Fundamental Oscillation Research Articles

Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations

The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase ($\lambda$) that is subleading in powers of the field; $\lambda$ is measurable in the phase offset of the de Haas-van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, $\lambda/\pi$ are robustly integer-valued owing to the symmetry of the extremal orbit, i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which $\lambda$ is a topological invariant, as well as identifies the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalchogenides, 3D Weyl and Dirac metals, and crystalline and $\mathbb{Z}_2$ topological insulators. In particular, we point out that a $\pi$ phase offset in the fundamental oscillation should \emph{not} be viewed as a smoking gun for a 3D Dirac metal.

Search for quasi-periodic signals in magnetar giant flares

Quasi-periodic oscillations (QPOs) discovered in the decaying tails of giant flares of magnetars are believed to be torsional oscillations of neutron stars. These QPOs have a high potential to constrain properties of high-density matter. In search for quasi-periodic signals, we study the light curves of the giant flares of SGR 1806-20 and SGR 1900+14, with a non-parametric Bayesian signal inference method called D3PO. The D3PO algorithm models the raw photon counts as a continuous flux and takes the Poissonian shot noise as well as all instrument effects into account. It reconstructs the logarithmic flux and its power spectrum from the data. Using this fully noise-aware method, we do not confirm previously reported frequency lines at ν ≳ 17 Hz because they fall into the noise-dominated regime. However, we find two new potential candidates for oscillations at 9.2 Hz (SGR 1806-20) and 7.7 Hz (SGR 1900+14). If these are real and the fundamental magneto-elastic oscillations of the magnetars, current theoretical models would favour relatively weak magnetic fields B̅ ~ 6× 1013–3 × 1014 G (SGR 1806-20) and a relatively low shear velocity inside the crust compared to previous findings.

Analysis of pendulums coupled by torsional springs for energy harvesting

Harvesting energy from ambient sources has been a recent topic of interest. A typical linear harvester is effective only near resonance, limiting its frequency bandwidth. In order to increase the efficiency and bandwidth of harvesters, various strategies have been proposed. Using multiple harvesters in a single device can harvest enough power over wider frequency band. In the present work, the effect of torsional coupling of the harvesters for low frequency vibration energy harvesting is investigated. Two pendulums with electromagnetic induction as the energy conversion mechanism is proposed. The performance of the device is studied theoretically and numerically. Cubic polynomials are used to model the pendulum nonlinearity. Fundamental harmonic oscillation are assumed to obtain the analytical solution. The effect of torsional coupling and pendulum length on the power harvested are reported.

Fundamental FH-stretching transition frequencies and oscillator strengths in hydrogen bonded FH complexes

Vibrational transition frequencies and oscillator strengths of the FH-stretching transitions in the FH⋯CO, FH⋯FH, FH⋯CO2 and FH⋯N2 complexes were calculated with different vibrational models. The calculated vibrational frequencies were found to agree well with experimental values. The experimental oscillator strengths of the FH-stretches in the FH monomer and FH dimer were also predicted well by the different vibrational models. However, with our best theoretical methods there is still a factor of 2–4 between the experimental and calculated oscillator strengths for the FH-stretches in the FH⋯CO, FH⋯CO2 and FH⋯N2 complexes.

CMOS Cross-Coupled Oscillator Operating Close to the Transistor’s $f_{\max }$

A design methodology of CMOS cross-coupled oscillator operating close to the transistor's maximum oscillation frequency (f max ) is proposed by utilizing the loop impedance matching and phase shift control technique to maximize the oscillator's loop gain. A fundamental oscillator following the proposed design methodology has been implemented in 65-nm CMOS. The measured results show that the oscillator achieves 192.3-GHz oscillation frequency, which is 71.1% of the transistor's f max . The spectrum output power is -10.4 dBm with the phase noise of -100 dBc/Hz at 10 MHz offset. The oscillator draws only 14-mA current from a 1.2-V power supply.

