Harmonic Oscillator Research Articles

Ultrafast and Coherent Dynamics in a Solvent Switchable "Pink Box" Perylene Diimide Dimer.

Perylene diimide (PDI) dimers and higher aggregates are key components in organic molecular photonics and photovoltaic devices, supporting singlet fission and symmetry breaking charge separation. Detailed understanding of their excited states is thus important. This has proven challenging because interchromophoric coupling is a strong function of dimer architecture. Recently, a macrocyclic PDI dimer was reported in which excitonic coupling could be turned on and off simply by changing the solvent. This presents a useful case where coupling is modified without synthetic changes to tune supramolecular structure. Here we present a detailed study of solvent dependent excited state dynamics in this dimer by means of coherent multidimensional spectroscopy. Spectral analysis resolves the different coupling strengths, which are consistent with solvent dependent changes in dimer conformation. The strongly coupled conformer forms an excimer within 300 fs. The low-frequency Raman active modes recovered from two-dimensional electronic spectra reveal frequencies characteristic of exciton coupling. These are assigned to modes modulating the coupling from the corresponding DFT calculations. Further analysis reveals a time dependent frequency during excimer formation. Analysis of two-dimensional "beatmaps" reveals features in the coupled dimer which are not predicted by the displaced harmonic oscillator model and are assigned to vibronic coupling.

Electromagnetic Field and Variable Inertia Analysis of a Dual Mass Flywheel Based on Electromagnetic Control

The moment of inertia of the primary flywheel and the secondary flywheel in a dual mass flywheel (DMF) directly affects the vibration damping performance in an automotive driveline. To enable better minimization of vibration and noise by changing the moment of inertia of the DMF to adjust the frequency characteristics of the automotive driveline, a new variable inertia DMF structure is proposed by introducing electromagnetic devices. The finite element simulation model of the electromagnetic field of an electromagnetic device is established, the electromagnetic field characteristics in the structure are analyzed, and the variation in the electromagnetic force under different air gaps and current conditions is obtained. The electromagnetic force test system of the electromagnetic device is constructed, and the validity of the finite element simulation analysis of the electromagnetic field of the electromagnetic device is verified. A mechanical model of the electromagnetic device is established to analyze the characteristics of the displacement of the moving mass in the structure as well as the variation in the moment of inertia of the DMF at different rotational speeds and currents. The maximum adjustable proportion of its moment of inertia can reach 15.07%. A torsional model of the automotive driveline is established to analyze the effect of variable inertia DMF on the resonance frequency of the system under different currents. The results show that the electromagnetic device introduced in the DMF can realize the active adjustment of the moment of inertia and enable the resonance frequency to decrease with increasing rotational speed, which expands the idea of optimizing the vibration damping performance of the DMF and provides a reference for better control of the torsional vibration of the automobile or other mechanical transmission systems.

Thermoelastic damping in asymmetric vibrations of nonlocal circular plate resonators with Moore-Gibson-Thompson heat conduction

Precise estimation of the amount of thermoelastic damping (TED) in small-sized resonators is one of the crucial issues in their optimal design. According to several experimental, numerical and theoretical findings, the behavior of structures with such small dimensions in structural and thermal domains does not follow classical elasticity theory and the Fourier law of heat conduction. The objective of this work is to develop a nonclassical formulation for computing TED in asymmetric vibrations of circular nanoplates according to nonlocal theory (NT) and Moore-Gibson-Thompson (MGT) heat transfer model. To do so, first, the coupled equations of motion and heat are derived in the purview of NT and MGT model. Then, the real and imaginary parts of the system frequency are extracted from the frequency equation affected by thermoelastic coupling. Finally, by means of the existing definition for TED, a mathematical expression including nonlocal parameter of NT and nonclassical constants of MGT model is obtained to make an estimate of TED value. In the numerical examples section, to ensure the credibility of the provided formulation, the results obtained through this model are compared with those reported in the literature in the context of simpler models. Then, by presenting various graphical data, the type and extent of the role of different factors in TED changes are appraised. The obtained results indicate that employing NT and MGT model can substantially impact the amount of TED compared to the estimations of the classical formulation. Furthermore, the comparison of results reveals that the magnitude of TED in asymmetric vibration modes surpasses that in symmetric ones, and consequently incorporating asymmetric vibration modes is crucial for thorough analysis of TED in circular nanoplates. Thus, the formulation presented in this article can aid in achieving an optimal design for such plates, particularly in terms of minimizing energy loss.

