Search Results (23)

Sub-harmonic oscillations are a key stability concern in fast-switched inductor power supplies using clocked constant-period peak/valley-current loops. Using generalized models, IC designers can predict and suppress sub-harmonic oscillations with minimal overhead. This work presents an insightful, generalized, and comprehensive time-domain analysis of sub-harmonic oscillation propagation and suppression via slope compensation in constant-period peak/valley-current control. Since it is unstated and unvalidated in the literature, an exact, easy-to-apply expression for the slope compensation boundary is derived in terms of basic circuit operating parameters, showing that it is half of the difference in the drain and energize slopes in peak mode, and half of the difference in the energize and drain slopes in valley mode, lying beyond the conventionally accepted half drain (peak) and energize (valley) slope criteria. The prior literature also does not account for the impact of parasitic resistances on the duty-cycle-based stability boundary beyond which sub-harmonic oscillations begin. We address these gaps and establish a theoretical basis for the absence of sub-harmonic oscillations in DCM. Additionally, existing approaches to slope selection ensure stability but do not target the rate of suppression. We address this by proposing a compensation slope that achieves 90% suppression of the initial imbalance within three switching periods. Full article

In electrical power systems, the extraction of the fundamental positive sequence (FPS) is paramount for synchronization, power calculation, and a wide variety of metering and control tasks. This work shows that a moving average filter (MAF) used in the synchronous reference frame to extract the FPS from electrical systems is equivalent to the cascade connection of a comb filter (CF) with a second-order harmonic oscillator (SOHO), with all its variables expressed in fixed reference frame coordinates. On the one hand, the CF introduces an infinite number of notches tuned at all integer harmonics of the fundamental frequency ${\omega }_0$, thus suppressing harmonic distortion in the incoming signal and acting as a repetitive-based pre-filter (RPF). On the other hand, the SOHO is responsible for delivering the fundamental component of the input signal with a unitary gain, while additionally reducing the effect of harmonic distortion. Then, it is shown that other RPFs built from previously reported repetitive schemes (all-harmonics, odd-harmonics, and the $6\ell \pm 1$ harmonics) can be placed instead of the CF, giving rise to a family of FPS detectors. In particular, this work also shows that the CF-SOHO is a special case of the FPS detector based on the all-harmonics RPF. This work provides the mathematical derivation of the FPS detector structure, tuning rules for the SOHO gain associated with each FPS detector, as well as experimental results under a reference signal subject to perturbations such as unbalance, harmonic distortion, phase, and amplitude jumps, exhibiting convergence in only half the fundamental period in most carried out tests. Full article

Forest trees have emerged as a promising passive solution for mitigating low-frequency ground vibrations generated by railway operations, offering ecological and cost-effective advantages. This study proposes a three-dimensional semi-analytical method developed for evaluating the dynamic responses of the coupled track–ground–tree system. The thin-layer method is employed to derive an explicit Green’s function corresponding to a har-monic point load acting on a layered half-space, which is subsequently applied to couple the foundation with the track system. The forest trees are modeled as surface oscillators coupled on the ground surface to evaluate the characteristics of multiple scattered wavefields. The vibration attenuation capacity of forest trees in mitigating railway-induced ground vibrations is systematically investigated using the proposed method. In the direction perpendicular to the track on the ground surface, a graded array of forest trees with varying heights is capable of forming a broad mitigation frequency band below 80 Hz. Due to the interaction of wave fields excited by harmonic point loads at multiple locations, the attenuation performance of the tree system varies significantly across different positions on the surface. The influence of variability in tree height, radius, and density on system performance is subsequently examined using a Monte Carlo simulation. Despite the inherent randomness in tree characteristics, the forest still demonstrates notable attenuation effectiveness at frequencies below 80 Hz. Among the considered parameters, variations in tree height exert the most pronounced effect on the uncertainty of attenuation performance, followed sequentially by variations in density and radius. Full article

