Orbit Oscillations Research Articles

Dual effect of string cloud and dark matter halos on particle motions, shadows and epicyclic oscillations around Schwarzschild black holes

In this work, we study the particle dynamics, shadows and quasi-periodic oscillations around the Schwarzschild black hole with three different dark matter halos and string cloud parameters. The motion of particles is considered with the string cloud parameter α and investigated for massive and massless particles. The photon orbits and inner stable circular orbits of these black holes are obtained from the effective potential. The black hole shadows are calculated using three different dark matter halos. The shadow radius of these black holes increases compared to a pure Schwarzschild black hole for different values of the string cloud parameter. Further, quasi-periodic oscillations are also discussed in the current analysis. Our study examines how the radial profiles of orbital and radial harmonic oscillation frequencies change with the string cloud parameter. This study examines the major properties of test particle's quasi-periodic oscillations near stable circular orbits in the black hole equatorial plane. Our findings indicate that observational tests for black holes influenced by dark matter halos and cloud strings are also feasible and viable.

Measurements of total ozone content in the 4.7 µm region with a medium-resolution FTIR spectrometer and comparison with satellite data

The total ozone content (TOC) measurements results by the ground-based MR-32 instrument in 2015–2022 at the Obninsk station (55.11N; 36.60E) are presented. Solar radiation was measured by the FTIR spectrometer of medium resolution of 0.12 cm−1. Based on the analysis of the absorption spectra the relevant spectral intervals in the region of 4.7 microns were determined. The SFIT4 program was applied to retrieve total ozone content. A comparison of the results of TOC measurements by the MR-32 instrument with satellite data of OMPS, OMI, and SBUV(MOD) showed good agreement. The correlation coefficients are 0.93–0.97. According to spectral and cross-correlation wavelet analysis, ground and satellite oscillations with periods from 4 to 60 months occur of almost synchronously. The systematic discrepancies between daily average ground-based and satellite TO measurements are (−0.8 ± 3.6)%, (−0.2 ± 3.7)% and (−2 ± 5)% for OMPS, OMI and SBUV(MOD), respectively.

Enhanced magnetically coupled rotational piezoelectric energy harvesting based on tailored centrifugal distance

To tackle the issue of limited operating bandwidth encountered by energy harvesters in high-speed rotating contexts, this paper proposes a method for achieving rotational energy harvesting over a relatively high bandwidth through stabilizing high-energy orbit oscillations based on theoretically tailored centrifugal distance. The interaction between the cantilever beam tip permanent magnet and the fixed end magnet introduces nonlinear factors into the rotating piezoelectric energy harvesting system. By exploiting the non-linear matching relationship between the jump-down frequency under bistable condition and the rotational frequency of the external environment, the centrifugal distance theoretically derived is divided into five distinct conditions. Notably, when the centrifugal distance is in condition of 6.5 cm, optimal alignment and overlap are observed between the jump-down curve and the rotational frequency curve within the rotational frequency range of 40–80 rad s−1. Tailoring of different centrifugal distances across the five conditions is then explored and validated through simulations, including velocity profiles and energy harvesting capabilities. Finally, a rotating experimental platform was constructed and the experimental results validate that, at the theoretically tailored centrifugal distance of 6.5 cm, the rotating energy harvester achieves a peak power output of 127.4 μW within the effective bandwidth of 40–80 rad s−1. This study underscores the significance of tailoring centrifugal distance to stabilize high-energy orbit oscillations, thereby enhancing the energy harvesting potential of the device across a relatively wide range of external rotational frequencies.

Strong gravitational lensing, quasi-periodic oscillations and constraints from EHT observations for quantum-improved charged black hole

We investigate strong gravitational lensing by quantum-improved charged black holes characterized by an additional parameter denoted as ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}, in addition to the mass M and charge Q. Our findings reveal that when both the parameters Q/2M and ω/4M2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega /4M^2$$\\end{document} increase simultaneously, various astrophysical consequences, such as the deflection angle αD(u)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D(u)$$\\end{document} and angular image separation increase. Concurrently, the angular position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document}, relative magnification rmag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{mag}$$\\end{document}, and the time delay ΔT2,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta T_{2,1}$$\\end{document} between the first and second relativistic images also decrease with the growing values of the parameters Q/2M and ω/4M2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega /4M^2$$\\end{document}. It is also observed that the Einstein ring θ1E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _1^E$$\\end{document} for the quantum-improved charged black hole is more significant than those for Schwarzschild, quantum-improved Schwarzschild, and Reisner–Nordström black holes. As with supermassive black holes such as M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} and SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SgrA^*$$\\end{document}, it is observed that to be a viable astrophysical black hole, the EHT results constrain the parameter space (ω/4M2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega /4M^2$$\\end{document}, Q/2M). Remarkably, the EHT results for SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SgrA^*$$\\end{document} impose more stringent limits on the parameter space of quantum-improved charged black holes compared to those established by the EHT results forM87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document}. We investigate the radial profiles of orbital and radial harmonic oscillation frequencies as a function of the dimensionless coupling constants and black hole mass. The main characteristics of test particle quasi-periodic oscillations close to stable circular orbits in the black hole equatorial plane are also examined. We study the positioning of resonant radii in the background of quantum-improved charged black holes for high-frequency quasi-periodic oscillations models: warped disc (WD) models, relativistic precession (RP) and its types, and epicyclic resonance (ER) and its variants.

