Harmonic Oscillator Model Research Articles

Wave‐to‐Wire Model and Output Performance Analysis of a Point Absorption Wave Energy Converter Based on Triboelectric Nanogenerator

Herein, a point absorption wave energy converter (WEC) model combined with a contact–separation mode triboelectric nanogenerator (PAW TENG) is proposed. The model considers the interaction between the hydrodynamic forces captured by a point absorption conversion device of wave energy and the electrostatic force of the TENG. According to the established harmonic oscillation model of the buoy, the buoy's hydrodynamic properties and power generation characteristics are studied using finite element simulation and numerical simulation calculations. The best matching resistor circuit for PAW TENG in regular waves is investigated and analyzed. The electrical characteristics of the PAW TENG in the irregular wave spectrum are also solved. This work will provide design ideas for the experimental design of a novel point absorption WEC.

Effect of Benzo-Annelation on Triplet State Energies in Polycyclic Conjugated Hydrocarbons.

In a series of earlier studies, the effect of benzo-annelation was found to be a useful tool for tuning the aromaticity in polycyclic conjugated compounds to desired level. In this work we studied the (anti)aromaticity of benzo-annelated derivatives of three conjugated hydrocarbons (anthracene, fluoranthene and biphenylene) in their lowest lying singlet (S0) and triplet (T1) states by means of the energy effect (ef), harmonic oscillator model of aromaticity (HOMA), multicentre delocalization indices (MCI), magnetically induced current densities (MICDs) and nucleus independent chemical shifts (NICS). We showed that benzo-annelation is a topology-based effect which can be used to modify the T1 state excitation energies (E(T1)). A quantitative model was established being able to accurately predict the E(T1) based only on the numbers of angularly, linearly and geminally annelated benzene rings. In addition, it was demonstrated that the E(T1) can be directly related to the (anti)aromatic character of the central ring in the studied molecules in their S0 state.

Manipulation of plasmon dephasing time via the coupling between localized surface plasmon resonance and waveguide modes

Manipulation of plasmon dephasing time of the hybrid modes has gained much attention in recent years, which plays critical roles in many important applications of plasmonics. Here, we manipulate the dephasing time of plasmonic field resulting from coupling of the localized surface plasmon (LSP) of the nanosphere array and the waveguide mode supported by the indium tin oxide film with quasi-normal mode-assisted harmonic oscillator model method. It results in the formation of two distinct modes, transverse electric (TE) and transverse magnetic (TM) modes. Such coupling can significantly modify the dynamics of the original plasmonic modes. The dephasing time of the hybrid plasmon modes, encompassing both TE and TM modes, can be extended from 1.25fs to 4.95fs, which is about 2–7 times compared to that of a single localized surface plasmon resonant mode. More importantly, by changing the structural parameters, we can flexibly manipulate either the dephasing time with a fixed wavelength or the resonant wavelength with a fixed dephasing time.

Theoretical and kinetic study of the hydrogen abstraction reactions of ethyl propionate

Ethyl propionate shows great promise as a biodiesel molecule model. However, the current oxidation kinetic model falls short in accurately predicting its combustion behavior. Therefore, this study employed ab initio quantum chemistry methods to analyze the hydrogen abstraction reactions of ethyl propionate with various reactive radicals, including OH, O, H, CH3, C2H3, C2H5, HO2, CH3O and CH3O2, which play a critical role in refining the oxidation kinetics. Theoretical calculations were conducted to determine the rate constants and branching ratios for these reactions at temperatures ranging from 500 K to 2500 K using transition state theory, quasi-rigid rotor harmonic oscillator model, and tunneling correction. After updating the kinetics of hydrogen abstraction reactions in the oxidation mechanism proposed by Metcalfe et al., the modified model was validated by comparing the simulated mole fraction evolutions of ethyl propionate and major products in a jet-stirred reactor, ignition delay in a closed homogeneous batch reactor, and laminar flame speed with experimental data. The findings indicate that the modified model reliably reproduces the experimental data and significantly improves the prediction accuracy for low-temperature combustion of ethyl propionate when compared to the original model.