This article aims to clarify the applicability of He’s two-scale fractal dimension transform by replacing $t^{\mathsf{\alpha }}$ with $\mathsf{\tau }$. It demonstrates the potential to capture the influence of the fractal parameter on the system’s damping frequency, particularly when the viscoelastic term (damping) does not equal half of the fractional inertia force term. The analysis examines the elastomer materials’ dynamic fractal amplitude–time response, considering the viscohyperelastic effects related to the material’s energy dissipation capacity. To determine the amplitude of oscillations for the nonlinear equation of motion of a body supported by a viscohyperelastic elastomer subjected to uniaxial stretching, the harmonic balance perturbation method, combined with the two-scale fractal dimension transform and Ross’s formula, is employed. Numerical calculations demonstrate the effectiveness of He’s two-scale fractal transformation in capturing fractal phenomena associated with the fractional time derivative of deformation. This is due to a correlation between the fractional rate of viscoelasticity and the fractal structure of media in elastomer materials, which is reflected in the oscillation amplitude decay. Furthermore, the approach introduced by El-Dib to replace the original fractional equation of motion with an equivalent linear oscillator with integer derivatives is used to further assess the qualitative and quantitative performance of our derived solution. The proposed approach elucidates the applicability of He’s two-scale fractal calculus for determining the amplitude of oscillations in viscohyperelastic systems, where the fractal derivative order of the inertia and damping terms varies. Full article

The degenerate optical parametric oscillator (OPO) is demonstrated to generate high-power, broadband mid-infrared MgO-doped periodically poled lithium niobate (MgO:PPLN) femtosecond laser at 151 MHz, synchronously pumped by a commercial Kerr-lens mode-locked Yb:KGW oscillator at 1028 nm. The average power of the degenerate OPO centered at 2056 nm is as high as 740 mW, which is the highest output power from a reported 2 μm degenerate femtosecond OPO, pumped by a bulk solid-state laser. The full width at half maximum (FWHM) spectral bandwidth of the degenerate OPO is 87.4 nm, corresponding to a theoretical, Fourier-limited pulse duration of 51 fs. These remarkable results indicate that degenerate OPO is a great potential candidate technology for generating high-power and few-cycle femtosecond pulses around 2 μm. Such mid-infrared sources are well-suited for high harmonic generation, a pumping source for mid- to far-infrared OPO. Full article

In the present paper, an affordable innovative physical experimental equipment consisting of an upper computer, an ultrasonic sensor module, and an Arduino microcontroller has been designed. The relationship between the position of the slider fixed on two springs and time is measured by using the ultrasonic sensor module. A system for slider motion data and image acquisition is constructed by using the LabVIEW interface of Arduino UNO R3. The purpose of this experiment is to demonstrate and interpret the propagation of waves represented by harmonic motion. The spring oscillator system including a slider and two springs is measured and recorded, and the motion can be realized using curve fitting to the wave equation in Sigmaplot. The vibration periods obtained from experimental measurements and curve fitting of the wave equation are 1.130 s and 1.165 s, respectively. The experimental data are in good agreement with the theoretical model. The experimental measurement results show that the maximum kinetic energy is 0.0792 J, the maximum potential energy is 0.0795 J, and the total energy at the position of half the amplitude is 0.0791 J. The results verify the mechanical energy conservation of spring oscillator system in a short time. This self-made instrument has improved the visualization and the automation level of the corresponding experiments. Full article