Characterization of magnetostrictive bi-stable rotational vibration energy harvester with integrated centrifugal effect

Rotational machinery is a common presence in dust still production, and the occurrence of operational failures in components like engines and turbine blades necessitates effective measures. To solve this challenge, remote structural health monitoring using energy harvesting and wireless sensors has been widely employed to realize self-powered sensing. This study proposes a magnet-induced bi-stable rotational energy harvester (REH), which utilizes the centrifugal effect to broaden the effective frequency bandwidth, enabling efficient energy harvesting in complex environments. A comprehensive mathematical model has been established to facilitate the dynamic characteristics of the bi-stable system, taking into account the centrifugal effect. The theoretical results demonstrate that the gap distance of magnetic configuration has great effects on the bi-stable system. Additionally, the centrifugal effect decided by the centrifugal radius and rotational speeds also affects the stable high-energy orbit oscillations. Furthermore, experimental results indicate that the proposed REH can effectively operate within the frequency range of 230–290 rpm, with a maximum RMS voltage of 780 mV and corresponding power of 4.35 mW. These findings validate the performance of the bi-stable magnetostrictive REH with the centrifugal effect and indicate its potential to effectively address the power supply challenges for wireless sensors. Overall, this study presents a promising solution for enhancing the energy harvesting performance of REH and also provides insights into the design of high-efficiency REH by magnet-induced nonlinearity and the centrifugal effect.

Motion of spinning particles around dynamic phantom AdS black holes

This work is devoted to discussing spinning particles’ motion in the surrounding dynamic phantom AdS Black hole (BH) with phantom scalar field k. The primary goal of this research is to differentiate between the effects of electric and magnetic charges on dynamic phantom AdS BH. The study analyzes the dependence of the innermost stable circular orbit (ISCO), responsible for interactions between charged particles and the external magnetic field, and observes the circular orbits of particles revolving around the compact object. It is also observed that as electric and magnetic charges increase, the ISCO radius decreases. Additionally, stability of orbit, Keplerian frequency, and harmonic oscillations of charged particles are also discussed. We also find the condition, electric and magnetic charges of the dynamic phantom AdS BH effect the energy of the center of mass with magnetized, electrically charged, and neutral particles due to the collision. Lastly, we discuss the accretion process and obtain generalized equations for the speed of sound cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c^2_{s}$$\\end{document} sec, 4-velocity u(r), energy density ρ(r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho (r)$$\\end{document} and mass (M˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\dot{M}}$$\\end{document}). We also plot these physical parameters against constant values of mass, electric and magnetic charges, and distinct values of state parameter ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} to study the accretion process. We observe that radial velocity and energy density of the fluid remain positive and negative, and the rate of change of mass is increased and decreased for stiff, dust, quintessence, and phantom-like fluid, respectively.