Thermophysical Properties for Alkylphosphonate and Alkylphosphate Compounds

Organophosphorus compounds have a wide range of applications; they are commonly used as drugs or pesticides or in the production of ion batteries. However, some organophosphorus compounds, which were developed as warfare nerve agents, are neurotoxic and potentially lethal to living organisms. On the basis of the literature search, certain properties of these compounds are not well known. Knowledge of thermodynamic properties and the availability of reliable data are fundamental in the development of methods for detecting, treating, and safely analyzing decontamination. For research purposes, substitutes, called simulants, which have similar molecular structures and properties but are less toxic, are often employed. This work presents a thermodynamic study of four organophosphorus nerve agent simulants: trimethyl phosphate, triethyl phosphate, dimethyl methylphosphonate, and diethyl methylphosphonate. Differential scanning calorimeter and a Tian–Calvet type calorimeter were used to analyze their phase behavior and measure the liquid heat capacities, respectively. Vapor pressures were experimentally determined with the static method. Ideal-gas heat capacities were calculated using the R1SM approach, which combines the rigid rotor–harmonic oscillator model, the one-dimensional hindered rotor model, and the mixing model. The results obtained were compared with the data from the literature and simultaneously correlated to obtain a highly reliable thermodynamic description.Graphical

Revenue Management in Airlines and External Factors Affecting Decisions: The Harmonic Oscillator Model

The Revenue Management (RM) problem in airlines for a fixed capacity, single resource and two classes has been solved before by using a standard formalism. In this paper we propose a model for RM by using the semi-classical approach of the Quantum Harmonic Oscillator. We then extend the model to include external factors affecting the people’s decisions, particularly those where collective decisions emerge.

A theoretical study on 1H-indole-2,3-dione complexes with lithium, sodium, and potassium cations.

A comparative study of the change in different properties of electronic and structural of the free 1H-indole-2,3-dione molecule and its complexes has been obtained. HOMA analysis was performed to investigate the effects of lithium sodium and potassium cations on the aromaticity of lithium sodium and potassium complexes of 1H-indole-2,3-dione. Several 1H-indole-2,3-dione complexes with lithium, sodium, and potassium cations were optimized at the B3LYP/6-311G(d,p) level. The cation and π interaction has been investigated from different aspects, including interaction energy calculations, charge transfer values, and changes in the aromaticity of the ring upon complexation. The charge transfer and natural population analysis for the complexes were performed with the natural bond orbital (NBO) analysis. The properties of bond critical points in complexes were studied by applying the quantum theory of atoms in molecules (QTAIM). Finally, the aromaticity change of phenyl induced upon complex formation was evaluated by applying the harmonic oscillator model of aromaticity (HOMA). [Li-INa]+ and [[Li-INb]+ were optimized with the wB97XD function using a version of Grimme's D2 dispersion model, and the absorption energy was compared with the calculation made with the B3LYP functional.

Decay process within the QCDSR approach* *Supported in part by the National Natural Science Foundation of China (12265010, 12265009) and the Project of Guizhou Provincial Department of Science and Technology (ZK[2021]024, ZK[2023]142)

In this paper, we investigate the charmed meson rare decay process using an approach based on QCD sum rules. First, the pion twist-2, 3 distribution amplitude (DA) moments and are calculated up to the tenth and fourth orders, respectively, in the QCD sum rules according to the background field theory. After constructing the light-cone harmonic oscillator model for the pion twist-2, 3 DAs, we obtain their behaviors by matching the calculated ξ-moments. Then, the transition form factors (TFFs) are calculated using an approach based on QCD light-cone sum rules. The vector form factor at the large recoil region is . Using the rapidly converging simplified series expansion of , we present the TFFs and corresponding angular coefficients in the whole squared momentum transfer physical region. Based on non-standard neutrino interactions, the decay can be related to the decay indirectly. Thus, we first describe the semileptonic decay process , differential decay widths, and branching fraction with . The differential/total predictions for forward-backward asymmetry, -differential flat terms, and lepton polarization asymmetry are also reported. The prediction for the branching fraction is .

Planar terahertz multi-resonator meta-waveguide based upon strongly coupled nested split-ring resonator

In this paper, we propose terahertz (THz) meta-waveguide geometry based on one-dimensional array of nested split-ring resonators (SRRs) comprising three split gaps. The meta-waveguide geometry consists of three layers of materials namely copper, dielectric and meta-molecules. The meta-molecules of aluminum with nested split gaps are placed periodically in one dimension along the wave propagation direction. The numerically obtained waveguide transmission spectrum shows the excitation of multiple resonances, resulting from three split gaps and a strong coupling between them. We found that the resonant frequencies of the guided modes can be tuned by varying the inter-split gaps separation which controls the coupling. The meta-waveguide geometry offers greater interaction of meta-molecules with the propagating terahertz radiation which can be sensitive to various applications. Further, the proposed design offers a flexibility in tuning resonant behavior owing to nested split gaps and coupling between them. We have examined the electric field distribution to confirm the multiple resonance excitations supported by the meta-waveguide geometry. We have also suggested a coupled harmonic oscillator model to interpret and analyze the numerically simulated waveguide transmission results. The study opens up new avenues for terahertz meta-waveguide based highly sensitive devices such as sensors, storage applications etc. where properties can be controlled via coupling within a resonator in a nested split gaps approach.

