Undamped Oscillations Research Articles

ON THE MECHANISM OF ICE MELTING

Based on the theory of the Jahn-Teller effect (JTE), a model of a possible mechanism of ice melting is proposed. The increase in the heat capacity of ice near 0 ⁰C by 1.5 times, compared with the Dulong and Petit law, suggests that the initial excitation of rotational vibrational modes of water molecules occurs in it. First, the excitation of the rotational low-frequency mode occurs, then the excitation of the intermediate mode. The effect of mode coupling and instability of rotational modes of molecule vibrations at an intermediate rotational frequency is associated with the presence of a connection between all low-frequency and high-frequency rotational modes of the molecule through the Euler equations. Therefore, excitation of the intermediate frequency in ice leads to the possibility of excitation of all rotational vibrational modes, which occurs in it at a temperature of 0 ⁰C after it receives the heat of fusion. Excitation of rotational vibrational modes leads to the emergence of possibilities for the addition of vibrational modes and their synchronization. The increase in the amplitude of rotational oscillations, the convergence of the frequencies of their oscillation modes and their subsequent synchronization leads to the appearance of rotations of hydrogen atoms of a water molecule around their axes of intermolecular bonds, to a stable bending of hydrogen bonds and their subsequent weakening in water. As a result of this weakening of the bond forces, we have a decrease in the rotational frequencies of oscillations for water molecules and their local charges. As a result of this decrease in frequencies, oscillations of local charges of water molecules become less radiating and less damped. Therefore, in the liquid phase of water, these rotational oscillation modes become new undamped independent oscillation modes of its molecules. The appearance of new oscillation modes in molecules leads to a doubling of the heat capacity of water compared to ice. Excitation of all three of its rotational oscillation modes during melting of ice leads to the appearance of an anomalously large value of the heat of fusion.

Solving Undamped and Damped Fractional Oscillators via Integral Rohit Transform

Background: The dynamics of fractional oscillators are generally described by fractional differential equations, which include the fractional derivative of the Caputo or Riemann-Liouville type. These equations induce classical oscillator equations like the harmonic oscillator equation, to include fractional order derivatives. Solving fractional differential equations numerically can be challenging due to the non-local nature of fractional derivatives. Objective: In this paper, a recently developed integral Rohit transform is utilized for solving systems of undamped and damped fractional oscillators characterized by differential equations of fractional or non-integral order involving the Caputo-fractional derivative operator. The solutions of fractional systems which include undamped-simple fractional oscillators, undamped-driven fractional oscillators, damped-driven fractional oscillators, and damped-fractional oscillators are obtained. Methods: by applying the integral Rohit transform, also written as RT. Differential equations of fractional or non-integral order are generally solved by utilizing methods which include the fractional variational iteration approach, the homotopy-perturbation method, the equivalent linearized method, the Adomian decomposition method, etc. Results: This paper demonstrates the effectiveness, reliability, and efficiency of the integral Rohit transform in solving fractional systems, which include undamped-simple fractional oscillators, undamped-driven fractional oscillators, damped-driven fractional oscillators, and damped-fractional oscillators and are characterized by differential equations of fractional or non-integral order involving the Caputo-fractional derivative operator. Conclusions: The Rohit transform brought the progressive principles or methodologies that offer new insights or views on the problems examined in the paper, distinguishing itself from existing methods and doubtlessly beginning up new research instructions. It provided precise results for the specific problems discussed in the paper, surpassing the capabilities of other methods in terms of decision, constancy, or robustness to noise and disturbances.

Exact analytical investigation of Duffing oscillator vibration spectra under time-periodic oscillatory external force

This work introduces an analytical technique for determining solutions to a highly nonlinear Duffing-harmonic oscillator model problem. The parametric solutions of Duffing oscillator vibrations for an undamped case are achieved analytically in terms of Adomian polynomials by implementing the straightforward approach of the Laplace Transformation, known as the Laplace Decomposition Procedure (LDP). Possible plots of both numerical and analytical results sketched for various parameters are also presented to support our discussion. These graphs demonstrate variations of position-time, speed-time, and speed-position for an undamped Duffing oscillator case. When analyzed in general, they can provide vibration pattern descriptions for a variety of physical and engineering system configurations. We also examine their physical structures and behavioral characteristics within the conceptual framework of chaotic formalism.

Interference aided finite resonant response in an undamped forced oscillator

We apply perturbative techniques to a driven undamped sinusoidal oscillator at resonance. The angular displacement, θ, obeys the dynamics θ¨+ω2sin⁡θ=Hcos⁡ωt . The linearized approximation gives a divergent response (at long times) but the nonlinear terms make the response finite. We address the nonlinearity-induced finiteness in two ways by separately treating the short and long time scales. At long times, we use the traditional perturbative techniques to extract two drive dependent behaviours—one, the amplitude of oscillation scales as (H/ω2)1/3 and, two, the time period of the slow mode varies as (H/ω2)−2/3 . For the early time behaviour, on the other hand, we devise an alternate perturbative expansion where the successive terms get larger with the order of evaluation but have alternating signs. The alternating signs (phase differences) between these terms leads to adestructive interference like effect. A careful consideration of this destructive interference like effect between successive terms leads to a finite response which describes the initial behaviour of the amplitude of the response reasonably correctly. We further note that for larger drive values, the system seems to undergo a first order transitional behaviour with a sudden jump in the largest Lyapunov exponent

Generalized threshold of longitudinal multibunch instability in synchrotrons

Beam stability is a crucial requirement for all particle accelerators. Coupled-bunch instability (CBI) is driven by beam interaction with narrowband impedance of the resonant accelerator components. Loss of Landau damping (LLD) for a single bunch is mainly determined by broadband impedance and can lead to undamped bunch oscillations. For the first time, we solve numerically the longitudinal stability problem in a self-consistent way for a general case of two impedance types and propose a simple analytical criterion describing how the obtained LLD and CBI thresholds are combined. We demonstrate that LLD can modify the CBI mechanism and reduce the instability threshold even below the LLD threshold. These findings allow the existing beam observations in CERN Super Proton Synchrotron and Large Hadron Collider to be explained and should be considered in design of the future accelerators. Published by the American Physical Society 2024

Nonlinear dynamics of a laser diode subjected to both optical injection and optical feedback.

We analyse theoretically the nonlinear dynamics of a single-mode laser diode subjected to both optical injection and optical feedback. Detailed mappings of the laser dynamics reveal that, due to optical feedback (OF), the locking boundaries resulting from optical injection (OI) shift towards larger negative detunings and higher injection rates and display a periodic pattern of the injection locking boundaries. We demonstrate how feedback induces a cascade of quasiperiodic bifurcations associated with abrupt dynamic changes, hence altering the route to locking. A close inspection of the laser optical spectra for increasing feedback rate reveals the complex interplay between undamped relaxation oscillations and external cavity frequencies.

Modeling of Granulation in Red Supergiants in the Magellanic Clouds with the Gaussian Process Regressions

The granulation of red supergiants (RSGs) in the Magellanic Clouds is systematically investigated by combining the latest RSG samples and light curves from the Optical Gravitational Lensing Experiment and the All-Sky Automated Survey for Supernovae. The present RSG samples are first examined for foreground stars and possible misidentified sources, and the light curves are sequentially checked to remove the outliers by white noise and photometric quality. The Gaussian process (GP) regression is used to model the granulation, and the Markov Chain Monte Carlo is applied to derive the granulation amplitude σ and the period of the undamped oscillator ρ, as well as the damping timescale τ. The dimensionless quality factor Q is then calculated through Q = π τ/ρ. RSGs around Q=1/2 are considered to have significant granulation signals and are used for further analysis. Combining granulation parameters with stellar parameters, robust scaling relations for the timescale ρ are established, while the scaling relations for amplitude σ are represented by a piecewise function, possibly related to the tendency of amplitudes in faint RSGs to converge toward a certain value. Comparing results between the Small Magellanic Cloud and the Large Magellanic Cloud confirms that amplitudes and timescales become larger with metallicity. In examining the scaling relations between the two galaxies, it is found that ρ is nearly independent of metallicity, whereas σ is more significantly affected by metallicity. The GP method is compared with the periodogram fitting of the granulations, and the advantages of either are discussed.

Analysis of Undamped Oscillator Subjected to Triangular Pulse via Gupta Integral Transform

An undamped (mechanical as well as electrical) oscillator subjected to a triangular pulse is generally analyzed via ordinary methods such as calculus. In this paper, an undamped (mechanical as well as electrical) oscillator subjected to a triangular pulse was analyzed to obtain its response via the Gupta integral transform (GT). It put forward a new technique for obtaining the response of an undamped oscillator subjected to a triangular pulse force and proves that the GT is an effective integral transform than calculus.

