Terms Of Harmonics Research Articles

Beyond Numbers: Investigating the Impact of COVID-19 on Suicide Rates in Austria

Abstract During the COVID-19 pandemic, individuals’ mental health faced substantial challenges. This study aims to provide a comprehensive examination of the pandemic’s impact on suicide rates in Austria, with a particular focus on variations by gender, region, and age. The study employs a regression discontinuity in time design and an interrupted time series analysis, utilising monthly death records from January 2015 to December 2021. To account for seasonal variations and potential underreporting of suicides, harmonic Fourier terms are incorporated into the analysis, and both suicides with intended self-harm and self-harm with undetermined intent are included. While existing research offers valuable insights into the impact of the pandemic on suicidal behaviour, it does not yet allow for specific conclusions to be drawn for Austria. In contrast to the methods typically employed in previous research on other countries, this approach enables a comprehensive examination of the temporal effects surrounding the implementation and lifting of pandemic-related measures. The study reveals a significant negative trend in Austria’s suicide rates before the start of the pandemic and more suicides than expected after its onset. In particular, the number of suicides among men aged 64-85 and women in the age groups 0-19, 20-34, and 65-84 was significantly higher than expected. Conversely, the data indicated a positive impact among women aged 35-64. This study contributes to understanding the impact of the pandemic on suicide rates in Austria. It demonstrates that, even within the same country, the impact can differ by gender, age, and region, thereby supporting the need for subgroup analysis. It also highlights that potential underreporting of suicides may result in an underestimation of the impact of the pandemic on suicides in previously conducted studies. Understanding these nuances is crucial for suicide prevention and informing policy decisions to improve health system resilience. Key messages • The study found higher than expected suicide rates in Austria during the COVID-19 pandemic, especially among men aged 64-85 and women aged 0-19, 20-34, and 65-84. • The underreporting of suicides may result in an underestimation of the impact of COVID-19 on suicides in previously conducted studies.

Epidemiological characteristics and transmission dynamics of dengue fever in China

China has experienced successive waves of dengue epidemics over the past decade. Nationwide data on 95,339 dengue cases, 89 surveillance sites for mosquito density and population mobility between 337 cities during 2013-20 were extracted. Weekly dengue time series including time trends and harmonic terms were fitted using seasonal regression models, and the amplitude and peak timing of the annual and semiannual cycles were estimated. A data-driven model-inference approach was used to simulate the epidemic at city-scale and estimate time-evolving epidemiological parameters. We found that the geographical distribution of dengue cases was expanding, and the main imported areas as well as external sources of imported cases changed. Dengue cases were predominantly concentrated in southern China and it exhibited an annual peak of activity, typically peaking in September. The annual amplitude of dengue epidemic varied with latitude (F = 19.62, P = 0.0001), mainly characterizing by large in southern cities and small in northern cities. The effective reproduction number Reff across cities is commonly greater than 1 in several specific months from July to November, further confirming the seasonal fluctuations and spatial heterogeneity of dengue epidemics. The results of this national study help to better informing interventions for future dengue epidemics in China.

An accurate and efficient second-order J2 model for the draper semianalytic satellite theory

Semi-analytical orbit propagation methods combine the advantages of analytical and numerical methods to achieve an excellent balance between efficiency and accuracy. The increasingly congested space has led to the growing prevalence of semi-analytical methods, driven by the requirements for efficient and accurate orbit propagation in Space Situational Awareness (SSA). However, the accuracy of semi-analytical methods is only retained by considering the contribution of the J2 zonal harmonic second order terms, namely the J22 term, which has not been completely modeled in semi-analytical methods due to the complex mathematical formulations. This paper proposes a complete semi-analytical solution for the J22 contribution consistent with the Draper Semianalytic Satellite Theory (DSST), including the fully closed-form and nonsingular mean element rate equations and computationally efficient short-period terms. Firstly, for the direct application of DSST in the construction of the J22 solution, the difficulties of high computational costs induced by multiplying infinite Fourier series together are analyzed. Next, an improved construction process for the J22 solution is developed by introducing a new general form of the partial derivatives of osculating elements rates to eliminate these difficulties. Considering the complexity of the construction process, the computation details for each term in this process are then presented. Numerical experiments demonstrate that the proposed J22 solution achieves remarkable accuracy and efficiency compared to previous works.

Stability mechanism of crystalline CO2 and Xe.