Two-Dimensional Electronic Spectroscopy Resolves Relative Excited-State Displacements.

Knowledge of relative displacements between potential energy surfaces (PES) is critical in spectroscopy and photochemistry. Information on displacements is encoded in vibrational coherences. Here we apply ultrafast two-dimensional electronic spectroscopy in a pump-probe half-broadband (HB2DES) geometry to probe the ground- and excited-state potential landscapes of cresyl violet. 2D coherence maps reveal that while the coherence amplitude of the dominant 585 cm-1 Raman-active mode is mainly localized in the ground-state bleach and stimulated emission regions, a 338 cm-1 mode is enhanced in excited-state absorption. Modeling these data with a three-level displaced harmonic oscillator model using the hierarchical equation of motion-phase matching approach (HEOM-PMA) shows that the S1 ← S0 PES displacement is greater along the 585 cm-1 coordinate than the 338 cm-1 coordinate, while Sn ← S1 displacements are similar along both coordinates. HB2DES is thus a powerful tool for exploiting nuclear wavepackets to extract quantitative multidimensional, vibrational coordinate information across multiple PESs.

Charger-Mediated Energy Transfer for Quantum Battery With Constant Time Dependent Step Function and Open System Approach

The energy charging of quantum battery is analysed by open quantum approach. The modelled of the charger and battery are described by harmonic oscillator model. We choose this model because the harmonic oscillator battery gives the largest maximum energy albeit having the longest maximum time. In this paper, the interaction as actual quantum system whose dynamic is determined by Lindblad Master Equation in terms of constant is a step function to set the time when energy flow and what time that energy stop to flow or the interaction between charger and battery has stopped. The energy equation was determined by solving the master equation with second order differential equation to find the first momenta from charger and battery. Based on the equation, the energy of charger will not be zero which mean after interaction in several times, the charger will not one hundred percent lose its energy when the energy storage in battery already done.

Quantum harmonic oscillator model for simulation of intercity population mobility

Quantum harmonic oscillator model for simulation of intercity population mobility

Probing Temperature-Induced Plasmonic Nonlinearity: Unveiling Opto-Thermal Effects on Light Absorption and Near-Field Enhancement.

Precise measurement and control of local heating in plasmonic nanostructures are vital for diverse nanophotonic devices. Despite significant efforts, challenges in understanding temperature-induced plasmonic nonlinearity persist, particularly in light absorption and near-field enhancement due to the absence of suitable measurement techniques. This study presents an approach allowing simultaneous measurements of light absorption and near-field enhancement through angle-resolved near-field scanning optical microscopy with iterative opto-thermal analysis. We revealed gold thin films exhibit sublinear nonlinearity in near-field enhancement due to nonlinear opto-thermal effects, while light absorption shows both sublinear and superlinear behaviors at varying thicknesses. These observations align with predictions from a simple harmonic oscillation model, in which changes in damping parameters affect light absorption and field enhancement differently. The sensitivity of our method was experimentally examined by measuring the opto-thermal responses of three-dimensional nanostructure arrays. Our findings have direct implications for advancing plasmonic applications, including photocatalysis, photovoltaics, photothermal effects, and surface-enhanced Raman spectroscopy.

Demonstrating Shrodenger equation involving harmonic oscillator potential with a position dependent mass in an external electric field

An external electric field is provided to the familiar one-dimensional quantum harmonic oscillator model with a various position mass m(x)=(a m_0)/(a+x). The Nikiforov-Uvarov approach is involved to investigate a particular solution to the exact Schrödinger equation. The exactly solvable confined model of the quantum harmonic oscillator in an external electric field was proposed. Starting with the BenDanial-Duke kinetic energy operator approximations, the construction of the position-dependent mass Schrödinger equation is studied. The analytic representation of the wave functions of the stationary states is expressed analytically and graphically using modified Laguerre polynomials as well as the energy spectrum. In contrast with the absence of an external electric field, when the energy spectrum totally overlaps with that of the harmonic oscillator potential in an external electric field: the energy spectrum becomes non-equidistant and varies depending on some factors. The Nikiforov-Uvarov approach succeeds broadly in demonstrating the wave function and energy spectrum and showing good sense.