Fundamental (f) oscillations in a magnetically coupled solar interior-atmosphere system – An analytical approach

Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω=gk), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to gain further insight into solar magnetic structures by means of solar magneto-seismology, and could provide further insight into the role of magnetism in solar oscillations.

An Efficient High-Power Fundamental Oscillator Above $f_{\max }/2$ : A Systematic Design

A novel approach to design efficient high-output-power fundamental oscillators beyond $f_{\max }/2$ of the employed process is presented. The idea is to shape and maximize the unilateral power gain ( $U$ ) of the network at the desired frequency using optimum passive internal and external feedback networks. The proposed technique significantly improves the output power and dc-to-RF efficiency of the oscillator. To show the feasibility of this novel approach, a 175 GHz fundamental oscillator is designed in a 130 nm SiGe BiCMOS process ( $f_{\max }\simeq ~280$ GHz), which achieves a measured dc-to-RF efficiency of 11.7% that is markedly higher than all reported oscillators above $f_{\max }/3$ of their active device. Measurements show that the designed oscillator generates a peak power of 3 mW (4.8 dBm) with a phase noise figure of merit (FoM) of −195.4 dBc/Hz at 1 MHz offset frequency, which is the highest phase noise FoM among all reported CMOS/BiCMOS millimeter-wave and terahertz oscillators. The proposed method considers the possible process, voltage, temperature variations as well as modeling errors of the passive components in the design stage.

Fundamental and Harmonic Oscillations in Neighboring Coronal Loops

Abstract We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale.

InP HBT Technologies for THz Integrated Circuits

Highly scaled indium phosphide (InP) heterojunction bipolar transistor (HBT) technologies have been demonstrated with maximum frequencies of oscillation ( $f_{\max}$ ) of >1 THz and circuit operation has been extended into the lower end of the terahertz (THz) frequency band. InP HBTs offer high radio-frequency (RF) output power density, millivolt (mV) threshold uniformity, and high levels of integration. Integration with multilevel thin-film wiring permits the realization of compact and complex THz monolithic integrated circuits (TMICs). Circuit results reported from InP HBT technologies include: 200-mW power amplifiers at 210 GHz, 670-GHz amplifiers and fundamental oscillators, and fully integrated 600-GHz transmitter circuits. We review the state of the art in THz-capable InP HBT devices and integrated circuit (IC) technologies. Challenges in extending transistor bandwidth and in circuit design at THz frequencies will also be addressed.

DC‐offset elimination method for grid synchronisation

For three-phase power system, the synchronous reference frame (SRF) phase-locked loop (PLL) is probably the most widely used synchronisation technique under ideal grid condition. However, the presence of dc-offset causes fundamental frequency oscillations errors in estimated phase. To deal with this problem, delay signal cancellation (DSC) operator is utilised in SRF-PLL in recent published literature at the cost of slowing down the dynamic behaviour. The aim is to propose a rapid dc-offset rejection method in three-phase PLL for grid synchronisation. With the employment of modified DSC operator, the dynamic performance of the conventional DSC-based PLL is improved. The effectiveness of the proposed method is confirmed through simulation results.

Constraining color flavor locked strange stars in the gravitational wave era

We perform a detailed analysis of the fundamental mode of non-radial pulsations of color flavor locked strange stars. Solving the general relativistic equations for non-radial pulsations for an equation of state derived within the MIT bag model, we calculate the frequency and the gravitational damping time of the fundamental mode for all the parametrizations of the equation of state that lead to self-bound matter. Our results show that color flavor locked strange stars can emit gravitational radiation in the optimal range for present gravitational wave detectors and that it is possible to constrain the equation of state's parameters if the fundamental oscillation mode is observed and the stellar mass is determined. We also show that the $f$-mode frequency can be fitted as a function of the square root of the average stellar density $\sqrt{M/R^3}$ by a single linear relation that fits quite accurately the results for all parametrizations of the equation of state. All results for the damping time can also be fitted as a function of the compactness $M/R$ by a single empirical relation. Therefore, if a given compact object is identified as a color flavor locked strange star these two relations could be used to determine the mass and the radius from the knowledge of the frequency and the damping time of gravitational waves from the $f$ mode.

Vibrational transitions in hydrogen bonded bimolecular complexes – A local mode perturbation theory approach to transition frequencies and intensities

The local mode perturbation theory (LMPT) model was developed to improve the description of hydrogen bonded XH-stretching transitions, where X is typically O or N. We present a modified version of the LMPT model to extend its application from hydrated bimolecular complexes to hydrogen bonded bimolecular complexes with donors such as alcohols, amines and acids. We have applied the modified model to a series of complexes of different hydrogen bond type and complex energy. We found that the differences between local mode (LM) and LMPT calculated fundamental XH-stretching transition wavenumbers and oscillator strengths were correlated with the strength of the hydrogen bond. Overall, we have found that the LMPT model in most cases predicts transition wavenumbers within 20cm−1 of the experimental values.

New neutrino physics and the altered shapes of solar neutrino spectra

Neutrinos coming from the Sun's core are now measured with a high precision, and fundamental neutrino oscillations parameters are determined with a good accuracy. In this work, we estimate the impact that a new neutrino physics model, the so-called generalized Mikheyev-Smirnov-Wolfenstein (MSW) oscillation mechanism, has on the shape of some of leading solar neutrino spectra, some of which will be partially tested by the next generation of solar neutrino experiments. In these calculations, we use a high-precision standard solar model in good agreement with helioseismology data. We found that the neutrino spectra of the different solar nuclear reactions of the proton-proton chains and carbon-nitrogen-oxygen cycle have quite distinct sensitivities to the new neutrino physics. The $HeP$ and $^8B$ neutrino spectra are the ones for which their shapes are more affected when neutrinos interact with quarks in addition to electrons. The shape of the $^{15}O$ and $^{17}F$ neutrino spectra are also modified, although in these cases the impact is much smaller. Finally, the impact in the shape of the $PP$ and $^{13}N$ neutrino spectra is practically negligible.

Study of complex dynamics of DC-DC buck converter

Switched-mode power converter circuits are non-linear and time varying in nature. In this work, non-linear dynamics for both voltage- and current-mode-controlled DC-DC buck converter has been investigated through simulation and practical study. The converter is controlled by naturally sampled constant frequency pulse width modulation signals in continuous conduction mode and converter exhibits fundamental, subharmonics and chaotic oscillations for the variation of circuit parameters. In computational study, the model of buck converter is simulated by non-autonomous differential equations and finally the computational waveforms have been verified with experimental results. Here, the main objective of this research work is to study the experimental chaos and to identify the subharmonic and chaotic oscillation zones for specific parameter values that will help the power electronic engineers to design chaos-free power supply. It has been observed that the route to chaos is achieved by period doubling in the buck converter. In order to verify the computational study, laboratory prototype of closed-loop buck converter has been fabricated. The results obtained from simulation and experimental study have been presented and compared.

Study on chaos and bifurcation in DC-DC flyback converter

In this work, the chaos and bifurcation of peak current mode (PCM) controlled DC-DC switched-mode flyback converter has been studied by varying the converter's circuit parameters. Generally, the converter is controlled by naturally sampled constant frequency pulse width modulated (PWM) signals and converter exhibits fundamental, subharmonics and chaotic oscillations for the smooth variation of circuit parameters for a certain range. Here, the circuit parameters like input voltage, load resistance, output capacitor, etc. have been chosen as primary bifurcation parameters for identifying the complex behaviours (i.e., chaos and bifurcation) of flyback converter in continuous conduction mode (CCM) of operation. It has been noticed that the route to chaos is achieved in flyback converter by period-doubling bifurcation. In order to verify, the computational study of PCM control in flyback converter has been demonstrated to investigate complex behaviours by varying the circuit parameters.

