A priori estimates for solutions to homogeneous Neumann problems for uniformly elliptic equations in open subsets ­ of R^n are established, with data in the limiting space L^{n\2} or, more generally, in the Lorentz spaces L^{n\2, q}(\Omega). These estimates are optimal as far as either constants or norms are concerned.

The strongest possible norms in a priori estimates for solutions to a class of second-order nonlinear elliptic boundary value problems are exhibited.

We study the behaviour of an initially spherical bunch of particles accelerated along trajectories parallel to the symmetry axis of a rotating black hole. We find that, under suitable conditions, curvature and inertial strains compete to generate jet-like structures. This is a purely kinematical effect which does not account by itself for physical processes underlying the formation of jets. In our analysis a crucial role is played by the property of the electric and magnetic part of the Weyl tensor to be Lorentz-invariant along the axis of symmetry in Kerr spacetime.

Objective. Empirical observations show that rowers demonstrate higher efficiency working on the rowing ergometer than working on water. The aim of the study was to determine the difference in efficiency levels and to verify its validity using a model based on fluid dynamics principles. Methods. A part of work done by rowers is lost in boat deformation and in the friction caused by the oarblades moving through the water. Load conditions for training on a rowing ergometer need to be increased by a certain quantity with respect to those set for on-water training. Results. Times were measured during on-water runs and rowing ergometer tests. Discussion and Conclusions. Times measured during on-water runs matched fairly well those calculated on rowing ergometer tests.

Nondestructive evaluation of hidden surface damage by means of stationary thermographic methods requires the construction of approximated solutions of a boundary identification problem for an elliptic equation. In this paper, we describe and test a regularized reconstruction algorithm based on the linearization of this class of inverse problems. The problem is reduced to an infinite linear system whose coefficients come from the Fourier discretization of the Robin boundary value problem for Laplace's equation.

We introduce a degenerate nonlinear parabolic-elliptic system, which describes the chemical aggression of limestones under the attack of SO_2, in high permeability regime. By means of a dimensional scaling, the qualitative behavior of the solutions in the fast reaction limit is investigated. Explicit asymptotic conditions for the front formation are derived.

We investigate the qualitative behavior of solutions to the initial-boundary value problem on the half-line for a nonlinear system of parabolic equations, which arises to describe the evolution of the chemical reaction of sulphur dioxide with the surface of calcium carbonate stones. We show that, both in the fast reaction limit and for large times, the solutions of this problem are well described in terms of the solutions to a suitable one phase Stefan problem on the same domain.

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are studied as graphs composed by arcs that meet at some nodes, corresponding to junctions, which play a key-role. Indeed interactions occur at junctions and there the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which processes each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

We study the asymptotic time behavior of global smooth solutions to general entropy, dissipative, hyperbolic systems of balance laws in m space dimensions, under the Shizuta-Kawashima condition. We show that these solutions approach a constant equilibrium state in the L p -norm at a rate O(t -(m/2)(1-1/ p) ) as t -> ? for p ? [min{m, 2}, ?]. Moreover, we can show that we can approxi- mate, with a faster order of convergence, the conservative part of the solution in terms of the linearized hyperbolic operator for m >= 2, and by a parabolic equa- tion, in the spirit of Chapman-Enskog expansion in every space dimension. The main tool is given by a detailed analysis of the Green function for the linearized problem.

An application in cultural heritage is introduced. Wavelet decomposition and Neural Networks like virtual sensors are jointly used to simulate physical and chemical measurements in specific locations of a monument. Virtual sensors, suitably trained and tested, can substitute real sensors in monitoring the monument surface quality, while the real ones should be installed for a long time and at high costs. The application of the wavelet decomposition to the environmental data series allows getting the treatment of underlying temporal structure at low frequencies. Consequently a separate training of suitable Elman Neural Networks for high/low components can be performed, thus improving the networks convergence in learning time and measurement accuracy in working time.

A shear-improved Smagorinsky model is introduced based on recent results concerning shear effects in wall-bounded turbulence by Toschi et al. (2000). The Smagorinsky eddy-viscosity is modified subtracting the magnitude of the mean shear from the magnitude of the instantaneous resolved strain-rate tensor. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at two different Reynolds numbers. First comparisons with the dynamic Smagorinsky model and direct numerical simulations, including mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition of being physically sound, has a low computational cost and possesses a high potentiality of generalization to more complex non-homogeneous turbulent flows.

A multiscale model for the evolution of the velocity gradient tensor in turbulence is proposed. The model couples ‘‘restricted Euler’’ (RE) dynamics describing gradient self-stretching with a cascade model allowing energy exchange between scales. We show that inclusion of the cascade process is sufficient to regularize the finite-time singularity of the RE dynamics. Also, the model retains geometrical features of real turbulence such as preferential alignments of vorticity and joint statistics of gradient tensor invariants. Furthermore, gradient fluctuations are non-Gaussian, skewed in the longitudinal case, and derivative flatness coefficients are in good agreement with experimental data.

We derive the pair correlation function of spatial Hawkes processes and discuss its connections with the Bartlett spectrum and other summary statistics.

For a risk process with reserve dependent premium rate, we study sample path large deviations and provide a fast simulation procedure to estimate the corresponding ruin probability.

We prove scalar and sample path large deviations principles for Poisson cluster processes and apply the results to Hawkes processes.