One of the challenging riddles that is set by light is: do photons have wavefunctions like other elementary particles do? Wave–particle duality has been a prevailing fact since the beginning of quantum theory thought; in electromagnetism, light is already a kind of undulation, so what about the waves of probability then? Well, Quantum Field Theory (QFT) has a rigorous explanation and supports the idea when they are considered as fields of particles via second quantization; they do have wavefunctions of probability, and it does not have anything to do with the regular oscillations. They can be related to the energy and momentum signatures of harmonic oscillations, resembling an imitation of the behavior of a classical harmonic oscillator, which then has a wavefunction to solve the corresponding time-independent Schrödinger equation. For the last half century, electrical engineering has owned the best out of these implications of Quantum Electrodynamics (QED) and QFT by engineering better semiconductor techniques with finely miniaturized transistors and composite devices for digital electronics and optoelectronics fields. More importantly, these engineering applications have also greatly evolved into combined fields like quantum computing that have introduced a completely new and extraordinary world to electronics applications. The study takes advantage of the power of QFT to mathematically reveal the bosonic modes (Laguerre–Gaussian) that appear in a sub-diffraction cylindrical aperture. In this way, this may lead to the construction of the techniques and characteristics of room-temperature photonic quantum gates which can isolate photon modes under a diffraction limit. Full article

Double modulation wave carrier-based pulse width modulation (CBPWM) is a solution for eliminating the deviations of the neutral-point voltage (NPV) in three-level neutral-point clamped inverters. In this paper, a new hybrid CBPWM strategy is proposed that not only eliminates the neutral-point voltage oscillations but also reduces the common-mode voltage (CMV) by half. Furthermore, the harmonic content is also reduced compared with the available reduced CMV modulation by adjusting the modulation waves based on the location of the reference vector in the space vector diagram. An active neutral-point voltage controller is also realized in order to maintain the performance of the modulation strategy under the NPV perturbations. The performance of the proposed algorithm is compared to the available CBPWM-based techniques in the literature. The effectiveness of the proposed method is also verified by experimental results. Full article

This research studies how the angle and dimensions of a single baffle affect the dynamics of a fluid in a closed rectangular tank under an accelerated harmonic vibration in resonance. A half-filled non-deformable rectangular tank with a single centered submerged baffle has been simulated using ANSYS^® FLUENT. The study aims to characterize the effect of changing the baffle’s angle; hence, 10 simulations have been performed: without a baffle, 90°, 30°, 60°, 120° and 150°, either maintaining the baffle’s length or the projected height constant. The computational fluid dynamics (CFD) method using volume of fluid (VOF) and large eddy simulation (LES) are used to predict the movement of the fluid in two dimensions, which have been benchmarked against experimental data with excellent agreement. The motion is sinusoidal in the +X direction, with a frequency of oscillation equal to its first vibration mode. The parameters studied have been the free surface elevation, values at three different points and maximum; the center of gravity’s position, velocity, and acceleration; and the forces against the tank’s walls. It has been found that the 90° angle has the most significant damping effect, stabilizing the free-surface elevation, reducing the center of gravity dispersion, and leveling the impacting forces. Smaller angles also tame the sloshing and stabilize it. Full article

Canonical quantization has created many valid quantizations that require infinite-line coordinate variables. However, the half-harmonic oscillator, which is limited to the positive coordinate half, cannot receive a valid canonical quantization because of the reduced coordinate space. Instead, affine quantization, which is a new quantization procedure, has been deliberately designed to handle the quantization of problems with reduced coordinate spaces. Following examples of what affine quantization is, and what it can offer, a remarkably straightforward quantization of Einstein’s gravity is attained, in which a proper treatment of the positive definite metric field of gravity has been secured. Full article

The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of more realistic field theory models. Full article

We examined the heave motion of a spherical buoy during a free-decay drop test. A comprehensive approach was adopted to study the oscillations of the buoy involving experimental measurements and complementary numerical simulations. The experiments were performed in a wave tank equipped with an array of high-speed motion-capture cameras and a set of high-precision wave gauges. The simulations included three sets of calculations with varying levels of sophistication. Specifically, in one set, the volume-of-fluid (VOF) method was used to solve the incompressible, two-phase, Navier–Stokes equations on an overset grid, whereas the calculations in other sets were based on Cummins and mass-spring-damper models that are both rooted in the linear potential flow theory. Excellent agreements were observed between the experimental data and the results of VOF simulations. Although less accurate, the predictions of the two reduced-order models were found to be quite credible, too. Regarding the motion of the buoy, the obtained results indicate that, after being released from a height approximately equal to its draft at static equilibrium (which is about 60% of its radius), the buoy underwent nearly harmonic damped oscillations. The conducted analysis reveals that the draft length of the buoy has a profound effect on the frequency and attenuation rate of the oscillations. For example, compared to a spherical buoy of the same size that is half submerged at equilibrium (i.e., the draft is equal to the radius), the tested buoy oscillated with a period that was roughly 20% shorter, and its amplitude of oscillations decayed almost twice faster per period. Overall, the presented study provides additional insights into the motion response of a floating sphere that can be used for optimal buoy design for energy extraction. Full article

