Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique.

We consider a weakly nonlinear system of the form (I + phi(x)A)x = p, where phi(x) is a real function of the unknown vector x, and (I + phi(x)A) is an M-matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (I + phi(x(r))A)x(r + 1) = p, r = 0, 1, ... . The global convergence is proved by considering a related fixed-point problem.

We design and analyse a numerical method for the solution of a particular second order integro-differential boundary value problem on the semiaxis, which arises in the study of the kinetic theory of dusty plasmas. The method we propose represents a first insight into the numerical solution of more complicated problems and consists of a discretization of the differential and integral terms and of an iteration process to solve the resulting non-linear system. Under suitable hypotheses we prove the convergence. We will show the characteristics of the method by means of some numerical simulations.

It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a nonstationary diffusion equation. Implications of this result for adaptive kernel density estimation of the condensed density of the generalized eigenvalues of a random matrix pencil useful for solving the exponential analysis problem are discussed.

Pencils of matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which allows to get a closed form approximation of the condensed density of the generalized eigenvalues of the pencils. Implications of this result for solving several moments problems are discussed and some numerical examples are provided.

The cerebral cortex of primates is endowed with neurons specifi- cally tuned for biological actions. These neurons are located in a network of areas comprising the visual areas of the region of the superior temporal sulcus (STS) and the visuomotor areas of the inferior parietal lobule and premotor cortex. It is generally assumed that action understanding depends on a serial recruitment of these areas. The observed actions, following an initial processing in striate and extrastriate visual areas, are encoded in STS. Subsequently, they are transformed into a motor format in the parietal and premotor areas. This transformation is done via the mirror mechanism. Here we present evidence for a fundamental role in action perception of backward projections to the occipital lobe. The evidence is based on two studies. In the first one, using high-density EEG, we showed that, during hand- action observation, following an early activation of occipital, parietal and premotor areas, late waves occur in the occipital lobe; in the second study, using TMS, we showed a clear impairment of action perception following occipital stimulation at the time of the late occipital waves. We conclude that, backward projections from motor cortex ‘bind’ the understanding of the goal of an action with the pictorial descriptions of the same action. This binding allows the full perception of the observed actions as a joint function of visual and motor areas and overcomes the traditional functional separation between the two systems

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlev\'e-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the G\"odel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.

Gravitational perturbations of the de Sitter spacetime are investigated using the Regge--Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gauge- and tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.

The turning circle maneuver of a self-propelled tanker like ship model is numerically simulated through the integration of the unsteady Reynolds averaged Navier-Stokes (uRaNS) equations coupled with the equations of the motion of a rigid body. The solution is achieved by means of the unsteady RANS solver ?navis developed at CNR-INSEAN. The focus here is on the analysis of the maneuvering behavior of the ship with two different stern appendages configurations; namely, a twin screw with a single rudder and a twin screw, twin rudder with a central skeg. Each propeller is taken into account by a model based on the actuator disk concept; anyhow, in order to correctly capture the turning maneuvering behavior of the model, a suitable model which takes into account for oblique flow effects has to be considered. Results from a preliminary verification assessment are discussed; validation of the predicted trajectory and the kinematical parameters is provided by comparison with experimental data from free running tests. Maneuvering abilities of the two configurations are discussed; in order to better understand the different behavior of the two configurations, an in depth analysis of the force and moments on the hull and on the individual appendages is provided.

In applied hydrodynamics it is presently a general common task to simulate flow around complex shaped ships with moving appendages. As an example the simulation of a turning circle manoeuvre of a full-appended combatant ship is common in manoeuvrability studies. Nevertheless the accurate numerical simulation of turbulent, unsteady flow around a full appended maneuvering complex-shaped hull is a challenging task, because of the geometrical complexity of the appendages present and their relative movement, generating a very complex hydrodynamic flow.