Quantum instability and Ehrenfest time for inverted harmonic oscillator

Abstract We used out-of-time order correlators (OTOCs) to investigate the quantum instability and Ehrenfest time for the inverted harmonic oscillator (IHO). For the initial states located in the stable manifolds of IHO, we find that the corresponding OTOC exhibits identical evolutionary characteristics as the saddle point before the Ehrenfest time. For the initial states located in the unstable manifolds,
the OTOCs still grow exponentially but the time to maintain exponential growth is related to the center position of its wave packet in the phase space. Moreover, we use the Husimi Q function to visualize the quantum wave packets during the OTOC’s exponential growth. Our results show that the quantum instability exists at arbitrary orbits in the IHO system, and the Ehrenfest time in the IHO system depends not only on the initial system photon number, but also on the central positions of the initial states in the phase space.

Eluding Zeno effect via dephasing and detuning.

Abstract We analyze some variants of the Zeno effect in which the frequent observation of the population of an intermediate state does not prevent the transition of the system from the initial state to a certain final state. This is achieved by considering system observation involving suitably introduced phase shifts and detunings that leads to a rather rich measurement-induced dynamics by the alteration of the interference governing quantum evolution. For initial nonclassical states this includes entanglement as a way of evolution from the initial to the final state avoiding the intermediate state. This possibility is presented in a particular physical scenario in the form of a chain of three coupled harmonic oscillators, but we readily show then that the idea can be applied to other physical systems as well, such as atomic-level dynamics. These results are significant for a better knowledge of fundamental quantum concepts as well as regarding suitable applications in the proper control of quantum dynamics, as this is a key feature of modern applications of the quantum theory.

An influence of electronic structure theory method, thermodynamic and implicit solvation corrections on the organic carbonates conformational and binding energies.

An impact of an electronic structure or force field method, gas-phase thermodynamic correction, and continuum solvation model on organic carbonate clusters (S)n conformational and binding energies is explored. None of the tested force field (GFN-FF, GAFF, MMFF94) and standard semiempirical methods (PM3, AM1, RM1, PM6, PM6-D3, PM6-D3H4, PM7) can reproduce reference RI-SCS-MP2 conformational energies. Tight-binding GFNn-xTB methods provide more realistic conformational energies which are accurate enough to discard the least stable conformers. The effect of thermodynamic correction is moderate and can be ignored if the gas phase conformational stability ranking is a goal. The influence of continuum solvation is stronger, especially if reinforced with the Gibbs free energy thermodynamic correction, and results in the reduced spread of conformational energies. The cluster formation binding energies strongly depend on a particular approach to vibrational thermochemistry with the difference between traditional harmonic and modified scaled rigid - harmonic oscillator approximations reaching 10 kcal mol-1.

Diffusion coefficients preserving long-time correlations: consequences on the Einstein relation and on entanglement in a bosonic Bogoliubov system

Abstract We analytically derive the diffusion coefficients that drive a system of N coupled harmonic oscillators to an equilibrium state exhibiting persistent correlations. It is shown that the main effect of the latter consists in a renormalization of the natural frequencies and the friction coefficients of the oscillators. We find that the Einstein relation may be satisfied at low temperatures with frequency-dependent effective friction coefficients provided that the physical constraints are fulfilled. We also investigate entanglement evolution in a bipartite bosonic Bogoliubov system initially prepared in a thermal squeezed state. It is found that, in contrast to what one may expect, strong coupling slows down sudden death of the entanglement, and for initially separable states entanglement generation may occur.

Fundamental Laws and Quantum Dynamics

Background: Recently, we obtained a unitary theory of quantum mechanics and general relativity, where a quantum particle is a continuous distribution of matter in the two conjugate spaces of the coordinates and momentum, quantized by the equality of the mass parameter describing the relativistic dynamics of the matter, with the mass as an integral of the matter density. However, in this framework, we have not explicitly revealed the connection between our new theory and the fundamental laws of quantum mechanics. Methods: We analyzed in detail the three fundamental laws of quantum mechanics, explicitly describing experimental data: 1) Planck’s law of the blackbody electromagnetic radiation of a system of electrically charged harmonic oscillators, 2) Einstein’s law of the photon energy proportionality with the photon frequency, and 3) de Broglie’s law of the quantum particle as an oscillator in space. Results: We reobtained the two dynamical equations, in the conjugate spaces of the coordinates and momentum, as functions of the Lagrangian system, unlike the Schrödinger equation, depending on the Hamiltonian. Conclusion: According to the fundamental laws of quantum mechanics, a quantum particle is a continuous distribution of matter with an intrinsic mass, unlike the conventional quantum mechanics for the state occupation probabilities of punctual entities moving with the light velocity and getting an apparent mass only by collisions with some bosons pervading the whole universe. According to these laws, we obtained a quantum theory in agreement with common sense, classical logic, and general relativity.

Emergence of squeezed coherent states in Kaluza–Klein cosmology

In this work, we consider a propagating scalar field on Kaluza–Klein-type cosmological background. It is shown that this geometrical description of the Universe resembles – from a Hamiltonian standpoint – a damped harmonic oscillator with mass and frequency, both time-dependents. In this scenario, we construct the squeezed coherent states (SCSs) for the quantized scalar field by employing the invariant operator method of Lewis–Riesenfeld (non-Hermitian) in a non-unitary approach. The non-classicality of SCSs has been discussed by examining the quadrature squeezing properties from the uncertainty principle. Moreover, we compute the probability density, which allows us to investigate whether SCSs can be used to seek traces of extra dimensions. We then analyze the effects of the existence of supplementary space on cosmological particle production in SCSs by considering different cosmological eras.

Inductive mode selective damping of structural vibrations

AbstractStructural vibrations pose significant challenges in various engineering applications and require effective damping strategies to improve the overall performance and longevity of systems. While some oscillations can significantly reduce the longevity of systems, others might contribute positively to the overall system performance. Thus, this contribution presents a novel method of an inductive damping concept, that targets only specific vibrational modes based on their mode shapes. By analyzing the used inductive damping element in the context of a single degree of freedom oscillator, it is shown, that it functions as an ideal viscous damper only if the dynamics of the electric part of the system are neglected. The concept of mode selective damping is presented, using two of these damping elements in an oscillator chain with three masses. By altering the wiring configurations connecting the two damping elements in the electrical domain, the damping behavior can be manipulated to selectively damp only specific modes according to their mode shapes.

Giant Cushioning Effect in Facile Polymer/Nanoclay-Coated Flexible Polyurethane Foams.

In this work, a flexible polyurethane (PU) foam/polymer/clay (PUF/PAASep) composite is prepared via a simple dip-coating method. The composite exhibits excellent damping properties under quasi-static compression, vibration transmissibility, and impact resistance. For the composite preparation, sepiolite (Sep) dispersion in a polyacrylic acid (PAA) solution is first homogenized and evaluated using microscopy, and the obtained PAASep suspension is used to coat the PU foam uniformly for optimization of the quasi-static mechanical performance of the foam composites. The PU foam struts coated with 1 wt % PAA and 3 wt % sepiolite are strengthened, resulting in an 8-fold improvement of the stiffness and three-times increase of the impact force resistance compared to the uncoated PU foams. More importantly, the PU foam composites show a remarkable vibration damping capability, with the loss modulus 57 times that of the uncoated PU foams, enabled by micro friction and stick-slip effects mediated by the PAASep coatings. The facile prepared PAASep-coated PU foams have significant potential for cushioning, packaging, and broad engineering applications involving energy absorption.

Design, fabrication and vibration characteristics of a novel composite auxetic structure embedded with resonators

With the rapid development of shipbuilding and aerospace industries, the mechanical performance requirements for structures are becoming increasingly demanding. Conventional vibration reduction structures cannot meet the requirements for lightweight, high load capacity, low frequency and broadband vibration reduction. Therefore, it is necessary to consider new structural topologies and material systems. Inspired by the lightweight and high strength characteristics of composite materials, the negative Poisson's ratio characteristics and the locally resonating phononic crystal, the carbon fiber composite auxetic structure embedded with resonators is proposed. Embedded resonators within composite auxetic structures can be strategically positioned to introduce gaps, thereby enhancing the vibration damping performance. The basic auxetic structure is prepared by simpler methods including molding and bonding, and the outer shell of resonator is made by 3D printing technology. The method enables the design of appropriate outer shell based on various cavity types within the structure, ensuring a stable connection between resonators and the structure itself. The range of the band gap can be predicted based on the negative effective mass. Vibration behavior and band gap characteristics of the structure are proved through vibration experiments and numerical simulations. It is revealed that the structure can generate local resonant band gaps at lower frequencies. Meanwhile, the coupling relationship between the auxetic structure and the resonator makes an impact to the band gap range. Therefore, the proposed structure can meet the required multi-functional integrated performance requirements. Furthermore, the parametric analysis is carried out, and the relevant conclusions can provide theoretical guidance for designing porous composite structures with effective low-broadband vibration reduction capabilities.

Observational signature of QPOs with particle motion around non-commutative Schwarzschild black hole surrounded by perfect fluid dark matter

We analyze the orbital and oscillatory motion of test particles in the vicinity of a non-commutative black hole submerged in perfect fluid dark matter and derive analytical solutions for the specific angular momentum and radial profiles of energy. Using the effective potential approach, we discuss the stability of circular orbits. Furthermore, we calculate the innermost stable circular orbits. The effective force acting on particles has also been discussed. We find the expressions for frequencies of radial and latitudinal harmonic oscillations as a function of the black hole mass and the model’s parameters. The key features of quasi-periodic oscillations of test particles near the stable circular orbits in an equatorial plane of the black hole are discussed. Furthermore, Periastron precession has been discussed. We demonstrate that the parameters of the model have a strong influence on particle motion around black holes. By using the observational data of four different X-ray binary systems GRO J1655-40, XTE J1550-564, XTE J1859+226, and GRS 1915+105, within the scope of Monte Carlo Markov Chain, we constrain the involved parameters α and β. It is necessary to mention that our presented investigations through graphical behavior are viable with required physical behavior.

Orbital motion, epicyclic oscillations, and collision of particles around conformally coupled charged black hole

The orbital and oscillatory motion of test particles around a non-rotating, conformally coupled charged black hole with scalar hair is studied in this work. The impact of the black hole parameters on particle motion is investigated. The stable circular orbits, specific angular momentum, and radial profiles with specific energy are computed using an analytical approach. We discuss the stability of circular orbits using the effective potential technique. We also compute the effective force and innermost stable circular orbits around a conformally connected charged black hole with scalar hair. In addition, we display the trajectories of particles around a conformally connected charged black hole with scalar hair and numerically integrate the equations of motion for the test particle. Additionally, we determine the formulae for the frequencies of latitudinal and radial harmonic oscillations about the mass of the black hole and the model’s parameters. The main characteristics of quasi-periodic oscillations close to stable circular orbits in the black hole’s equatorial plane are examined for test particles. Furthermore, the Periastron precession process is explored. We show particle motion around black holes strongly depends on the model parameters. It is important to note that the graphical behavior describing our findings is viable.

Particle dynamics with trajectories and epicyclic oscillations around a piece-wise black hole immersed in dark matter

We investigate the dynamics of neutral test particles revolving around a non-rotating black hole immersed in dark matter DM. We derive exact solutions for the radial profiles of specific angular momentum and energy for equatorial stable circular orbits as a function of the parameters of the black hole. Using the effective potential approach, we explore the stability of these circular orbits and the effective force acting on particles in the presence of dark matter. Additionally, we examine the impact of dark matter on the innermost stable circular orbits. By numerically integrating the equations of motion, we plot the trajectories of particles around the black hole and analyze how dark matter affects these trajectories. We also calculate the analytical frequencies of radial and latitudinal harmonic oscillations as functions of the dark matter parameter for both local and distant observers. We compare these results with scenarios where dark matter is absent. Furthermore, we study the effects of dark matter on periastron precession. We present an analysis of the constraints on the dark matter and black hole mass parameters using Markov Chain Monte Carlo (MCMC) methods. Our study focuses on QPOs observed in X-ray binaries, in particular, the microquasars GRO J1655-40 and XTE J1550-564, and the centers of the galaxies M82 X-1 and Sgr A⁎. We also analyze the particle collisions, discussing the center-of-mass energy of the colliding particles. Our observations reveal that the motion of particles revolving around the black hole is significantly affected by varying the model parameters.

Classical and quantum analysis of gravitational singularity from Raychaudhuri equation

The present work deals with the Raychaudhuri equation (RE) to examine the space-time singularity both from classical and quantum point of view. The RE has been looked upon in terms of a classical linear Harmonic oscillator and Focusing theorem has been studied. Also, the Raychaudhuri scalar has been shown to affect the convergence and singularity formation in Black-holes and cosmology. Finally, resolution of initial big-bang singularity has been attempted quantum mechanically in two ways namely by canonical quantization and by formulation of Bohmian trajectories.

Design and evaluation of self-tuning optimal control for vibration suppression of magnetorheological semi-active suspension

The objective of this paper is to enhance the vibration damping capabilities of magnetorheological (MR) semi-active suspension by utilizing a self-tuning LQG control method. Firstly, to determine the mechanical model of MR damper using the hyperbolic tangent model, mechanical experiments were performed with a damping force test machine under various input excitations. Experimental and simulation data were compared to confirm the accuracy of the mechanical model for MR damper. The MR damper is then incorporated into the vehicle’s semi-active suspension system to create a quarter-car suspension model. In order to tackle the problems associated with low control accuracy and poor dynamic adjustment in traditional LQG controllers where the weighting matrix coefficients are difficult to determine, a self-tuning LQG controller based on gravity search algorithm (GSA-LQG) was designed. Finally, the designed controller performance was evaluated by the simulation and experimental results obtained from the random and sinusoidal excitation roads. Experimental data reveal that when subjected to GSA-LQG control, the suspension control performance is considerably enhanced compared to the passive control, PID control and conventional LQG control suspension. Based on these outcome, it can be concluded that the proposed algorithm is effective and the experimental platform is feasible.

Improved light-cone harmonic oscillator model for the ϕ -meson longitudinal leading-twist light-cone distribution amplitude and its effects to Ds+→ϕℓ+νℓ

In the present paper, we study the properties of ϕ-meson longitudinal leading-twist light-cone distribution amplitude ϕ2;ϕ∥(x,μ) by starting from a light-cone harmonic oscillator model for its wave function. To fix the input parameters, we derive the first ten order ξ moments of ϕ2;ϕ∥(x,μ) by using the QCD sum rules approach under the background field theory. The curves of ϕ2;ϕ∥(x,μ=2 GeV) tend to be a single-peak behavior, which is consistent with the latest lattice QCD result. To show how the twist-3 light-cone distribution amplitudes (LCDAs) affect the results, we consider two scenarios for the ϕ-meson chiral twist-3 LCDAs ϕ3;ϕ⊥(x) and ψ3;ϕ⊥(x), i.e., the ones using the Wandzura-Wilczek approximation with ϕ2;ϕ∥(x,μ) (S1) and the ones using self-consistent conformal expansion with second-order Gegenbauer moments a2;ϕ2 in this work (S2). As an application, we derive the Ds+→ϕ transition form factors (TFFs) by using the QCD light-cone sum rules. The TFFs at large recoil point for those two scenarios are given separately. As for the two TFF ratios γV and γ2, we obtain γV(S1)=1.755−0.005+0.008, γ2(S1)=0.852−0.133+0.135, γV(S2)=1.723−0.021+0.023, and γ2(S2)=0.785−0.104+0.100. After extrapolating those TFFs to the physically allowable region, we then obtain the transverse, longitudinal, and total decay widths for semileptonic decay Ds+→ϕℓ+νℓ. Then the branching fractions are B(S1)(Ds+→ϕe+νe)=(2.347−0.191+0.342)×10−3, B(S1)(Ds+→ϕμ+νμ)=(2.330−0.190+0.341)×10−3, B(S2)(Ds+→ϕe+νe)=(2.367−0.132+0.256)×10−3, and B(S2)(Ds+→ϕμ+νμ)=(2.349−0.132+0.255)×10−3, which show good agreement with the data issued by the BESIII, CLEO, and Collaborations. We finally calculate Ds+→ϕℓ+νℓ polarization and asymmetry parameters, which can be measured and tested in future experiments. Published by the American Physical Society 2024

Evaluation of Vibration Damping Enhancement in Laminated Aluminum Sheets for Automotive Application.

In this research, the vibration damping characteristics of the laminated aluminum sheets (LAS) were evaluated in a sheet specimen and an automotive dash panel and compared with those of the monolithic aluminum sheet (MAS). The LAS was fabricated with two 5xxx series aluminum alloy (AA) sheets (AA5052-O) with a thickness of 0.7 mm by inserting an acryl-based adhesive in between. The automotive dash panels were manufactured by multi-step stamping processes for the LAS and the MAS with a similar thickness. The shaker vibration test in a sheet specimen and the impact hammer test in an automotive dash panel were conducted to measure the frequency response function (FRF) of LAS, compared with those of MAS. The results show that the frequency response function made by the LAS has less noise and fluctuation than that of the MAS in a sheet specimen and an automotive dash panel. The damping ratios in a sheet specimen and an automotive dash panel made by the LAS have higher values than those of the MAS. This proves that the LAS has better vibration damping characteristics and a larger damping effect than the MAS in a sheet specimen and an automotive dash panel.

Optimization Study of a Tuned Mass Damper for a Large Monopile Wind Turbine

Passively tuned mass dampers (TMDs) are known to effectively mitigate the vibration of wind turbines. However, existing literature predominantly examines their application in damping vibrations of the tower or platform, overlooking the potential benefits of installing TMDs on the turbine blades themselves. This study investigates the impact of wind and wave loads on TMD damping effectiveness and proposes a comprehensive damping strategy involving TMDs installed in both the nacelle and the blades. The design optimized the mass and stiffness of these TMDs to enhance their performance. Results indicate that, as wind speeds increased from 12 m/s to 24 m/s, the power spectral density at the tower’s natural frequency (0.22 Hz) more than doubled. Notably, TMDs exhibited robust vibration damping capabilities under high wind speeds. Specifically, at wind speeds of 24 m/s, TMDs reduced anterior–posterior and lateral displacement at the tower top by 61.2% and 166.8%, respectively, when two TMDs were combined. Conversely, the study found that TMDs did not significantly improve vibration damping at lower to moderate wind speeds. This research underscores the importance of optimizing TMDs for high wind conditions to ensure wind turbine stability and mitigate potential vibration-related risks effectively under varying environmental loads, including wind and waves. It offers valuable insights for the refined design and deployment of TMDs in wind energy applications.