We explore the phase behaviors of simple molecular crystals in order to investigate the molecular basis of the stability mechanism relative to their liquid counterparts. The free energies of the face centered cubic crystals of Xe and CO2 are calculated as a collection of oscillators, and those of the liquids are from an equation of state via molecular dynamics simulations. The vibrational free energy in the solid is separated into the harmonic and anharmonic terms. The harmonic free energies decrease harshly with the expansion of the volume manifested as the large positive Grüneisen parameters, but the anharmonic free energies are positive and increase with volume, both of which originate from the deviation of the potential surface from the parabolic curve. The anharmonic free energies, though less significant in magnitude and destabilize the solids thermodynamically, serve to enhance their mechanical stability. The solid-liquid phase boundaries cannot be settled correctly without the exquisite balance between the two opposing contributions. A sharp contrast regarding the solid free energy is found in low-pressure ice, where the harmonic free energy does not decrease monotonically with volume and its anharmonic free energy is negative.

A Novel Friction Compensation Method for Machine Tool Drive Systems in Insufficient Lubrication.

Friction is the dominant factor restricting tracking accuracy and machining surface quality in mechanical systems such as machine tool feed-drive. Hence, friction modeling and compensation is an important method in accurate tracking control of CNC machine tools used for welding, 3D printing, and milling, etc. Many static and dynamic friction models have been proposed to compensate for frictional effects to reduce the tracking error in the desired trajectory and to improve the surface quality. However, most of them focus on the friction characteristics of the pre-sliding zone and low-speed sliding regions. These models do not fully describe friction in the case of insufficient lubrication or high acceleration and deceleration in machine tool systems. This paper presents a new nonlinear friction model that includes the typical Coulomb-Viscous friction, a nonlinear periodic harmonic friction term for describing the lead screw property in insufficient lubrication, and a functional component of acceleration for describing the friction lag caused by the acceleration and deceleration of the system. Experiments were conducted to compare the friction compensation performance between the proposed and the conventional friction models. Experimental results indicate that the root mean square and maximum absolute tracking error can be significantly reduced after applying the proposed friction model.

Exploring gradual material rigidity degradation effects on the nonlinear coupled axial-transversal nonlinear response of a capacitive micro-beam

The accumulation of damage in materials due to crack propagation can lead them to unpredicted failures. This phenomenon is particularly relevant in materials science, engineering, and other fields where structures or components are subjected to repeated loading, cyclic stresses, or environmental factors. In this paper, the mechanical behavior of a microelectromechanical system subjected to cyclic loads has been modeled, when the stiffness of the material gradually is decreased. As a case study the dynamic response of a micro-beam to DC bias voltage as a static load and AC harmonic voltage as a cyclic load has been studied. The nonlinear coupled equations have been formed and converted to time-dependent ones using a spatial discretization method. Due to long-term integration over time, to achieve more accurate results besides direct 4th order Runge-Kutta integration method, a temporal decomposition method has been used to solve the coupled nonlinear ordinary differential equations. To realize this method, a temporal decomposed solution based on the physical nature of the problem is presented in the form of slow-growing terms and fast-altering harmonic terms with gradually-growing amplitudes. To find the coefficient of these terms a least square method has been utilized to minimize a cost function in a given dynamic time-interval, where the independency of the results to this interval has been assessed. Also, the nonlinear frequency behavior of the proposed model has been studied when the system has suffered various damages. Due to considering gradual rigidity degradation of the material interesting dynamic responses have been observed, that can help to expand the insight in the design of structures.

Haque’s approach with mickens’ iteration method to find a modified analytical solution of nonlinear jerk oscillator containing displacement time velocity and time acceleration

AbstractHaque’s approach with Mickens’ iteration method has been used to obtain the modified analytical solutions of the nonlinear jerk oscillator, including displacement time velocity and acceleration. The jerk oscillator represents the features of chaotic behavior in numerous nonlinear phenomena, cosmological analysis, kinematical physics, pendulum analysis, etc., such as electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. In this paper, we have used different harmonic terms for different iterative stages using the truncated Fourier series. A comparison is made between the iteration method, the improved harmonic balance method, and the homotopy perturbation method. After comparison, the suggested approach has been shown to be more precise, efficient, simple, and easy to use. Furthermore, there was remarkable accuracy in the comparison between the numerical results and the generated analytical solutions. For the third approximate period, the maximum percentage error is 0.014.