IMPACT OF HIGH RADIO FREQUENCY SATELLITE OSCILLATIONS ON INITIATING EARTHQUAKES

Advanced satellite technology is worse than all the disasters on Earth due to the lack of dynamic security. The study of earthquakes is the most innovative research of all man-made disasters - no doubt, but there are new horizons of wonder for the thoughtful. Earthquakes are increasing unexpectedly in different countries of the world. People of most countries are worried about sudden earthquakes, but no one is able to reveal the main secret of these earthquakes. Many are blaming nature for this earthquake. Through this survey the exact origin of the matter has been presented to the whole world with proper evidence. Research shows that climate criminals are misusing advanced satellite technology to cause these earthquakes. According to research, misuse of advanced satellite technology causes artificial earthquakes at specific GPS locations on Earth, resulting in severe damage to humans, animals, plants and other objects. The intensity of these earthquakes is so intense that everyone is surprised. Studies have shown that the misuse of satellite technology has caused massive damage in man-made technological earthquake at a particular tectonic plate and other disasters. Due to these sudden earthquake, human suffering increases, standing institutions are demolished, road communication systems are ruptured, crop lands and residential areas are destroyed, individuals lose their lives. The study revealed that artificial earthquakes are caused by sudden radio-waves and strong oscillations of variable magnitude anywhere on earth. The study also showed the climate criminals use various fake messages and wireless tracking to influence policy-makers, the public and the media, as can be doubted in this study, All citizens and administrations should be aware and vigilant to prevent the rise of earthquake terror. The research shows that using advanced satellite technology, earthquakes can be created in time on any tectonic plate on the Earth. Moreover, the question remains that when technology was not invented, but earthquakes occurred - which were natural. Humans now generate artificial oscillations at specific GPS locations through earthquake simulation coding by multiplying the magnetosphere of previous natural earthquakes. The study shows that the EMMAST (Earthquake Mitigation and Management through Advanced Satellite Technology) model will make disaster mitigation systems safer and more efficient, saving millions of lives. The study on earthquakes is unique with world- class scientific research, which will open many research gateways for future generations.

Correction of storage ring optics with an improved closed-orbit modulation method

We improved a previously proposed method of using closed-orbit modulation for linear optics and coupling correction. Instead of fitting individual closed orbits, the improved method decomposes the orbit oscillation data into two orthogonal modes and fits the amplitudes of the modes at all beam position monitors. While the original method is limited to process around tens to a hundred orbits, the improved method can process thousands of orbits, which are easily available when alternating-current waveforms are applied to the two modulating correctors. The method has been experimentally demonstrated on the National Synchrotron Light Source (NSLS)-II storage ring.

Beam-based reconstruction of the shielded quench-heater fields for the LHC main dipoles

Small orbit oscillations of the circulating particle beams have been observed immediately following quenches in the LHC’s superconducting main dipole magnets. Magnetic fields generated during the discharge into the quench heaters were identified as the cause. Since the resulting, shielded field inside the beam screen cannot be measured in-situ, the time evolution of the field has to be reconstructed from the measured beam excursions.In this paper, the field-reconstruction method using rotation in normalized phase space and the optimized fitting algorithm are described. The resulting rise times and magnetic field levels are presented for quench events that occurred during regular operation as well as for dedicated beam experiments. Finally, different approaches to model the shielding behavior of the beam screen are discussed.

Tunable stochastic resonance based on the optimization of centrifugal distance for rotation-induced energy harvesting

Energy harvesting from rotating systems has been developed into an important topic as a promising solution for realizing the powering applications of tire monitoring systems. Because of relatively narrow bandwidth of the efficiently operating response, this paper proposes a principle for optimizing the centrifugal distance for tuning frequency matching between stochastic resonance and the external rotation environments. It can minimize the negative effect of a low energy orbit owing to the optimally stabilized stochastic resonance, particularly over the low frequency range before high energy orbit oscillation. The centrifugal force caused by the behavior of rotation acting on the tip mass of the cantilever changes the equivalent stiffness of the cantilever and thus can tune the variation in the Kramers escape rate. Through the match-able relationship of a non-linear bitable system between the Kramers rate and the external rotation frequency, the expression of the optimally centrifugal distance can be solved by theoretical derivation and numerical analysis. The results of simulations and laboratory experiments simultaneously demonstrate that the centrifugal distance is tuned to be the optimal 6.45 cm as theoretically analyzed, and the effective bandwidth of energy harvesting can be stabilized from 30 rad s−1 to 50 rad s−1. While its maximum root mean square voltage can reach the value of 1.23 V corresponding to a harvesting average power of 45.55 μW, owing to the high matching relationship between stochastic resonance and external rotation frequencies. Thus, by the theoretical optimization of centrifugal distance, the frequency of stochastic resonance can be tuned for matching the externally rotating environments, and further improving the operating performance of rotating-induced energy harvesting.