DC Offset Rejection Improvement in Single-Phase SOGI-PLL Algorithms: Methods Review and Experimental Evaluation

DC offset in the input of phase-locked loops (PLLs) is a challenging problem since it will result in fundamental frequency oscillations in the estimated phase and frequency. In this paper, a comprehensive analysis and performance evaluation of several advanced second-order generalized integrator (SOGI)-based PLL methods in enhancing the dc offset rejection capability for single-phase grid-connected power converters is presented. These methods include the cascade SOGI, modified SOGI, $\alpha \beta $ -frame delayed signal cancellation (DSC), complex coefficient filter, in-loop dq-frame DSC, notch filter, and moving average filter-based SOGI-PLL. Main characteristics and design aspects of these methods are presented. Main performance indexes, such as the setting time, frequency or phase errors are defined and these methods are systematically compared under various scenarios with both numerical and experimental results.

Localization phenomena in annular-type oscillator arrays

This paper investigates intrinsic localized modes (ILMs) in a system where N nonlinear oscillators are arranged in a circle and connected by weak springs when the system is subjected to sinusoidal, harmonic excitation torque. These oscillators consist of point masses at the tip of pinned, massless rigid rods, nonlinear springs, and dashpots. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves for N=3 are shown in the cases of both soft-spring and hard-spring nonlinear arrays and compared with the results of the numerical simulations. As a result, in the case of the soft-spring nonlinear arrays, eight stable oscillation patterns may appear when the connecting spring constants are comparatively small, and ILMs appear in six patterns depending on the initial conditions and the excitation frequency. The number of the oscillation patterns decreases as the connecting spring constants are increased. Comparatively, small values of the connecting spring constants may cause Hopf bifurcation to appear followed by amplitude modulated motions (AMMs), including regular ILMs, moving ILMs, and chaotic vibrations. In the case of the hard-spring nonlinear arrays, similar phenomena are observed except for moving ILMs. ILMs do not appear when the values of connecting springs exceed specific values in the both cases.

Frequency-multiplying optoelectronic oscillator with a tunable frequency multiplication technique

An optoelectronic oscillator (OEO) for the generation of a frequency-doubled or -quadrupled microwave signal with a tunable frequency multiplication technique is proposed and demonstrated. In the proposed OEO, a modulated signal is generated by a Mach–Zehnder modulator (MZM). The modulated signal is then divided into two parts. One part is sent to a photodetector (PD1) via an optical domain dual-loop composite cavity and then fed back to the MZM to form the OEO loop that can generate an oscillation signal with the frequency determined by the center frequency of an electrical bandpass filter used in the loop and the length difference of the dual-loop composite cavity. The other part is sent to a fiber-optic recirculating delay line (RDL) structure and then applied to another PD (PD2) for the formation of a microwave photonic (MWP) notch filter. Through using the cascade characteristics of the RDL loop in the fiber-optic RDL structure and the notch response of the MWP notch filter, a frequency-doubled or -quadrupled microwave signal is generated. A detailed theoretical analysis is provided and the results are verified by an experiment. A fundamental oscillation signal at 5.592 GHz is generated in the OEO loop, which is multiplied to generate a frequency-doubled microwave signal at 11.184 GHz or a frequency-quadrupled microwave signal at 22.368 GHz, respectively. The performance of the generated microwave signals is also investigated.

Experimental observation of phase-flip transitions in two inductively coupled glow discharge plasmas.

We report an experimental observation of a phase-flip transition in the frequency synchronization of two dc glow discharge plasma sources that are coupled in a noninvasive fashion. When the fundamental oscillation frequency of the potential fluctuations of one of the sources is progressively increased, by raising its discharge voltage, a frequency pulling regime is observed, followed by a synchronized regime that shows a frequency jump phenomenon. The jump is associated with a phase-flip transition that takes the synchronized state from an in-phase to an antiphase state. When the process is reversed, the transition takes place at a different frequency, thereby exhibiting a hysteresis effect. A heuristic model, consisting of two van der Pol oscillators that are coupled to each other through a dynamic common medium, eminently captures the essential features of our experimental observations.