A numerical study of turbulence seeded with light particles is presented. We analyze the statistical properties of coherent, small-scale structures by looking at the trapping events of light particles inside vortex filaments. We study the properties of particles attracting set, measuring its fractal dimension and the probability that the separation between two particles remains within the dissipative scale, even for time lapses as long as the large-scale correlation time, T(L).

We compute the continuum thermohydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed by Sbragaglia [J. Fluid Mech. 628, 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible Fourier-Navier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-Beacutenard compressible systems and against direct comparison with finite-difference schemes.

The definition of the Simon tensor, originally given only in Kerr spacetime and associated with the static family of observers, is generalized to any spacetime and to any possible observer family. Such generalization is obtained by a standard '3 + 1' splitting of the Bianchi identities, which are rewritten here as a 'balance equation' between various spatial fields, associated with the kinematical properties of the observer congruence and representing the spacetime curvature.

The (first-order) gravitational self-force correction to the spin-orbit precession of a spinning compact body along a slightly eccentric orbit around a Schwarzschild black hole is computed through the ninth postNewtonian order and to second order in the eccentricity, improving recent results by Kavanagh et al. [Phys. Rev. D 96, 064012 (2017)]. We show that our higher-accurate theoretical estimates of the spin precession exhibits an improved agreement with corresponding numerical self-force data.

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts.

The energy content of (exact) electromagnetic and gravitational plane waves is studied in terms of super-energy tensors (the Bel, Bel-Robinson and the-less familiar-Chevreton tensors) and natural observers. Starting from the case of single waves, the more interesting situation of colliding waves is then discussed, where the nonlinearities of the Einstein's theory play an important role. The causality properties of the super-momentum four vectors associated with each of these tensors are also investigated when passing from the single-wave regions to the interaction region.

We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the z axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism).

Twisted gravitational waves (TGWs) are nonplanar waves with twisted rays that move along a fixed direction in space. We study further the physical characteristics of a recent class of Ricci-flat solutions of general relativity representing TGWs with wave fronts that have negative Gaussian curvature. In particular, we investigate the influence of TGWs on the polarization of test electromagnetic waves and on the motion of classical spinning test particles in such radiation fields.