Multivariate Mittag-Leffler Solution for a Forced Fractional-Order Harmonic Oscillator

The harmonic oscillator is a fundamental physical–mathematical system that allows for the description of a variety of models in many fields of physics. Utilizing fractional derivatives instead of traditional derivatives enables the modeling of a more diverse array of behaviors. Furthermore, if the effect of the fractional derivative is applied to each of the terms of the differential equation, this will involve greater complexity in the description of the analytical solutions of the fractional differential equation. In this work, by using the Laplace method, the solutions to the multiple-term forced fractional harmonic oscillator are presented, described through multivariate Mittag-Leffler functions. Additionally, the cases of damped and undamped free fractional harmonic oscillators are addressed. Finally, through simulations, the effect of the fractional non-integer derivative is demonstrated, and the consistency of the result is verified when recovering the integer case.

The role of perceived negative partner behavior in daily snacking behavior: A dynamical systems approach

Past work suggested that psychological stress, especially in the context of relationship stress, is associated with increased consumption of energy-dense food and when maintained for long periods of time, leads to adverse health consequences. Furthermore, this association is moderated by a variety of factors, including emotional over-eating style. That being said, few work utilized a dynamical system approach to understand the intraindividual and interindividual fluctuations within this process. The current study utilized a 14-day daily diary study, collected between January–March 2020, where participants reported their partner's negative relationship behavior and their own snacking behavior. A differential equation model was applied to the daily dairy data collected. Results showed that snacking behavior followed an undamped oscillator model while negative relationship behavior followed a damped coupled oscillator model. In other words, snacking behavior fluctuated around an equilibrium but was not coupled within dyadic partners. Negative relationship behavior fluctuated around an equilibrium and was amplified over time, coupled within dyadic partners. Furthermore, we found a two-fold association between negative relationship behavior and snacking: while the association between the displacement of negative relationship behavior and snacking was negative, change in negative relationship behavior and snacking were aligned. Thus, at any given time, one's snacking depends both on the amount of negative relationship behaviors one perceives and the dynamical state a dyad is engaging in (i.e., whether the negative relationship behavior is “exacerbating” or “resolving”). This former association was moderated by emotional over-eating style and the latter association was not. The current findings highlight the importance of examining dynamics within dyadic system and offers empirical and methodological insights for research in adult relationships.

A Note on a Simple Equation for Solving Nonlinear Undamped Oscillations

A Note on a Simple Equation for Solving Nonlinear Undamped Oscillations

Application of information technology to create the digital acoustic models of VVER

The IT used to create DAMPS is based on an interdisciplinary approach. DAMNR is presented as a self-oscillatory system, belonging to a special class of nonlinear dissipative systems capable of generating undamped oscillations. The use of DAMNR in the design and operation of NPP makes it possible to identify the sources of occurrence of ASW in the coolant, the conditions for their occurrence and frequency, and determine the influence of geometric parameters and the layout of coolant circuit equipment on the interaction of neutronic-physical, thermal–hydraulic and vibroacoustic processes. The use of DAMNR makes it possible to optimize engineering and design solutions when creating NPP by eliminating the conditions that cause the occurrence of unwanted self-oscillations of the coolant and vibroacoustic resonances in normal and emergency operating modes, as well as under conditions of shock impacts and seismic loads. Universal models and analysis methods were verified at Novovoronezh NPP.

Exact periodic solution of the undamped Helmholtz oscillator subject to a constant force and arbitrary initial conditions

The Helmholtz oscillator is a nonlinear mixed‐parity oscillator that models the asymmetric vibrations of many engineering and scientific systems. This paper investigated a general and completely integrable form of the Helmholtz oscillator and derived its exact periodic solution from the first integral of the governing differential equation. The considered Helmholtz oscillator has general linear and nonlinear stiffness constants, is subject to a constant force, and has arbitrary initial conditions. Its exact time period was derived in terms of the complete elliptic integral of the first kind, while the exact displacement was derived in terms of the Jacobi elliptic sine function. The validity of the exact solutions was verified for various combinations of the system parameters and initial conditions by comparing with numerical solutions. The exact solutions and numerical solutions were found to match perfectly. Furthermore, the exact solution was applied to analyze the vibration response of real‐world systems that could be modeled as Helmholtz oscillators. The present exact solutions provide benchmark solutions that could be used to determine the accuracy of new and existing approximate solutions for the Helmholtz oscillator.

Euclid: The search for primordial features

Primordial features, in particular oscillatory signals, imprinted in the primordial power spectrum of density perturbations represent a clear window of opportunity for detecting new physics at high-energy scales. Future spectroscopic and photometric measurements from the Euclid space mission will provide unique constraints on the primordial power spectrum, thanks to the redshift coverage and high-accuracy measurement of nonlinear scales, thus allowing us to investigate deviations from the standard power-law primordial power spectrum. We consider two models with primordial undamped oscillations superimposed on the matter power spectrum described by 1 + 𝒜X sin (ωXΞX + 2 πϕX), one linearly spaced in k space with Ξlin ≡ k/k* where k* = 0.05 Mpc−1 and the other logarithmically spaced in k space with Ξlog ≡ ln(k/k*). We note that 𝒜X is the amplitude of the primordial feature, ωX is the dimensionless frequency, and ϕX is the normalised phase, where X = {lin, log}. We provide forecasts from spectroscopic and photometric primary Euclid probes on the standard cosmological parameters Ωm, 0, Ωb, 0, h, ns, and σ8, and the primordial feature parameters 𝒜X, ωX, and ϕX. We focus on the uncertainties of the primordial feature amplitude 𝒜X and on the capability of Euclid to detect primordial features at a given frequency. We also study a nonlinear density reconstruction method in order to retrieve the oscillatory signals in the primordial power spectrum, which are damped on small scales in the late-time Universe due to cosmic structure formation. Finally, we also include the expected measurements from Euclid’s galaxy-clustering bispectrum and from observations of the cosmic microwave background (CMB). We forecast uncertainties in estimated values of the cosmological parameters with a Fisher matrix method applied to spectroscopic galaxy clustering (GCsp), weak lensing (WL), photometric galaxy clustering (GCph), the cross correlation (XC) between GCph and WL, the spectroscopic galaxy clustering bispectrum, the CMB temperature and E-mode polarisation, the temperature-polarisation cross correlation, and CMB weak lensing. We consider two sets of specifications for the Euclid probes (pessimistic and optimistic) and three different CMB experiment configurations, that is, Planck, Simons Observatory (SO), and CMB Stage-4 (CMB-S4). We find the following percentage relative errors in the feature amplitude with Euclid primary probes: for the linear (logarithmic) feature model, with a fiducial value of 𝒜X = 0.01, ωX = 10, and ϕX = 0: 21% (22%) in the pessimistic settings and 18% (18%) in the optimistic settings at a 68.3% confidence level (CL) using GCsp+WL+GCph+XC. While the uncertainties on the feature amplitude are strongly dependent on the frequency value when single Euclid probes are considered, we find robust constraints on 𝒜X from the combination of spectroscopic and photometric measurements over the frequency range of (1, 102.1). Due to the inclusion of numerical reconstruction, the GCsp bispectrum, SO-like CMB reduces the uncertainty on the primordial feature amplitude by 32%–48%, 50%–65%, and 15%–50%, respectively. Combining all the sources of information explored expected from Euclid in combination with the future SO-like CMB experiment, we forecast 𝒜lin ≃ 0.010 ± 0.001 at a 68.3% CL and 𝒜log ≃ 0.010 ± 0.001 for GCsp(PS rec + BS)+WL+GCph+XC+SO-like for both the optimistic and pessimistic settings over the frequency range (1, 102.1).

Suppression of the height deviation on metal bumps manufacturing by an ultrasonic vibration control

On-demand droplet printing based on piezoelectric micro-jet device (PMJD) is considered a flexible and high-precision method to generate metal droplets directly for flip-chip bonding in industrial electronics. However, the quality of flip-chip bonding is closely related to the height deviation of the solidified droplets (the metal bumps), which is influenced by the complicated hydrodynamics of impacting and oscillation of the droplet with oxide film. Here, the numerical and experimental investigations are first conducted to study the effect of the liquid bridge and deposition parameters on the height deviation of the solidified droplets. The rapid oxidation of the liquid bridge and under-oscillation during the deposition process are the main reasons for height deviation. In addition, the undamped oscillation with high-speed impact and instantaneous solidification also deteriorates the height deviation. To this end, an oscillation control strategy based on ultrasonic-assisted metal droplet deposition (UAMDD) is proposed and verified to be a reliable regulation strategy to suppress the height deviation of the printed bumps. The effective regulating range of height deviation is studied experimentally by changing the ultrasonic vibration amplitude. Finally, a 10 × 10 array composed of 100 solidified metal droplets is printed with the UAMDD, which has the height deviation of 554 ± 6 μm. And the dimensionless height deviation (Δh/h) of solidified bumps is stayed below 2.1 %.

