Oscillator Model Research Articles

HOMAc: A Parameterization of the Harmonic Oscillator Model of Aromaticity (HOMA) That Includes Antiaromaticity.

The harmonic oscillator model of aromaticity (HOMA) offers a straightforward route to quantifying aromaticity that requires no other information than the bond lengths of the conjugated ring in question. Given that such information is often readily obtainable from quantum-chemical calculations, it is pertinent to improve this parametrized model as much as possible. Here, a new version of HOMA is presented where, atypically, the corresponding parameters are derived from the actual bond lengths of both aromatic and antiaromatic (rather than nonaromatic) reference compounds, as calculated with a high-level method. The resulting model, which we denote HOMAc, covers CC, CN, NN, and CO bonds and is tested at eight different levels of theory for 45 (single-ring, multi-ring, carbocyclic, N,O-heterocyclic) molecules across the aromatic-antiaromatic spectrum. Thereby, it is found that HOMAc provides a description of aromaticity and antiaromaticity in better accord with magnetic, energetic, and π-delocalization-based reference data than does the standard parametrization of HOMA. Altogether, the results highlight the possibility to realize more reliable geometry-based probing of (anti)aromaticity with the use of HOMAc and with substantial freedom in the choice of quantum-chemical method.

Mathematical Modeling for Oscillations Driven by Noncoding RNAs.

In this chapter, we first survey strategies for the mathematical modeling of gene regulatory networks for capturing physiologically important dynamics in cells such as oscillations. We focus on models based on ordinary differential equations with various forms of nonlinear functions that describe gene regulations. We next use a small system of a microRNA and its mRNA target to illustrate a recently discovered oscillator driven by noncoding RNAs. This oscillator has unique features that distinguish it from conventional biological oscillators, including the absence of an imposed negative feedback loop and the divergence of the periods. The latter property may serve crucial biological functions for restoring heterogeneity of cell populations on the timescale of days. We describe general requirements for obtaining the limit cycle oscillations in terms of underlying biochemical reactions and kinetic rate constants. We discuss future directions stemming from this minimal, noncoding RNA-based model for gene expression oscillation.

ESTUDO COMPUTACIONAL DA INFLUÊNCIA DE CO2 NO EMPILHAMENTO-π DE MONÔMEROS DE CORONENO SUBSTITUÍDOS COM ENXOFRE

COMPUTATIONAL STUDY OF THE INFLUENCE OF CO2 ON THE π-STACKING OF SULFUR-SUBSTITUTED CORONENE MONOMERS. Asphaltenes are complex molecules with a tendency to aggregate. This property can be an issue for the oil industry due to CO2 reinjection into reservoirs to mitigate these gas emissions. The present theoretical study aimed to study the CO2 interaction with no-substitute and substituted coronene as an asphaltene model compound at CAM-B3LYP-D3/6-311G(d,p) level. The electronic properties were evaluated using harmonic oscillator model of aromaticity (HOMA), quantum theory of atoms in molecules (QTAIM), and reduced density gradient (RDG) methods. The results showed that the coronene’s functionalization by a sulfur atom changes the coronene’s electronic structure. However, functionalization does not change the type of interactions between the monomers, as they remain predominantly van der Waals interactions. CO2 interaction with substituted coronene barely changed due to the presence of sulfur atoms. However, in dimers, the position of the heteroatom directly influences the interaction with CO2, although it is insufficient to change the interaction’s magnitude. For this reason, our results indicate that the sulfur heteroatom in asphaltenes should be addressed. However, new studies must be conducted by increasing the number of substituents, CO2 numbers, and the model size.

