For the effective operation of sonar systems mounted inside the bulb of fast ships, it is important to reduce all the possible noise and vibration sources that radiate noise and interfere with sonar sensor response. In particular, pressure fluctuations induced by turbulent boundary layers on the sonar dome surface represent the major source of self-noise for on-board sensors. Reliable calculations of structural vibrations and noise radiated inside the dome require valid statistical descriptions of wall pressure fluctuations beneath the turbulent boundary layer.

Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic 'hair' that must be shed before final collapse.

We raise the analytical knowledge of the eccentricity expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the e(2) and e(4) contributions, and up to the 4th post-Newtonian order for the higher eccentricity contributions through e(20). We convert this information into an analytical knowledge of the effective-one-body radial potentials (d) over bar (u), p(u) and q(u) through the 9.5th post-Newtonian order. We find that our analytical results are compatible with current corresponding numerical self-force data.

Within the theoretical framework of the numerical stability analysis for the Volterra integral equations, we consider a new class of test problems and we study the long-time behavior of the numerical solution obtained by direct quadrature methods as a function of the stepsize. Furthermore, we analyze how the numerical solution responds to certain perturbations in the kernel.

We present the first analytic computation of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in eccentric equatorial orbit around a spinning black hole. Our results give the redshift contributions that mix eccentricity and spin effects, through second order in eccentricity, second order in spin parameter, and the eight-and-a-half post-Newtonian order.

We consider Detweiler's redshift variable z for a nonspinning mass m(1) in circular motion (with orbital frequency Omega) around a nonspinning mass m(2). We show how the combination of effective-one-body (EOB) theory with the first law of binary dynamics allows one to derive a simple, exact expression for the functional dependence of z on the (gauge-invariant) EOB gravitational potential u = (m(1) + m(2))/R.

The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes.

In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.

Numerical optimisation of a ship hull requires, like every shape design optimisation problem, the definition of a parametric expression of the object to be deformed. In this phase, some decisions are taken regarding the shape variability and the portion of the hull to be modified: the parameterisation of the hull is problem-dependent, with implications from the performances to be optimised (objective functions), and the right choice is not easy.