This book focuses on advances in physics research. Chapter 1 reviews simple relationships of classical mechanics and describes new proposed methods for the slowdown, localization and trapping of various micro- and nanoparticles by means of external electromagnetic fields of fixed spatial configurations and controlled strength. Chapter 2 introduces a new physical principle based on old relational ideas, whose direct applications to the Newtonian theory leads to a modified theory of gravity in which the gravitational constant G is replaced by a homogeneous function of thefirst degree on the system’s configuration space. Chapter 3 is aimed at primordial black holes in the pre-inflationary era, their quantum-gravitational corrections, shifts of inflationary parameters, and other implications. Chapter 4 focuses on Lorentz-invariant equations for weak gravitational fields, as well as studies theflux and the energy density of the gravitationalfield. Chapter 5 studies the auroral oval of the northern lights during a moderate magnetic storm on the Sun using the method of directed gravitational mass spectroscopy, GMS. Chapter 6 introduces a theoretical framework for studying the dynamics of the elastic cross section and important parameters in nuclear physics that are calculated for the three and two-body systems using the Faddeev equations. Chapter 7 carries out a study on the production of heavy neutrons. Chapter 8 gives the exact analytical solutions for two Kawahara equations. Chapter 9 explores new families of the KdV equation. Chapter 10 provides an analytical solution to a Duffing equation coupled with a linear equation. Finally, in Chapter 11, gravitational over-the-horizon noise (GN) from oscillations of the NGH void, which, from time to time, ejecting preon clouds in the direction of baryonic matter, is examined.