A 'temporal analogue' of the standard Poynting-Robertson effect is analyzed as induced by a dust of particles (instead of a gas of photons) surrounding a Schwarzschild black hole. Test particles inside this cloud undergo acceleration effects due to the presence of a friction force, so that the fate of their evolution can be completely different from the corresponding geodesic motion.

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.

The precession of a test gyroscope along unbound equatorial plane geodesic orbits around a Kerr black hole is analyzed with respect to a static reference frame whose axes point towards the "fixed stars." The accumulated precession angle after a complete scattering process is evaluated and compared with the corresponding change in the orbital angle. Limiting results for the nonrotating Schwarzschild black hole case are also discussed.

We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing quantitative central limit theorems.

The precession of a test gyroscope along stable bound equatorial plane orbits around a Kerr black hole is analyzed, and the precession angular velocity of the gyro's parallel transported spin vector and the increment in the precession angle after one orbital period is evaluated. The parallel transported Marck frame which enters this discussion is shown to have an elegant geometrical explanation in terms of the electric and magnetic parts of the Killing-Yano 2-form and a Wigner rotation effect.

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.

The development of high-efficiency porous catalyst membranes critically depends on our understanding of where the majority of the chemical conversions occur within the porous structure. This requires mapping of chemical reactions and mass transport inside the complex nanoscale architecture of porous catalyst membranes which is a multiscale problem in both the temporal and spatial domains.

Premixed combustion modes in compression ignition engines are studied as a promising solution to meet fuel economy and increasingly stringent emissions regulations. Nevertheless, PCCI combustion systems are not yet consolidated enough for practical applications. The high complexity of such combustion systems in terms of both air-fuel charge preparation and combustion process control requires the employment of robust and reliable numerical tools to provide adequate comprehension of the phenomena.

In this work a Discrete Boltzmann Model for the solution of transcritical 2D shallow water flows is presented and validated. In order to provide the model with transcritical capabilities, a particular multispeed velocity set has been employed for the discretization of the Boltzmann equation. It is shown that this particular set naturally yields a simple and closed procedure to determine higher order equilibrium distribution functions needed to simulate transcritical flow.