Experimental nonlinear model of a set of connecting elements in view of nonlinear modal coupling

The development process of mechanical systems involves the evaluation of its modes of vibrations in the frequency range of interest. In general, a linear modal analysis is sufficient to determine whether the system can operate in dynamic conditions. However, in some cases the assembly is composed of many subsystems connected through nonlinear connections which make the response depend on the amplitude and frequency of the excitation. In those cases, Linear Normal Modes (LNMs) are not sufficient to fully describe the dynamics of the system and Nonlinear Normal Modes (NNMs) must be used. Using substructuring techniques it is possible to treat nonlinear joints as independent subsystems. However, a reliable nonlinear model is needed to use this approach. The experimental characterization is the only way to correctly estimate the nonlinear behavior of the connection. Thus, the aim of this work is to develop and validate the experimental characterization to build an experimental nonlinear modal model of a strongly nonlinear element that can be used to connect different linear subsystems and can be regarded as a localized source of nonlinearity. The NNMs identification is performed using the single-point single-harmonic phase resonance method, and the experimental nonlinear modal model of the NLCE is obtained by retaining only the first harmonic term of each NNM in order to get nearly uncoupled modal equations.

A two-stage consensus model based on personalized individual semantics under linguistic preference relations with self-confidence

Linguistic preference relations with self-confidence (LPRs-SC) are the preference relation that can reflect the decision maker’s (DM) confidence psychology and has received widespread attention for their simple form and multiple information. Currently, arithmetic studies of LPRs-SC are conducted separately for preference relations and self-confidence. In addition, personalized individual semantics (PIS) is an important tool in large-scale decision-making to reflect the differences in the semantic understanding of DMs. However, the confidence level in LPRs-SC limits the preference relation to a certain extent and the linguistic representations of these two components are usually different. This means that it is not only necessary to propose an arithmetic rule that can express the restrictive relationship between the two but also to construct a model that can extract the PIS of preference relation and confidence respectively. Besides, we constructed a two-stage consensus reaching process (CRP) based on the specificity of the LPRs-SC structure when enhancing group harmony. The process takes self-confidence as an independent source of information, delineates the adjusted categories in detail, and builds an adjustment model accordingly. Finally, the example and comparative analyses verify the merits of the proposed PIS in terms of consistency enhancement and CRP in terms of speed and accuracy harmonization.

An improved Mickens’ solution for nonlinear vibrations

The Duffing equation and other nonlinear equations of motion of nonlinear vibrations are widely applied in the fields of engineering and science, especially mechanical and electrical engineering. The modified Mickens extended iteration method has been utilized in this article to investigate for further accurate solutions to the Duffing equation and an equation of motion of nonlinear vibrations. The third approximate frequency shows good agreement with the exact result for both oscillators. For simplicity in algebraic calculations, the increasing harmonic terms have been taken to the fifth order. In order to establish the reliability and effectiveness of the proposed approach, the results obtained through this method are compared with those available in the literature. The comparison of the obtained solutions with numerical solutions shows a remarkable accuracy. Also, it becomes evident that the modified Mickens extended iteration method is significantly simpler, more accurate, efficient, and straightforward than other existing methods. The highest percentage error in the third approximate frequency of an equation of motion of nonlinear vibrations is less than 0.0488, and the maximal percentage error in the third approximate frequency of the Duffing oscillator is less than 0.0065. The proposed technique is principally exhibited in nonlinear models where the nonlinear terms are strong, but it can also be broadly applicable to other problems arising in engineering. Mathematics Subject Codes34A34, 34C25, 37N15 (AMS Mathematics Subject Classification 2010)

Higher order investigation on modulated waves in the Peyrard–Bishop–Dauxois DNA model

Despite the widespread use of transcendental functions in the modeling of the dynamics of DNA, most research efforts are limited in their analytical studies of this enthralling system to cubic order polynomial approximations of the corresponding equations of motion. In this paper, we present an investigation of waves in the Peyrard–Bishop–Dauxois model of DNA; while extending the polynomial approximation of the Morse potential up to the sixth order. We show that, within a generalized version of the reductive perturbation method that we have adopted, the equations governing the envelop consist of the standard cubic nonlinear Schrödinger equation and its non homogeneous linearizations. Exact and explicit analytical solutions that correspond to bright solitary waves are obtained for these coupled amplitude equations. A notable qualitative feature of these solutions is the dependence of their propagation speeds and frequencies on their amplitudes. Our approach additionally unveils that these solutions contain some harmonic terms; which are missed in existing works. A very good agreement is found between our analytical analysis and the numerical simulations of the full discrete nonlinear equation of the lattice which use these solutions as initial conditions.

