We study the motion of test particles in the metric of a localized and slowly rotating astronomical source, within the framework of linear gravitoelectromagnetism, grounded on a Post-Minkowskian approximation of general relativity. Special attention is paid to gravitational inductive effects due to time-varying gravitomagnetic fields. We show that, within the limits of the approximation mentioned above, there are cumulative effects on the orbit of the particles either for planetary sources or for binary systems. They turn out to be negligible.

We show that causality violation in a Kerr naked singularity spacetime is constrained by the existence of (radial) potential barriers. We extend to the class of vortical non-equatorial null geodesics confined to $$\theta $$? $$=$$= constant hyperboloids (boreal orbits) previous results concerning timelike ones (Calvani et al. in Gen Rel Gravit 9:155, 1978), showing that within this class of orbits, the causality principle is rigorously satisfied.

In the present work the simulation of water impacts is discussed. The investigation is mainly focused on the energy dissipation involved in liquid impacts in both the frameworks of the weakly compressible and incompressible models. A detailed analysis is performed using a weakly compressible Smoothed Particle Hydrodynamics (SPH) solver and the results are compared with the solutions computed by an incompressible mesh-based Level-Set Finite Volume Method (LS-FVM). Impacts are numerically studied using single-phase models through prototypical problems in 1D and 2D frameworks.

The features of equatorial motion of an extended body in Kerr spacetime are investigated in the framework of the Mathisson-Papapetrou-Dixon model. The body is assumed to stay at quasiequilibrium and respond instantly to external perturbations. Besides the mass, it is completely determined by its spin, the multipolar expansion being truncated at the quadrupole order, with a spin-induced quadrupole tensor. The study of the radial effective potential allows us to analytically determine the innermost stable circular orbit shift due to spin and the associated frequency of the last circular orbit.

An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the worldline of the body are essential tools to investigate both geometrical and physical properties of the tidal interaction.

We study the behavior of massless Dirac particles in the vacuum C-metric spacetime, representing the nonlinear superposition of the Schwarzschild black hole solution and the Rindler flat spacetime associated with uniformly accelerated observers. Under certain conditions, the C-metric can be considered as a unique laboratory to test the coupling between intrinsic properties of particles and fields with the background acceleration in the full (exact) strong-field regime.

The generation of complex vorticity pattern in aft-finocyl solid rocket motors is inves- tigated in this paper by means of full-3D ILES CFD simulations with a high-order/low- dissipation class of centered numerical schemes with oscillation control and an immersed boundary treatment of the propellant grain surface, treated with a level-set approach. The development of vortical/shear structures is observed both at the motor axis, immediately downstream the igniter and across the finocyl region and in the submergence region.

Based on a new multiplication formula for discrete multiple stochastic integrals with respect to non-symmetric Bernoulli random walks, we extend the results of Nourdin et al. (2010) on the Gaussian approximation of symmetric Rademacher sequences to the setting of possibly non-identically distributed independent Bernoulli sequences. We also provide Poisson approximation results for these sequences, by following the method of Peccati (2011).

A sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz-Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces.