On the Relativistic Harmonic Oscillator

In view of interest in relativistic harmonic oscillations in media, through which the speed of light is orders of magnitude smaller than in vacuum, the solution of the equation of motion is analyzed in the extreme- and weak-relativistic limits. Using scaled variables, it is shown rigorously how the equation of motion exhibits the characteristics of a boundary-layer problem in the extreme-relativistic limit: The solution differs from a sharp asymptotic pattern only around the turning points of oscillations over a vanishingly small fraction of the period. The sharp asymptotic pattern of the solution is a saw-tooth composed of linear segments. The velocity profile tends to a periodic step function and the phase-space plot tends to a rectangle. An expansion of the solution in terms of a small parameter that measures the proximity to the limit (v/c) → 1 yields an excellent approximation for the solution throughout the whole period of oscillations. In the weak-relativistic limit the same approach yields an approximation to the solution that is significantly better than in traditional asymptotic expansion procedures.

Atmospheric Modes Excited by the 2021 August Eruption of the Fukutoku-okanoba Volcano, Izu-bonin Arc, Observed as Harmonic Oscillations of QZSS Total Electron Conte

Continuous Plinian eruptions of volcanoes often excite atmospheric resonant oscillations with several distinct periods of a few minutes. We detected such harmonic oscillations excited by the 2021 August eruption of the Fukutoku-Okanoba volcano, a submarine volcano in the Izu-Bonin arc, in ionospheric total electron content (TEC) observed from global navigation satellite system (GNSS) stations deployed on three nearby islands, Chichijima, Hahajima, and Iwojima. Continuous records with the geostationary satellite of Quasi-Zenith Satellite System (QZSS) presented four frequency peaks of such atmospheric modes. The harmonic TEC oscillations, started at ~5:16 UT, exhibited an unprecedented large amplitude but decayed in a few hours.

In Situ Consolidation of Thermoplastic Prepreg by Generating Harmonic Oscillations on the Consolidation Roller

Automation technologies such as Automated Fiber Placement (AFP) or Automated Tape Laying (ATL) are widely used in the aerospace industry today. However, these processes can still be further improved for higher productivity. Fiber-reinforced plastics allow the production of components with extremely high specific strength and stiffness. Regarding the automated manufacturing processes, the thermoplastic tape placement offers efficiency improvements compared to the nowadays more commonly used thermoset tape placement, especially through the substitution of the expensive and time-consuming autoclave process. The consolidation of thermoplastic Prepregs is achieved with an elastic or rigid roller according to the current state of the art. The Prepregs must be consolidated precisely on the substrate or on top of each other. The most important process parameters for high-quality laminate structure with low porosity are the control of heat source, consolidation force, consolidation roll speed, and tape tension. The efficiency of the AFP process can generally be improved by increasing the speed of the consolidation roller. By increasing the speed of the consolidation roller, porosity is increased and mechanical properties of the laminate are reduced significantly due to the short contact time between consolidation roller and Prepregs. This study investigates a process that can reduce these challenges by increasing the contact time and force duration of the consolidation roller on the Prepregs. The consolidation roller in this study is additionally to be driven by the harmonic oscillations. The new method allows the consolidation roller to oscillate forward and backward during the fiber placement process. This creates another force vector in addition to the compressive force of the consolidation roller and increases the bonding strength between the layers.

Research of oscillation mode in automated pulsed eddy current testing systems

The formation and analysis of eddy current probe signals obtained in pulsed excitation mode is considered. The proposed method of implementing pulsed eddy current testing with the formation of attenuating harmonic oscillations is more resistant to the effects of noise and interference that accompany the process of inspected object parameters evaluation. The equivalent scheme of the system “test object–eddy current probe” is developed and analyzed. The obtained mathematical model of the eddy current probe signals allowed proposing the natural frequency and the attenuation as informative signals parameters, which are determined from signals phase and amplitude characteristics. Developed algorithm and the proposed methodology was implemented for evaluation of eddy current signals parameters and related characteristics of testing objects. This method was experimentally verified on a series of different test specimens. The obtained results confirm the possibility to apply the proposed informative signals to solve some problems concerned with automated eddy current testing. The formation and analysis of eddy current probe signals obtained in pulsed excitation mode are considered. The proposed method of implementing pulsed eddy current testing with the formation of attenuating harmonic oscillations is more resistant to the effects of noise and interference that accompany the process of automated eddy current testing. The equivalent scheme of the system “test object–eddy current probe” is developed and analyzed. The obtained mathematical model of the eddy current probe signals allows proposing the natural frequency and the attenuation as informative signals parameters, which are determined from signal phase and amplitude characteristics. Methods of increasing the accuracy of determining the eddy current probe signals attenuation and frequency using trends of signals phase and amplitude characteristics are considered. The proposed signal processing method was verified by modeling the process of determining the eddy current probe signals attenuation and the frequency from the signal with Gaussian noise. Algorithmic and software were developed based on the simulation results and the proposed improved methodology was implemented for determining signals parameters and related parameters and characteristics of testing objects.

Studying the interaction of a reservoir with an ideal compressible fluid with an elastic half-space

We solve in a flat formulation the problem of harmonic oscillations for a basin with an ideal compressible fluid on an elastic half-space exposed to a localized surface vibration load. The problem reduces to an integral equation (IE) of the first kind for the amplitude of the contact hydrodynamic pressure with a kernel that depends on the difference and the sum of arguments. The IE was solved by the factorization method. A semi-analytical method is presented for determining the main parameters of the contact interaction in hydroelastic systems «liquid-soil» taking into account the effect of natural and man-made vibration loads on them. This makes it possible to identify the conditions for the occurrence of dynamic modes that are dangerous for the construction integrity and to estimate their frequencies range depending on defining characteristics of the system.

Dynamics of Magnetized and Magnetically Charged Particles around Regular Nonminimal Magnetic Black Holes

The present paper is devoted to the study of the event horizon properties of spacetime around a regular nonminimal magnetic black hole (BH), together with dynamics of magnetized and magnetically charged particles in the vicinity of the BH. It is shown that the minimum value of the outer horizon of the extreme charged BH increases with the increase in coupling parameter. It reaches its maximum value of 1.5M when q→∞, while the maximal value of the BH charge decreases and tends toward zero. We also present a detailed analysis of magnetized particles’ motion around a regular nonminimal magnetic black hole. The particle’s innermost circular stable orbits (ISCOs) radius decreases as the magnetic charge and the parameter β increase and the coupling parameter of Yang–Mills field causes a decrease at the values of the magnetic charge near to its maximum. We show that the magnetic charge can mimic the spin of a rotating Kerr black hole up to the value of a=0.7893M, providing the same value for an ISCO of a magnetized particle with the parameter β=10.2 when the coupling parameter is q=0. Moreover, Lyapunov exponents, Keplerian orbits and harmonic oscillations of magnetized particles motion are also discussed.

ANALYTICAL SUBSTANTIATION OF THE RATIONAL MODE OF VIBRATION IMPACT ON THE HONEYCOMB

Проблема и цель. Заключается в том, чтобы теоретически обосновать режим виброочистки воскового сырья, при котором происходит отделение частиц воска от перговых гранул. Методология. В результате вибрационного воздействия на соты с пергой действует вынуждающая сила, которая должна быть больше силы трения между перговой гранулой и восковой основой ячейки сота, для того чтобы гранулы перги отделились. Увеличить силу, действующую на гранулу, можно увеличением либо амплитуды, либо частоты колебаний. Управление частотой является более рациональным по сравнению с управлением амплитудой. Для расчета частоты и амплитуды вынуждающей силы используются следующие данные: 2h – толщина рамки с сотами, h = 0,01м; a – длина рамки с сотами, a = 0,3м; b – ширина рамки с сотами, b = 0,4м; ρ – плотность, ρ = 326 кг/м³; N – натяжение; g – ускорение свободного падения, g = 9,81 м/c²; E – модуль упругости, E = 206000 МПа; G – модуль сдвига, G = 74000 Мпа; ν – коэффициент Пуассона, ν = 0,3; υ – коэффициент вязкости. Моделирование исследуемого процесса выполняется в среде Mathcad встроенными средствами статистической обработки. При этом осуществляется математическое моделирование в определенных рамках технологического процесса. Результаты. При воздействии на рамки с сотами, в которых есть перга, гармоническими колебаниями, возникает резонанс на малых частотах, что помогает ускорять процесс очистки. Заключение. Для наиболее качественной очистки воскового сырья от примесей необходимо воздействие вибрации с частотой в диапозоне от 14 до 16 Гц. При этом возникает резонанс, который уменьшает затраты энергии на данный процесс. Problem and purpose. The aim of the study is to theoretical justify the mode of vibration cleaning of wax feedstock, in which wax particles are separated from beads. Methodology. As a result of the vibration action, a force force is exerted on the feather honeycombs, which must be greater than the frictional force, in order for the feather pellets to separate from the wax cells of the honeycombs. To calculate the frequency and amplitude of the force, the following data 2h are used - the thickness of the frame with cells, h = 0.01m; a is the length of the frame with cells, a = 0.3m; b is the width of the frame with cells, b = 0.4m; ρ - density, ρ = 326 kg/m3 ; N - tension; g - acceleration of free fall, g = 9.81 m/c2 ; E - modulus of elasticity, E = 206000 MPa; G - shear modulus, G = 74000 MPa; v is Poisson's coefficient, v = 0.3; υ - viscosity coefficient. Results. When acting on frames with cells in which there is a feather, harmonic oscillations, resonance at low frequencies occurs, which helps to accelerate the cleaning process. Conclusion. For the highest quality purification of wax raw materials from impurities, vibration is necessary with a frequency in the diapozone from 14 to 16. At the same time, a resonance occurs that reduces the energy consumption for this process.

Unveiling the structure and dynamics of peeling mode in quiescent high-confinement tokamak plasmas

Quiescent high-confinement mode plasmas with edge-harmonic oscillations do not exhibit the explosive instabilities associated with edge-localized modes. Instead, an additional means of enhanced transport is considered to maintain the plasma edge under conditions just below the boundary of the peeling mode instability. Although the potential of the peeling mode has been widely recognized in plasma physics, no direct evidence for this mode has been revealed previously because decisive diagnostics were lacking. Herein, we report evidence of the structure and dynamical steady state of peeling mode in quiescent high-confinement mode. Edge-harmonic oscillations are dominated by fundamental mode at both the low- and high-field sides. Edge perturbations are confirmed to have kink parity and exhibit the frozen-in-condition predicted by linear stability analysis. The envelope signal of the fundamental mode exhibits repeated cycles of growth and damping in association with minor changes in the edge gradient. Results from this study are quantitatively consistent with limit-cycle-oscillation model.