Experimental investigation on flow-induced vibration control of flexible risers fitted with new configuration of splitter plates

Experimental investigations within the Reynolds number range of 2600–9100 were performed to examine the effectiveness of serrated splitter plates in controlling the flow-induced vibration (FIV) of flexible risers. Conventional splitter plates were arranged for contrast to highlight the unparalleled features of the new splitter plates. Bending strains of FIV responses were measured and converted into critical parameters of displacement, dominant frequency, oscillation orbit, suppression efficiency, and fatigue damage for analysis. Test results illustrate that for flexible risers with conventional or serrated splitter plates, a galloping phenomenon occurs at a low reduced velocity, and standing wave characteristics invariably dominate their FIV responses. As the reduced velocity varies increasingly, the conventional splitter plate triggers a continuous monotonous increase in the FIV amplitudes of controlled risers. However, owing to the phase difference in the interaction of the shear layers between proximal plates and distal plates, the FIV amplitudes of the risers fitted with serrated splitter plates start to stay constant virtually and then distinctly decline with appearing chaotic oscillation trajectories. Moreover, the control performance of serrated splitter plates with uniformly distributed serrations in alleviating FIV amplitudes is optimal at high reduced velocities; whereas excessively dense or sparse serrations can reduce FIV inhibition.

Design and numerical investigation of an ultra-wide bandwidth rolling magnet bistable electromagnetic harvester

To realize broadband energy harvesting at low-frequency excitation, this paper proposes a rolling magnet bistable electromagnetic harvester (RM-BEH) which utilizes the rolling motion of a magnetically levitated magnet. The dynamic model of the RM-BEH is established, based on which the output of the RM-BEH is predicted through electromagnetic induction combined with finite element analysis. By calculating the parameter region for monostable and bistable configurations, the broadband response characteristics of a bistable system with shallower potential wells are investigated. Results show that the RM-BEH could achieve interwell oscillation in the frequency range between 5.8 Hz and 22 Hz under sweep frequency excitation with a level of 0.5 g. Under constant frequency excitation, multiple vibrational patterns of the RM-BEH are presented and examined. To identify the multiple solutions, harmonic balance method results are presented, indicating that high-energy orbit oscillation can be achieved with appropriate initial conditions. Furthermore, the response of RM-BEH under Gaussian white noise and human motion excitations is considered and results indicate that the RM-BEH could travel across the potential wells easily to generate large output. In general, the broadband response characteristic under harmonic excitation and considerable output under human motion excitation demonstrate the excellent application foreground of the RM-BEH.

Natural orbitals for theab initiono-core configuration interaction approach

Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of such calculations is limited by the finite dimensions which are computationally feasible for the truncated many-body space. We therefore seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupation of low-lying orbitals, thus accelerating convergence in a configuration-interaction basis, while also possibly providing physical insight into the single-particle structure of the many-body wave function. We describe the implementation of natural orbitals in the NCCI framework and examine the nature of the natural orbitals thus obtained, the properties of the resulting many-body wave functions, and the convergence of observables. After taking ${}^{3}\mathrm{He}$ as an illustrative testbed, we explore aspects of NCCI calculations with natural orbitals for the ground state of the $p$-shell neutron halo nucleus ${}^{6}\mathrm{He}$.

Simulation of synchrotron radiation from electron beams affected by vibrations and drifts

This paper presents results of simulations of synchrotron radiation from electron beams affected by instabilities in position and angle at the source point. The goal of this work is to develop and test instrumentation for studies of the effects of the electron beam's vibrations and drifts on beamline performance at synchrotron light sources. To perform these simulations, numerical methods were developed and implemented in the Python version of the Synchrotron Radiation Workshop (srw) code. The simulation results were compared against analytical formulas and experimental results obtained from an x-ray pinhole-camera diagnostics beamline at NSLS-II. We compared the measured data with the prediction by our code for amplitudes of orbit oscillation from $6--60\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and frequencies between 1 and 40 Hz, also taking into account the effects of misalignment of the pinhole. The simulation results are in good agreement with both analytical estimates and experimental data.

Piezoelectric unimorph and bimorph cantilever configurations: Design guidelines and strain assessment

Multi-stable configurations of piezoelectric harvester are quite successful in achieving the two important goals, the broadband frequency response and large orbit oscillations exhibiting periodic, multi-periodic, and chaotic solutions. However, in the quest of achieving large amplitude broadband frequency response, assessment of induced strain levels considering the limits on the strain in piezoelectric material has received minimal attention. In this context, the investigation presents analytical formulation for the assessment of induced strain and voltage(s) in piezoelectric unimorph and bimorph cantilevers. The formulation quantifies not only the induced voltages in individual piezoelectric layers of a bimorph, but also the equivalent voltages in parallel and series connection modes, respectively. Also, while computing the induced voltage in the first piezoelectric layer, the contribution from the induced voltage of second piezoelectric layer to the acting bending moment is captured in the formulation. The formulations are validated through the experiments and results from the literature. Further, we have applied two practically useful normalization schemes, the - and -normalizations to the analytical expressions. Using the two normalization schemes, influences of variation of substrate and adhesive layer thicknesses, elastic moduli of layers, and substrate-to-composite length fraction are visualized and discussed. Based on the results, summarized guidelines for design and selection of geometric and material parameters are presented, which may also be applicable for other sensing and actuation applications. At last, practically suitable ranges and optimum values for the normalized design variables are proposed.