Efficient multipole representation for matter-wave optics

Technical optics with matter waves requires a universal description of three-dimensional traps, lenses, and complex matter-wave fields. In analogy to the two-dimensional Zernike expansion in beam optics, we present a three-dimensional multipole expansion for Bose-condensed matter waves and optical devices. We characterize real magnetic chip traps, optical dipole traps, and the complex matter-wave field in terms of spherical harmonics and radial Stringari polynomials. We illustrate this procedure for typical harmonic model potentials as well as real magnetic and optical dipole traps. Eventually, we use the multipole expansion to characterize the aberrations of a ballistically interacting expanding Bose–Einstein condensate in (3 + 1) dimensions. In particular, we find deviations from the quadratic phase ansatz in the popular scaling approximation. The scheme is data efficient by representing millions of complex amplitudes of a field on a Cartesian grid in terms of a low order multipole expansion without precision loss. This universal multipole description of aberrations can be used to optimize matter-wave optics setups, for example, in matter-wave interferometers.

Large second-order Josephson effect in planar superconductor-semiconductor junctions

We investigate the current-phase relations of Al/InAs-quantum well planar Josephson junctions fabricated using nanowire shadowing technique. Based on several experiments, we conclude that the junctions exhibit an unusually large second-order Josephson harmonic, the \sin(2\varphi)sin(2φ) term. First, superconducting quantum interference devices (dc-SQUIDs) show half-periodic oscillations, tunable by gate voltages as well as magnetic flux. Second, Josephson junction devices exhibit kinks near half-flux quantum in supercurrent diffraction patterns. Third, half-integer Shapiro steps are present in the junctions. Similar phenomena are observed in Sn/InAs quantum well devices. We perform data fitting to a numerical model with a two-component current phase relation. Analysis including a loop inductance suggests that the sign of the second harmonic term is negative. The microscopic origins of the observed effect remain to be understood. We consider alternative explanations which can account for some but not all of the evidence.

A mechanical model of ocular bulb vibrations and implications for acoustic tonometry.

In this study, we propose a comprehensive mechanical model of ocular bulb vibrations and discuss its implications for acoustic tonometry. The model describes the eye wall as a spherical, pre-stressed elastic shell containing a viscoelastic material and accounts for the interaction between the elastic corneoscleral shell and the viscoelastic vitreous humor. We investigate the natural frequencies of the system and the corresponding vibration modes, expanding the solution in terms of scalar and vector spherical harmonics. From a quantitative point of view, our findings reveal that the eyebulb vibration frequencies significantly depend on IOP. This dependency has two origins: "geometric" stiffening, due to an increase of the pre-stress, and "material" stiffening, due to the nonlinearity of the stress-strain curve of the sclera. The model shows that the second effect is by far dominant. We also find that the oscillation frequencies depend on ocular rigidity, but this dependency is important only at relatively large values of IOP. Thus close to physiological conditions, IOP is the main determinant of ocular vibration frequencies. The vitreous rheological properties are found to mostly influence vibration damping. This study contributes to the understanding of the mechanical behavior of the eye under dynamic conditions and thus has implications for non-contact intraocular pressure measurement techniques, such as acoustic tonometry. The model can also be relevant for other ocular pathological conditions, such as traumatic retinal detachment, which are believed to be influenced by the dynamic behavior of the eye.

On the quantum problem with harmonic, Stark, Coulombian and centrifugal barrier potential terms, and biconfluent Heun functions


 
 
 We show here that the one dimensional Schro ̈dinger problem with a potential function with harmonic, Stark, Coulombian and centrifugal barrier terms can be described in terms of biconfluent Heun functions, and review some possible solutions of the problem. Considering the algebraic form of the quantum problem, we readily find two new relations between biconfluent Heun functions, which have not been considered before in the literature.
 
 

Fault Tolerant Control of a Dual Star Induction Machine Drive System using Hybrid Fractional Controller

Abstract This paper presents a novel fault tolerant control (FTC) strategy for a dual star induction machine (DSIM) based on the combination of two types of robust controllers, namely a proportional resonant (PR) controller for current regulation and a fractional order PI (FOPI) for speed regulation. This FTC is associated with an indirect rotor indirect rotor field-oriented control (IRFOC) strategy. Fault feedforward compensation of the current components is introduced using the residual signal generated by the calculations passing through the PR controller. The fractional-order PI controller is applied as a feedforward fractional-order perturbation observer to the speed control loop, which attempts to minimise the error induced by the fault. In this context, a fault-tolerant control scheme is achieved. The performance characteristics of the proposed fault tolerant control for a dual star induction machine drive are compared with the fault tolerant control based on the conventional integer order IP (IOPI) to verify the effectiveness of the proposed FTC scheme under various conditions, by examining the robustness of the control in the presence of faults. To evaluate the performance of the proposed technique, simulation results are obtained using the Matlab/Simulink environment. According to the obtained simulation results, the proposed FTC system achieves significantly better responses than the conventional IRFOC system in terms of harmonics in the stator currents, and low oscillations in the electromagnetic torque response.