Probing |Vcs| and lepton flavor universality through D→K0*(1430)ℓνℓ decays

In this paper, we calculate the semileptonic decays D→K0*(1430)ℓνℓ with ℓ=(e,μ) induced by c→sℓνℓ transition. For the key component, D→K0*(1430) transition form factors (TFFs) f±(q2) are calculated within the framework of QCD light cone sum rule. Then, we consider two scenarios for K0*(1430)-meson twist-2 distribution amplitude. For the scenario 1 (S1), we take the truncated form based on Gegenbauer polynomial series. Meanwhile, we also consider the scenario 2 (S2) constructed by light cone harmonic oscillator model, where the model parameters are fixed by the K0*(1430)-meson twist-2 distribution amplitude tenth-order ξ moments calculated by using the background field theory. For the TFFs at a large recoil point, we have f+(S1)(0)=0.597−0.121+0.122 and f−(S1)(0)=−0.136−0.035+0.023, f+(S2)(0)=0.663−0.134+0.135, and f−(S2)(0)=−0.202−0.046+0.026. After extrapolating TFFs to the whole physical q2 region, we calculate the branching fractions of D0→K0*+(1430)ℓ−ν¯ℓ and D+→K0*0(1430)ℓ+νℓ, which at 10−4-order level for the S1 and S2 cases. Meanwhile, we predict the CKM matrix |Vcs|(S1)=0.973−0.183+0.259, |Vcs|(S2)=0.880−0.165+0.234, and lepton flavor universality RK0*(S1)=0.768−0.368+0.560, RK0*(S2)=0.764−0.365+0.555. Finally, we discuss the angular observables of forward-backward asymmetries, lepton polarization asymmetries, and q2-differential flat terms for this decay. Published by the American Physical Society 2024

Emergence of multiple spontaneous coherent subnetworks from a single configuration of human connectome coupled oscillators model

Multi-state metastability in neuroimaging signals reflects the brain’s flexibility to transition between network configurations in response to changing environments or tasks. We modeled these dynamics with a Kuramoto network of 90 nodes oscillating at an intrinsic frequency of 40 Hz, interconnected using human brain structural connectivity strengths and delays. We simulated this model for 30 min to generate multi-state metastability. We identified global coupling and delay parameters that maximize spectral entropy, a proxy for multi-state metastability. At this operational point, multiple frequency-specific coherent sub-networks spontaneously emerge across oscillatory modes, persisting for periods between 140 and 4300 ms, reflecting flexible and sustained dynamic states. The topography of these sub-networks aligns with empirical resting-state neuroimaging data. Additionally, periodic components of the EEG spectra from young healthy participants correlate with maximal multi-state metastability, while dynamics away from this point correlate with sleep and anesthesia spectra. Our findings suggest that multi-state metastable functional dynamics observed in empirical data emerge from specific interactions of structural topography and connection delays, providing a platform to study mechanisms underlying flexible dynamics of cognition.

Mathematical Model of Cabin With Suspension System to Analyze its Oscillatory Stability During Vehicle Movement

This research focuses on the development of a methodology for the analysis of nonlinear oscillations of a vehicle cab with a suspension system. When designing vehicles with cab suspension systems, it is important to align their operation with other vehicle modules and systems that collectively ensure the required comfort and dynamic parameters and prevent resonant oscillations in the cab. A vehicle cab is a dynamic system with 6 degrees of freedom, therefore its oscillations are spatially complex and feature energy direction switching. Thus, the problems of suspended cab dynamics should be solved in a non-linear spatial setting that can account for oscillation energy redistribution between various spatial direc-tions. The purpose of this work is to develop a mathematical model for the spatial oscillations of a suspended cab relative to the vehicle undercarriage that can help analyze the non-linear oscillations that occur in the cab to study their stability during vehicle movement. This study helped identify the adverse frequency ratios for the disturbing impact on the can suspension system that can reduce cab comfort and result in the instability of its oscillations. The authors developed methods to reduce the amplitudes of suspended cab sway when its spatial oscillations are unstable. The developed methods and mathematical model help identify and prevent resonant spatial phenomena in the cab at all stages of designing vehicle cab suspension systems. The authors proposed specific solutions to design cab suspension systems to improve cab comfort and reduce cab sway, including the usage of air bellows that can form progressive non-linear load characteristics and controllable hydraulic dampers that can increase the damping coefficient in the cab suspension system during cab sway.

