We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced by us D. Bini and T. Damour, Phys. Rev. D 96, 104038 2017 PRVDAQ 10.1103/PhysRevD.96.104038, we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the effective one-body (EOB) Hamiltonian description of the dynamics of spinning binary systems.

We generalize to the Kerr spacetime existing self-force results on tidal invariants for particles moving along circular orbits around a Schwarzschild black hole. We obtain linear-in-mass-ratio (conservative) corrections to the quadratic and cubic electric-type invariants and the quadratic magnetic-type invariant in series of the rotation parameter up to the fourth order and through the ninth and eighth post-Newtonian orders, respectively. We then analytically compute the associated eigenvalues of both electric and magnetic tidal tensors.

We study tidal effects induced by a particle moving along a slightly eccentric equatorial orbit in a Schwarzschild spacetime within the gravitational self-force framework. We compute the first-order (conservative) corrections in the mass ratio to the eigenvalues of the electric-type and magnetic-type tidal tensors up to the second order in eccentricity and through the 9.5 post-Newtonian order. Previous results on circular orbits are thus generalized and recovered in a proper limit.

We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post-Newtonian expansions for the gauge invariant precession function along circular geodesics valid for an arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics.

The dynamics of a quasi two-dimensional isotropic droplet in a cholesteric liquid crystal medium under symmetric shear flow is studied by lattice Boltzmann simulations. We consider a geometry in which the flow direction is along the axis of the cholesteric, as this setup exhibits a significant viscoelastic response to external stress. We find that the dynamics depends on the magnitude of the shear rate, the anchoring strength of the liquid crystal at the droplet interface and the chirality.

We perform direct numerical simulations of three-dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective At wood number; the long-time growth is still self-similar, but no longer proportional to t(2) and depends on the singularity exponent c of the initial profile Delta T proportional to z(c). We show that universality is recovered when looking at the efficiency, defined as the ratio of the variation rates of the kinetic energy over the heat flux.

We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on a two-range pseudopotential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short-range repulsive interaction between species in the classical single-range model, a competing mechanism between the short-range attractive and midrange repulsive interactions is imposed within each species.

We present a boundary condition scheme for the lattice Boltzmann method that has significantly improved stability for modeling turbulent flows while maintaining excellent parallel scalability. Simulations of a three-dimensional lid-driven cavity flow are found to be stable up to the unprecedented Reynolds number Re = 5 x 10(4) for this setup. Excellent agreement with energy balance equations, computational and experimental results are shown. We quantify rises in the production of turbulence and turbulent drag, and determine peak locations of turbulent production.

Integral estimates for weak solutions to a class of Dirichlet problems for nonlinear, fully anisotropic, elliptic equations with a zero order term are obtained by symmetrization techniques. The anisotropy of the principal part of the operator is governed by a general n-dimensional Young function of the gradient which is not necessarily of polynomial type and need not satisfy the $\Delta_2$-condition.