In this paper, a new method for the exact solution of the stationary, one-dimensional Schrödinger equation is proposed. Application of the method leads to a three-parametric family of exact solutions, previously known only in the limiting cases. The method is based on solutions of the Ricatti equation in the form of a quadratic function with three parameters. The logarithmic derivative of the wave function transforms the Schrödinger equation to the Ricatti equation with arbitrary potential. The Ricatti equation is solved by exploiting the particular symmetry, where a family of discrete transformations preserves the original form of the equation. The method is applied to a one-dimensional Schrödinger equation with a bound states spectrum. By extending the results of the Ricatti equation to the Schrödinger equation the three-parametric solutions for wave functions and energy spectrum are obtained. This three-parametric family of exact solutions is defined on compact support, as well as on the whole real axis in the limiting case, and corresponds to a uniquely defined form of potential. Celebrated exactly solvable cases of special potentials like harmonic oscillator potential, Coulomb potential, infinite square well potential with corresponding energy spectrum and wave functions follow from the general form by appropriate selection of parameters values. The first two of these potentials with corresponding solutions, which are defined on the whole axis and half axis respectively, are achieved by taking the limit of general three-parametric solutions, where one of the parameters approaches a certain, well-defined value. Full article

In this study, a planar ultrasonic motor platform is presented that uses three half-side excited piezoelectric hemispherical shell resonators. To understand the working principle and the harmonic vibration behavior of the piezoelectric resonator, the trajectory of the friction contact was measured in free-oscillating mode at varying excitation frequencies and voltages. The driving performance of the platform was characterized with transport loads up to 5 kg that also serve as an influencing downforce for the friction motor. The working range for various transport loads and electrical voltages up to 30 V is presented. Undesirable noise and parasitic oscillations occur above the detected excitation voltage ranges, depending on the downforce. Therefore, minimum and maximum values of the excitation voltage are reported, in which the propulsion force and the speed of the planar motor can be adjusted, and noiseless motion applies. The multidimensional driving capacity of the platform is demonstrated in two orthogonal axes and one rotary axis in open-loop driving mode, by measuring forces and velocities to confirm its suitability as a planar motor concept. The maximum measured propulsion force of the motor was 7 N with a transport load of 5 kg, and its maximum measured velocity was 77 mm/s with a transport load of 3 kg. Full article

Laser structuring by remelting (WaveShape) is a manufacturing process for metal surfaces in which structures are generated without material removal. The structuring principle is based on the controlled motion of the three-phase line in the area of the solidification front. The contour of the solidification front is imprinted into the remelting track during the continuous solidification process. Typically, harmonic surface structures in the form of sinusoidal oscillations are generated by means of WaveShape with virtually no material loss. However, a significant shape deviation is often observed over a wide range of process parameters. In this study, it was found that much of the shape deviation is concentrated at a spatial wavelength equal to half the spatial wavelength used for structuring. Therefore, an approach to reduce the shape deviations was specifically investigated by superimposing a compensation signal on the harmonic structuring signal. In this approach, a compensation signal with half the spatial wavelength was varied in phase and amplitude and superimposed on the structuring signal. Amplitude and phase shift of the compensation signal were further investigated for selected laser beam diameters and spatial wavelengths. This demonstrated that a shape deviation of harmonic surface structures on titanium alloy Ti6Al4V could be reduced by up to 91% by means of an adapted compensation signal. Full article