respect to an arbitrary family of observers are discussed in a general spacetime in terms of certain \lq\lq tidal indicators.'' The features of such indicators are then explored by specializing our considerations to the family of stationary circularly rotating observers in the equatorial plane of the Kerr spacetime. There exist a number of observer families which are special for several reasons and for each of them such indicators are evaluated. The transformation laws of tidal indicators when passing from one observer to another are also discussed, clarifying the interplay among them. Our analysis shows that no equatorial plane circularly rotating observer in the Kerr spacetime can ever measure a vanishing tidal electric indicator, whereas the family of Carter's observers measures zero tidal magnetic indicator.

The gravitational-wave signal from inspiralling neutron-star--neutron-star (or black-hole--neutron-star) binaries will be influenced by tidal coupling in the system. An important science goal in the gravitational-wave detection of these systems is to obtain information about the equation of state of neutron star matter via the measurement of the tidal polarizability parameters of neutron stars. To extract this piece of information will require to have accurate analytical descriptions of both the motion and the radiation of tidally interacting binaries. We improve the analytical description of the late inspiral dynamics by computing the next-to-next-to-leading order relativistic correction to the tidal interaction energy. Our calculation is based on an effective-action approach to tidal interactions, and on its transcription within the effective-one-body formalism. We find that second-order relativistic effects (quadratic in the relativistic gravitational potential $u=G(m_1 +m_2)/(c^2 r)$) significantly increase the effective tidal polarizability of neutron stars by a distance-dependent amplification factor of the form $1 + \alpha_1 \, u + \alpha_2 \, u^2 + \cdots $ where, say for an equal-mass binary, $\alpha_1=5/4=1.25$ (as previously known) and $\alpha_2=85/14\simeq6.07143$ (as determined here for the first time). We argue that higher-order relativistic effects will lead to further amplification, and we suggest a Pad\'e-type way of resumming them. We recommend to test our results by comparing resolution-extrapolated numerical simulations of inspiralling-binary neutron stars to their effective one body description.

The motion of a particle in the Tolman metric generated by a photon gas source is discussed. Both the case of geodesic motion and motion with nonzero friction, due to photon scattering effects, are analyzed. In the Minkowski limit, the particle moves along a straight line segment with a decelerated motion, reaching the endpoint at zero speed. The curved case shows a qualitatively different behavior; the geodesic motion consists of periodic orbits, confined within a specific radial interval. Under the effect of frictional drag, this radial interval closes up in time and in all our numerical simulations the particle ends up in the singularity at the center.

To confront relativity theory with observation, it is necessary to split spacetime into its temporal and spatial components. The timelike threading approach involves fundamental observers that are at rest in space; indeed, this (1+3) splitting implies restrictions on the gravitational potentials $(g_{\mu \nu})$. On the other hand, the spacelike slicing approach involves (3+1) splittings of any congruence of observers with corresponding restrictions on $(g^{\mu \nu})$. These latter coordinate conditions exclude closed timelike curves (CTCs) within any such coordinate patch. While the threading coordinate conditions can be naturally integrated into the structure of Lorentzian geometry and constitute the standard coordinate conditions in general relativity, this circumstance does not extend to the slicing coordinate conditions. From this viewpoint, the existence of CTCs is not, in principle, prohibited by classical general relativity.

Tidal indicators are commonly associated with the electric and magnetic parts of the Riemann tensor (and its covariant derivatives) with respect to a given family of observers in a given spacetime. Recently, observer-dependent tidal effects have been extensively investigated with respect to a variety of special observers in the equatorial plane of the Kerr spacetime. This analysis is extended here by considering a more general background solution to include the case of matter which is also endowed with an arbitrary mass quadrupole moment. Relation with curvature invariants and Bel-Robinson tensor, i.e., observer-dependent super-energy density and super-Poynting vector, are investigated too.

The features of the scattering of massive neutral particles propagating in the field of a gravitational plane wave are compared with those characterizing their interaction with an electromagnetic radiation field. The motion is geodesic in the former case, whereas in the case of an electromagnetic pulse it is accelerated by the radiation field filling the associated spacetime region. The interaction with the radiation field is modeled by a force term entering the equations of motion proportional to the 4-momentum density of radiation observed in the particle's rest frame. The corresponding classical scattering cross sections are evaluated too.