The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries or quasars can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus fit the data of QPOs observed in the well known microquasars as well as active galactic nuclei (AGNs) in the framework of the model of geodesic oscillations of Keplerian disks modified for the epicyclic oscillations of spinning test particles orbiting Kerr BHs. We show that the modified geodesic models of QPOs can explain the observational fixed data from the microquasars and AGNs but not for all sources. We perform a successful fitting of the high frequency QPOs models of epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models, and discuss the corresponding constraints of parameters of the model, which are the spin of the test particle, mass and rotation of the BH.

We are fitting dynamics of electrically neutral hot-spot orbiting around Sagittarius A* (Sgr A*) source in Galactic center, represented by various modifications of the standard Kerr black hole (BH), to the three flares observed by the GRAVITY instrument on May 27, July 22, July 28, 2018. We consider stationary, axisymmetric, and asymptotically flat spacetimes describing charged BHs in general relativity (GR) combined with nonlinear electrodynamics, or reflecting the influence of dark matter (DM), or in so called parameterized dirty Kerr spacetimes, and test them using the hot-spot data. We show that the orbital frequencies as well as positions of the hot-spots orbiting the considered BHs fit the observed positions and periods of the flare orbits, and give relevant constraints on the parameters of the considered BH spacetimes and the gravity or other theories behind such modified spacetimes.

$G$-symplectic general linear methods are designed to approximately preserve symplectic invariants for Hamiltonian systems. In this paper, the properties of $G$-symplectic methods are explored computationally and theoretically. Good preservation properties are observed over long times for many parameter ranges, but, for other parameter values, the parasitic behavior, to which multivalue methods are prone, corrupts the numerical solution by the growth of small perturbations. Two approaches for alleviating this effect are considered. First, compositions of methods with growth parameters of opposite signs can be used to cancel the long-term effect of parasitism. Second, methods can be constructed for which the growth parameters are zero by design. Each of these remedies is found to be successful in eliminating parasitic behavior in long-term simulations using a variety of test problems.

A numerical approach basing on friction and lubrication analysis has been developed to determine the creep at cam/roller interface in end pivoted roller finger follower valve train. The kinematic and dynamic analysis at the geometrical mating surfaces of cam and roller follower has been carried out to predict the required instantaneous motion parameters and normal loading whereas the oil film thickness is determined using lubrication analysis. The tangential forces have been computed precisely using elastohydrodynamic and mixed lubrication concept for a complete cam cycle. At low camshaft operating speeds, the creep proves to be low whereas the creep increases significantly under the influence of high tangential loading at higher operating speeds.

Propagation characteristics (resonances, propagation regions, and cutoffs) of ordinary waves (perpendicularly propagating electromagnetic waves) are studied in a relativistic electron plasma by using the kinetic model. The dispersion relation for the ordinary mode (O-mode) in a relativistic electron plasma is investigated by employing the Maxwell-Boltzmann-Jüttner distribution function. As the integration in the relativistic dispersion relation cannot be done analytically so an approximated value is obtained using the trapezoidal rule. Various modes of propagation for the ordinary waves are observed for each harmonic number n due to the relativistic effects defined by the value η = m c 2 k B T e . We also observe that the high-temperature relativistic plasma environment is more transparent for the O-mode as compared to weakly relativistic and non-relativistic plasma environments. Moreover, the cutoff points are shifted to lower values in the relativistic limit.