Application of Nonlinear Correction Method for Attitude Control and Landing Oscillations Prevention

The purpose of this work is to demonstrate the application of the nonlinear correction method to prevent attitude oscillations of flying vehicles. This paper investigates the complications of manual control tasks in aeronautics caused by employing the integral component in the control loop. If the actuators of aircraft controlling surfaces reach their rate limits, the aircraft oscillations can appear for both manually and automatically piloted cases. In this paper, the oscillations alleviation problem is solved using the nonlinear correction method. A general methodology for pilot-induced oscillations prevention is described briefly by the example of an aircraft pitch control system. The obtained pilot model parameters are used for altitude control system examination. The nonlinear systems analysis is carried out by calculating the generalized sensitivity function for the control and disturbance input signal. In the second part, the application of the nonlinear correction method to prevent aircraft and satellite oscillations caused by integrator windup. A comparative analysis of the nonlinear correction and the customary anti-windup feedback is carried out. The results obtained demonstrate that a sequential nonlinear corrective device can be efficiently used to suppress pilot-induced and integrator windup oscillations.

Improved Automatic Detection of GPS Satellite Oscillator Anomaly using a Machine Learning Algorithm

<h3>Abstract</h3> This paper presents a random forest-based machine learning algorithm to automatically detect satellite oscillator anomalies using dual- or triple-frequency GPS carrier phase measurements. The algorithm can distinguish satellite oscillator anomalies from other GPS carrier phase disturbances including ionospheric scintillation and receiver oscillator anomalies. Carrier phase power spectral density and carrier phase ratios between carriers are extracted from measurements and applied as input features to the random forest algorithm. The method is trained using data collected at seven GNSS monitoring stations located in Alaska, Ascension Island, Greenland, Hong Kong, Peru, Puerto Rico, and Singapore. The overall detection accuracies of 98.4% and 99.0% are achieved for dual- and triple-frequency signals, respectively. The method outperforms other machine learning algorithms. The preliminary detection results demonstrate that the method presented can be employed on a global satellite oscillator anomaly monitoring system.

Explicit Solution of the Focus Locus Problem for the Harmonic Oscillator Orbits in the Plane

Dynamical orbits of the harmonic oscillator potential in the plane are ellipses which depend on a real parameter. Some time ago in this journal it has been proven by purely geometrical methods that the locus of the focuses of these ellipses are Cassinian ovals. Here we present several explicit analytic parameterizations of these remarkable curves. Nominally, their forms depend on the magnitude of the initial distance from the center of attraction and the magnitude of the initial velocity. We have found a few parameterizations in which the roles of the size and shapes can be clearly distinguished.

Non-linear resonant torus oscillations as a model of Keplerian disc warp dynamics

ABSTRACT Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime – non-linear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel non-linear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here, we uncover two distinct non-linear regimes as the warp amplitude is increased. Initially, we find a smooth modulation theory that describes warp evolution in terms of the averaged Lagrangian of the oscillatory vertical motions of the disc. This hints towards the possibility of connecting previous warp theory under a generalized secular framework. Upon the warp amplitude exceeding a critical value, which scales as the square root of the aspect-ratio of our ring, the disc enters into a bouncing regime with extreme vertical compressions twice per orbit. We develop an impulsive theory that predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasize the essential activation of non-linear vertical oscillations within the disc and may have important implications for energy and warp dissipation. Future work should search for this behaviour in detailed numerical studies of the internal flow structure of warped discs.

Reduction and regularization of the Kepler problem

The KS regularization connects the dynamics of the harmonic oscillator to the dynamics of bounded Kepler orbits. Using orbit space reduction, it can be shown that reduced harmonic oscillator orbits can be identified with re-parametrized Kepler orbits by factorizing the KS map as reduction mapping followed by a chart on the reduced phase space. In this note, we will show that also other regularization maps can be obtained this way. In particular, we will show how Moser’s regularization and Ligon–Schaaf regularization are related to KS-regularization. All regularizations are a result of choosing the right invariants to represent the reduced phase space, which is isomorphic to T^+S^3, and a chart on this reduced phase space. We show how this opens the way to directly reduce the KS transformed Kepler system and find other regularization maps that are valid for all values of the Keplerian energy similar to Ligon–Schaaf regularization.