Within the framework of the Lorentz-violating $(3{+}1)$-dimensional extended electrodynamics including the Lorentz-violating CPT-odd Chern-Simons term, we consider the electromagnetic field between two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one calculated in [1] and based on wrong equations of motion. Compared with the experimental data, our result places a constraint on the absolute value of the Chern-Simons term.
Show AbstractThe holomorphic function $h$ is constructed such that $hhz=z!$; this function is interpreted as square root of Factorial.
Show AbstractA normalized shallow water equation system is constructed based on a normalized Navier-Stokes system and the numerical algorithm of its solution is suggested. The test Riemann problem demonstrates the possibilities of the proposed numerical algorithm.
Show AbstractThe phase structure of the 2-dimensional Gross-Neveu model is studied in variables of the quark number and isospin chemical potentials at zero temperature in the limit of a large number of field components ${N_c\to\infty}$.
Show AbstractIt is shown that, under the action of a perturbation with a continuous frequency spectrum, the rate of the energy diffusion of a quantum oscillator is described by an expression that formally follows from the Fermi golden rule, even when the conditions of the validity of this rule are violated, that is, in the parameter range where the transition rate is comparable to the frequency of transition between the system levels or exceeds it. This circumstance provides the quantum-classical correspondence for the energy diffusion rate in the quasi-classical domain.
Show AbstractNumerical analysis of different configurations of a microscope based on evanescent wave trans- formation using total internal reflection was carried out using the discrete sources method.
Show AbstractStudying the interaction mechanism between gamma-quanta and atomic nuclei in the giant dipole resonance energy region gives us significant information about atomic nuclei. A large number of experiments for studying giant dipole resonance structure were accomplished using bremsstrahlung gamma-quanta. In such experiments cross sections of interactions are retrieved from reaction yields. To retrieve cross sections one needs to know the shape of the bremsstrahlung spectrum and to choose the optimal characteristics of the bremsstrahlung target. The purpose of this article is to choose the optimal characteristics of the bremsstrahlung target for experiments in the energy region $E<30$ MeV. The analysis that was carried out based on numerical simulation showed that the optimal bremsstrahlung target consists of two parts. The first part is a tungsten plate 2.5 mm thick. The second part is aluminum plate 3 cm thick.
Show AbstractThe physical properties of a new modification of RF discharge-hybrid RF discharge (HRFD)-are studied experimentally. A HRFD is sustained by both the vortical RF electric field and the potential one generated by the inductive and capacitive channels of the discharge. The inductive channel effect on the parameters of the space-charge electrode sheaths, which determine the capacitive component of the physical mechanism of a HRFD, is discussed.
Show AbstractThe process of generation of X-ray radiation formed during the free exit of a fast stream of water in a state of cavitation from a narrow channel was investigated both experimentally and theoretically. It was observed for the first time that the initial part of the stream and the outlet of the channel are the sources of intensive X-ray radiation (with an activity of 0.1 Cu), which is connected with the cavitation phenomena and the following excitation of shock waves. The frequency of the X-ray radiation depends on the composition of the radiating surface (water or the surface of the channel walls) and increases with the increase of the atomic number of the surface. The mechanism of radiation generation is connected with the influence of cavitation shock waves formed on the nearest interface (water-air, water-metal, metal-air, air-metal, etc.).
Show AbstractThe effect of quantum confinement formed by Ag nanoclusters on the self-organization of Cs adatoms on Ag(111) was studied. The existence of allowed and forbidden zones was found for the diffusion motion of Cs adatoms near and on top of the clusters. The formation of the orbits of an adatom’s motion was demonstrated for self-organization process in a Cs adatom ensemble near and on top of the clusters.
Show AbstractThe energy levels of the valence electrons of free ions with completely filled electron shells are analyzed. A linear correlation between term energies $E_{nl}$ and quantum defects $dn_{nl}$ is assumed to exist at constant values of orbital quantum numbers and ion charges for the Li, Na, Cu, Ag, and Au rows. The empirical dependence of quantum defects $dn_{nl}$ on the principle quantum number $n$ is found. It can be used to estimate unknown term energies. It is also demonstrated that the linear dependences of the smooth nonlocal model pseudopotential parameter $A_{nl}$ of free ions on the term energy $E_{nl}$ is the result of their linear dependences on quantum defects $dn_{nl}$.
Show AbstractThis paper discusses patterns in the distribution of Centaurs, scattered disks, and Kuiper belt objects according to the semi-major axes, eccentricities and inclinations of their orbits. Over half of them are found to move in resonant orbits and these were predicted earlier. An interpretation is given for the divergence of the maximum in the observed semi-major axis distribution with an exact orbital resonance determined within the classical three-body problem.
Show AbstractThe reflection of a wave of finite amplitude from a curvilinear unsteady shock wave has been analyzed. A formula connecting reflected wave parameters with that of the incident wave, curvature and shock wave intensity has been obtained in closed form.
Show AbstractA ring artefact suppression algorithm in x-ray tomography is proposed and allows one to process input data in real time. The algorithm is based on methods of the theory of inverse and ill-posed problems. Its numerical implementation uses minimisation of the smoothing Tikhonov’s functional with the conjugate gradient method.
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