Converter induced resonances in microgrids due to high harmonic distortion

This paper describes the resonance introduced by harmonics amplification and adverse interaction of electronic converters. An observation of undamped oscillation leading to instability in a microgrid is described. The term “converter induced resonances” is proposed to describe this phenomenon. The amount of distributed generation, active loads, FACTS and battery energy storage systems are expected to increase in future Smart Grids. All these resources will be interfaced with electronic converters. The potential impact of converter induced resonances in such grids is described. A coordinated design of the control systems of all converters is in practice not feasible. Each device will be independently tested to fulfil grid codes and have its own converter control implemented that can include functionality to modify voltage and /or current waveform.

The Mayan Transform: A Novel Integral Transform of Complex Power Parameters and Applications to Neutrosophic Functions

In this paper, a new type of integral transform with complex power parameters called the Mayan transform has been introduced. The definitions of the integral transform and its inverse are given in the classical case and the corresponding neutrosophic case. The classical analytical properties of the Mayan integral transforms are proven; the application of it to some essential functions and neutrosophic functions is introduced and proven. Also, its application to the neutrosophic derivatives (first, second, and third) then the generalization of the application on the Mayan integral transform on the neutrosophic derivatives are given. The worthiness of the introduced integral transform on the actual application is also proven by applying the integral transform in solving two problems: the response of an Undamped forced mechanical oscillator and the response of an undamped forced electrical oscillator.

Evolution of spin coherence of radical pairs due to spin-selective recombination: Comparison of three models.

This study looked for a way to evaluate the validity of previously suggested models for describing the spin-selective recombination of radical pairs. As an example, for analysis, we used the conventional model, the model by Jones and Hore [Chem. Phys. Lett. 488, 90 (2010)], and the model by Salikhov [Am. J. Phys. Chem. 11, 67 (2022)]. To do this, analytical solutions to the evolution of the radical pair density matrix due to a radical pair's spin-selective recombination and singlet-triplet transitions in a strong magnetic field were obtained for the conventional model and the Jones and Hore model. Spin interactions included in the Hamiltonian were time-independent exchange interactions as well as Zeeman and hyperfine interactions. The most striking difference between the models' predictions appeared when considering the fraction of singlet pairs among all currently existing ones. In the Jones and Hore model, this ratio has the form of damped oscillations for any values of the spin-hamiltonian parameters. The conventional model and the Salikhov model both predicted that this ratio had the form of undamped oscillations in the absence of exchange interaction and at a sufficiently low recombination rate. Besides, the conventional model predicts the possibility of a resonance-like behavior of this ratio when singlet-triplet transitions in a part of the radical pair ensemble are completely suppressed by tuning the magnetic field strength. Possible experimental conditions in which distinguishing between the models seems to be most straightforward were suggested.

СHARACTERISTIC PATTERNS OF UNDAMPED OSCILLATIONS EXITATION WITH ADAPTIVE PHASE ADJUSTMENT ANALYSIS IN LINEAR/NON-LINEAR VIBRATION SYSTEMS

The analysis of undamped oscillations with a discrete number of possible stable amplitudes excitation mechanism as a result of an external periodic force influence, nonlinear in the motion coordinate of the exciting (linear/non-linear) vibra-tion-oscillatory system is given.
 Characteristic phenomenon regularities are studied on two general models basis: a) the pendulum is under the external periodic force inhomogeneous in the coordinate influence; b) oscillator under the incident wave influence. It is shown that the phe-nomenon’s mechanism is related to phase capture and adaptive phase adjustment, which provides the necessary energy contribution to the vibrational process in this vibrating system.

Plausibility and Implications of Converter-Driven Oscillations Induced by Unstable Long-Term Dynamics

For decades, synchronous generators have dominated power system dynamics and have been the foundation for the comprehension of the physical phenomena involved in power system stability. This paradigm is rapidly changing; large synchronous generators that contribute to system strength are being replaced by inverter-based generators. Consequently, new kinds of instabilities are emerging. Slow-interaction converter-driven instability is one example in which undamped oscillations occur when inverter-based generators operate in weak areas. Transmission system operators have observed the phenomenon under the scope of short-term dynamics following a disturbance during a weak operating condition. This paper suggests that converter-driven oscillations can occur even in the case when the system's initial operating condition is strong. It concludes that the phenomenon can be triggered by long-term dynamics that slowly weaken the system in which small-signal and short-term simulations show an ample stability margin. The outcome is a combination of unstable long-term dynamics and undamped oscillations. Furthermore, this work suggests that classical emergency controllers that are effective against long-term instability may not be successful if undamped oscillations are also present. A method for instability detection and counteraction is proposed based on Prony analysis and time-domain simulations on the IEEE test system for voltage stability assessment.