Physics, Volume 1, Issue 2 (September 2019) – 7 articles

We study Gaussian wave beam and wave packet types of solutions to the linearized cold plasma system in a toroidal domain (tokamak). Such solutions are constructed with help of Maslov’s complex germ theory (short-wave or semi-classical asymptotics with complex phases). The term “semi-classical” asymptotics is understood in a broad sense: asymptotic solutions of evolutionary and stationary partial differential equations from wave or quantum mechanics are expressed through solutions of the corresponding equations of classical mechanics. This, in particular, allows one to use useful geometric considerations. The small parameter of the expansion is $h=\lambda /2\pi L$ where $\lambda$ is the wavelength and L the dimension of the system. In order to apply the asymptotic algorithm, we need this parameter to be small, so we deal only with high-frequency waves, which are in the range of lower hybrid waves used to heat the plasma. The asymptotic solution appears to be a Gaussian wave packet divided by the square root of the determinant of an appropriate Jacobi matrix (“complex divergence”). When this determinant is zero, focal points appear. Our approach allows one to write out asymptotics near focal points. We also claim that this approach is very practical and leads to formulas that can be used for numerical simulations in software like Wolfram Mathematica, Maple, etc. For the particular case of high-frequency beams, we present a recipe for constructing beams and packets and show the results of their numerical implementation. We also propose ideas to treat the more difficult general case of arbitrary frequency. We also explain the main ideas of asymptotic theory used to obtain such formulas. Full article

Rutile TiO₂, VO₂, CrO₂, MnO₂, NbO₂, RuO₂, RhO₂, TaO₂, OsO₂, IrO₂, SnO₂, PbO₂, SiO₂, and GeO₂ (space group P4₂/mnm) were explored for thermal shock resistance applications using density functional theory in conjunction with acoustic phonon models. Four relevant thermomechanical properties were calculated, namely thermal conductivity, Poisson’s ratio, the linear coefficient of thermal expansion, and elastic modulus. The thermal conductivity exhibited a parabolic relationship with the linear coefficient of thermal expansion and the extremes were delineated by SiO₂ (the smallest linear coefficient of thermal expansion and the largest thermal conductivity) and PbO₂ (vice versa). It is suggested that stronger bonding in SiO₂ than PbO₂ is responsible for such behavior. This also gave rise to the largest elastic modulus of SiO₂ in this group of rutile oxides. Finally, the intrinsic thermal shock resistance was the largest for SiO₂, exceeding some of the competitive phases such as Al₂O₃ and nanolaminated Ti₃SiC₂. Full article

We discuss the possibility of the transition magnetic moments (TMM) between the neutron n and its hypothetical sterile twin “mirror neutron” $n^{\prime }$ from a parallel particle “mirror” sector. The neutron can be spontaneously converted into mirror neutron via the TMM (in addition to the more conventional transformation channel due to $n-n^{\prime }$ mass mixing) interacting with the magnetic field $\mathbf{B}$ as well as with mirror magnetic field ${\mathbf{B}}^{\prime }$. We derive analytic formulae for the average probability of $n-n^{\prime }$ conversion and consider possible experimental manifestations of neutron TMM effects. In particular, we discuss the potential role of these effects in the neutron lifetime measurement experiments leading to new, testable predictions. Full article

The proof of the Abramovsky—Gribov—Kancheli (AGK) theorem for black hole physics is given. Based on the AGK relations, a formula for the luminosity of a black hole as a function of the mass of the black hole is derived. The correspondence to experimental data is considered. It is shown that the black holes of the galaxies NGC3842 and NGC4889 do not differ from those of the other galaxies. Full article

The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann’s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation–fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained. Full article

Gravitational Waves (GW) from coalescence of a Binary Neutron Star (BNS) and its accompanying short Gamma-Ray Burst (GRB) GW/GRB 170817A confirmed the presumed origin of these puzzling transients and opened up the way for relating properties of short GRBs to those of their progenitor stars and their surroundings. Here we review an extensive analysis of the prompt gamma-ray and late afterglows of this event. We show that a fraction of polar ejecta from the merger had been accelerated to ultra-relativistic speeds. This structured jet had an initial Lorentz factor of about 260 in our direction, which was $\mathcal{O}\left({10}^{\circ }\right)$ from the jet’s axis, and was a few orders of magnitude less dense than in typical short GRBs. At the time of arrival to circum-burst material the ultra-relativistic jet had a close to Gaussian profile and a Lorentz factor $\gtrsim 130$ in its core. It had retained in some extent its internal collimation and coherence, but had extended laterally to create mildly relativistic lobes—a cocoon. Its external shocks on the far from center inhomogeneous circum-burst material and low density of colliding shells generated slowly rising afterglows, which peaked more than 100 days after the prompt gamma-ray. The circum-burst material was somehow correlated with the merger. As non-relativistic outflows or tidally ejected material during BNS merger could not have been arrived to the location of the external shocks before the relativistic jet, circum-burst material might have contained recently ejected materials from resumption of internal activities, faulting and mass loss due to deformation and breaking of stars crusts by tidal forces during latest stages of their inspiral but well before their merger. By comparing these findings with the results of relativistic Magneto-Hydro-Dynamics (MHD) simulations and observed gravitational waves we conclude that progenitor neutron stars were most probably old, had close masses and highly reduced magnetic fields. Full article

The magnetic field created in proton–proton and nucleus–nucleus collisions at ultra-high energies are studied with models of point-like charges and hard sphere for distribution of the constituents for vacuum conditions. The various beam ions are considered from light to heavy nuclei at energies corresponding to the nominal energies of the proton beam within the projects of further accelerator facilities high-energy Large Hadron Collider (HE-LHC) and Future Circular Collider (FCC). The magnetic-field strength immediately after collisions reaches the value tens of GeV ${}^2$ , while in the approach with point-like charges, some overestimate the amplitude of the field in comparison with more realistic hard-sphere model. The absolute value of the magnetic field rapidly decreases with time and increases with growth of atomic number. The amplitude for $eB$ is estimated at level 100 GeV ${}^2$ to provide magnitude for quark–quark collisions at energies corresponding to the nominal energies of proton beams. These estimations are close to the range for onset of W boson condensation. Full article