Modelling plasmonic nanoparticles: Unveiling the optical torque potential with a dynamic driven damped harmonic oscillator model and width dependent effects

Linearly polarised light induces torque on anisotropic plasmonic nanoparticles, which allows for the manipulation of their orientation. In this study, we calculate the torque induced on a plasmonic nanocuboid by modelling the surface plasmon resonance (SPR) as a driven damped harmonic oscillator. Using numerical simulations, we demonstrate the model’s accuracy in predicting the torque induced for narrow nanocuboids. We also investigate the effects of varying the nanocuboid’s width on the torque and demonstrate that the torque behaviour exhibits drastic changes, with the formation and modification of additional modes, particularly at the transverse SPR wavelength. As the torque arises from the movement of charges, we utilize charge distribution profiles to explain this shift in torque behaviour.

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60.

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

On Some Origins of Tautomeric Preferences in Neutral Creatinine in Vacuo: Search for Analogies and Differences in Cyclic Azoles and Azines

In order to look for the origins of tautomeric preferences in neutral creatinine in vacuo, we examined prototropic conversions for model azoles, namely mono-hydroxy and mono-amino imidazoles, and also for their selected 1-methyl derivatives. All possible isomeric forms of creatinine and model compounds, resulting from intramolecular proton transfer (prototropy), conformational isomerism about –OH, and configurational isomerism about =NH, were studied in the gas phase (model of non-polar environment) by means of quantum-chemical methods. Because the bond-length alternation is a consequence of the resonance phenomenon, it was measured for all DFT-optimized structures by means of the harmonic oscillator model of electron delocalization (HOMED) index. Important HOMED analogies were discussed for investigated azoles and compared with those for previously studied cyclic azines, including pyrimidine nucleic acid bases. The internal effects were taken into account, and the stabilities of the investigated tautomers-rotamers were analyzed. Significant conclusions on the favored factors that can dictate the tautomeric preferences in creatinine were derived.

Probing dynamical sensitivity of a non-Kolmogorov-Arnold-Moser system through out-of-time-order correlators.

Non-Kolmogorov-Arnold-Moser (KAM) systems, when perturbed by weak time-dependent fields, offer a fast route to classical chaos through an abrupt breaking of invariant phase-space tori. In this work, we employ out-of-time-order correlators (OTOCs) to study the dynamical sensitivity of a perturbed non-KAM system in the quantum limit as the parameter that characterizes the resonance condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator (KHO) model, which displays stochastic webs resembling Arnold's diffusion that facilitate large-scale diffusion in the phase space. Although the Lyapunov exponent of the KHO at resonances remains close to zero in the weak perturbative regime, making the system weakly chaotic in the conventional sense, the classical phase space undergoes significant structural changes. Motivated by this, we study the OTOCs when the system is in resonance and contrast the results with the nonresonant case. At resonances, we observe that the long-time dynamics of the OTOCs are sensitive to these structural changes, where they grow quadratically as opposed to linear or stagnant growth at nonresonances. On the other hand, our findings suggest that the short-time dynamics remain relatively more stable and show the exponential growth found in the literature for unstable fixed points. The numerical results are backed by analytical expressions derived for a few special cases. We will then extend our findings concerning the nonresonant cases to a broad class of near-integrable KAM systems.

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Generalized Fano resonance theory based on Fabry-Perot cavity

Fano resonance is a pervasive phenomenon observed across many systems, which has traditionally been interpreted through the coupled harmonic oscillator model. However, the traditional model is limited, especially for different line shapes. In this study, we offer a generalized model by incorporating an imaginary coupling coefficient. This approach fundamentally differs from existing theories by identifying two unique Fano line shapes in the electric field of metallic Fabry–Perot cavity. The model connects the imaginary coupling coefficient with phase distribution of the coupling mode, thus revealing the relationship between Fano line shapes and the trend of phase shifts. This provides a new way for understanding and manipulating Fano resonance. The Fano resonance generation has been validated experimentally through reflection spectra. Our investigation offers a new perspective for understanding of Fano resonance via the coupled harmonic oscillator model and paves a way for the development of dynamically tunable Fano resonance devices.