The fundamental vibrational frequencies and spectroscopic constants of the C2O2H2 isomers: molecules known in simulated interstellar ice analogues.

While trans-glyoxal may not be easily observable in astronomical sources through either IR or radioastronomy due to its C2h symmetry, its cis conformer along with the cyc-H2COCO epoxide isomer should be ready targets for astrochemical detection. The present quantum chemical study shows that not only are both molecular isomers strongly polar, they also have notable IR features and low isomerisation energies of 4.1 kcal mol-1 and 10.7 kcal mol-1, respectively. These three isomers along with two other C2O2H2 isomers have had their full set of fundamental vibrational frequencies and spectroscopic constants characterised herein. These isomers have previously been shown to occur in simulated astrophysical ices making them worthy targets of astronomical search. Furthermore, the hybrid quartic force field (QFF) approach utilized herein to produce the needed spectral data has a mean absolute percent error compared to the experimentally-available, gas phase fundamental vibrational frequencies of 0.6% and rotational constants to better than 0.1%. The hybrid QFF is defined from explicitly correlated coupled cluster theory at the singles, doubles, and perturbative triples level [CCSD(T)-F12b] including core electron correlation and a canonical CCSD(T) relativity correction for the harmonic (quadratic) terms in the QFF and simple CCSD(T)-F12b/cc-pVDZ energies for the cubic and quartic terms, the so-called "F12-TcCR+DZ QFF." This method is producing spectroscopically-accurate predictions for both fundamental vibrational frequencies and principal spectroscopic constants. Hence, the values computed in this work should be notably accurate and, hence, exceptionally useful to the spectroscopy and astrochemistry communities.

An Efficient Method for Calculating Hysteretic Dry Friction Response of Dynamic Systems Subjected to Combined Harmonic and Random Excitation.

Many examples of dynamic analysis require modelling of dry friction. Often this is represented by a so-called Jenkins element or multiple Jenkins elements in parallel, which is sometimes termed a parallel-series Iwan element. This study considers the case where a system that includes these representations of dry friction are loaded dynamically with a combination of deterministic harmonic and random excitation. This paper presents a new efficient method for predicting the response of systems subject to combined deterministic and random excitation. The method is based on equivalent linearisation and involves averaging across both an ensemble of random responses as well as over a harmonic excitation period. The key novelty in the approach is the use of an auxiliary harmonic term to facilitate an analytical representation of the nonlinear force. This overcomes the challenge of analysing a discontinuous hysteretic nonlinearity in the presence of random excitation. Analytical solutions are presented and it is shown that the proposed approach can predict the approximate response at a significantly reduced computational cost.

A Computationally Efficient Model Predictive Control Method for Dual Three-Phase PMSM of Electric Vehicle With Fixed Switching Frequency

Aiming at the problems of large harmonic current, unfixed switching frequency and heavy calculation burden in the model predictive current control (MPCC) methods of dual three-phase permanent magnet synchronous motor (DT-PMSM). This paper presents a computationally efficient MPCC method with a fixed switching frequency. Firstly, the virtual voltage vectors (V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s) are synthesized by two large vectors and two medium-small vectors. The V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s effectively reduce the harmonic currents, and the goal of the synthetic V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> is that the harmonic current in the x-y subspace is zero. Therefore, the weighting factor of the harmonic term is eliminated in the cost function. Secondly, an optimal voltage vector selection method is designed to reduce the candidate voltage vectors in the control set and relieves the calculation burden. In addition, to further reduce ripple current and torque ripple, the duty cycle modulation method is introduced to calculate the dwell time of the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . The zero vector is inserted in the middle and both sides of the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s to achieve the purpose of fixing the switching frequency. Finally, the effectiveness of the proposed method is verified by experiments.

Continuous Harmonic Analysis and Power Quality Measurements in Three-Phase Systems.

A virtual instrument, named Power Quality Meter, is presented for (a) measuring power consumption and harmonics in three-phase systems, under non-sinusoidal and imbalance conditions (b) detecting, classifying and organizes power disturbance events. Measurement of the power consumption follows the formulation proposed by the members of the IEEE Working Group on Nonsinusoidal Situations (1996). So, definitions are based on the analysis of functions in the frequency domain, separating the fundamental terms from the harmonic terms of the Fourier series. The virtual instrument has been developed too for monitoring and measuring power disturbances, which are automatically classified and organized in a database while they are being recorded. Software tools use the database structure to present summaries of power disturbances and locate an event by severity or time of occurrence. Records of actual measurements are included to demonstrate the versatility of the instrument.