Terahertz Time-Domain Spectroscopy of Substituted Gadolinium Gallium Garnet

Temperature dependence of the lowest frequency transverse optical phonon (TO1) in a single crystal Substituted Gadolinium Gallium Garnet (SGGG, (001)) was studied using terahertz time-domain spectroscopy at temperatures between 80 K and 500 K. The complex dielectric constants were calculated from the optical constants fitting with the Lorentz oscillator model. The results show that the TO1 phonon of SGGG is at 2.5 THz at room temperature, the frequency of the TO1 phonon slightly decreases, and the dumping factor clearly increases with increasing temperature. Additionally, our results demonstrate that even a small substitution can induce a phonon shift, leading to higher absorption and causing a slight degradation in thermal stability. Our work is expected to support the development of magneto-optical and spintronic devices.

Theoretical insights into charge transfer plasmon lifetime

In this Letter, we present a theoretical study based on the Lorentz function and harmonic oscillator model to explore temporal dynamics of charge transfer plasmon (CTP) resonances. By fitting scattering curves and near-field oscillations, we determine the dephasing time of CTP modes in conductively connected gold nanodisk dimers. We show that, compared with the well-known particle plasmon and dimer plasmon modes, the CTP mode has a narrow spectral width and longer lifetime. Moreover, quantitative analysis of optical near-fields reveals that CTP modes oscillate completely out-of-phase with the particle plasmon and dimer plasmon modes. The dephasing time, near-field decay rate and charge transfer time of the CTP mode are found to be on a few femtosecond timescales, implying that conductively connected plasmonic nanoparticles hold great promise as channels for ultrafast transfer of information in all-optical computing and optoelectronic devices.

An Agent-Based Model of Metabolic Signaling Oscillations in Bacillus subtilis Biofilms.

Microbes of nearly every species can form biofilms, communities of cells bound together by a self-produced matrix. It is not understood how variation at the cellular level impacts putatively beneficial, colony-level behaviors, such as cell-to-cell signaling. Here we investigate this problem with an agent-based computational model of metabolically driven electrochemical signaling in Bacillus subtilis biofilms. In this process, glutamate-starved interior cells release potassium, triggering a depolarizing wave that spreads to exterior cells and limits their glutamate uptake. More nutrients diffuse to the interior, temporarily reducing glutamate stress and leading to oscillations. In our model, each cell has a membrane potential coupled to metabolism. As a simulated biofilm grows, collective membrane potential oscillations arise spontaneously as cells deplete nutrients and trigger potassium release, reproducing experimental observations. We further validate our model by comparing spatial signaling patterns and cellular signaling rates with those observed experimentally. By oscillating external glutamate and potassium, we find that biofilms synchronize to external potassium more strongly than to glutamate, providing a potential mechanism for previously observed biofilm synchronization. By tracking cellular glutamate concentrations, we find that oscillations evenly distribute nutrients in space: non-oscillating biofilms have an external layer of well-fed cells surrounding a starved core, whereas oscillating biofilms exhibit a relatively uniform distribution of glutamate. Our work shows the potential of agent-based models to connect cellular properties to collective phenomena and facilitates studies of how inheritance of cellular traits can affect the evolution of group behaviors.

Calculation of Adsorbate Free Energy Using the Damping Function Method.

Adsorbate free energies are important parameters in surface chemistry and catalysis. Because of its simplicity, the harmonic oscillator (HO) model remains the most widely used method for calculating adsorbate free energy in many fields, including microkinetic modeling. However, it is well-known that the HO method is ineffective for weak adsorption. In this study, we propose a translational model with a diffusion barrier to calculate the state functions of near free translation. Furthermore, an effective mass is introduced in this model. To address hindered translation uniformly, a diffusion barrier-based damping function (DF) is proposed that effectively links the harmonic vibration and translation limits. Adsorbates are divided into three categories according to their adsorption strength and diffusion barrier height. Adsorbed hydrogen atoms have a strong binding energy and relatively high vibrational frequency but a low diffusion barrier. The HT and our proposed DF methods predict that the adsorbed hydrogen atoms behave as translation above room temperature, while the previous DF method predicts that they behave as vibration at any temperature. At last, the dehydrogenation reaction of propane on the Pt(111) surface was taken as an example to illustrate the influence of different methods on the thermodynamic functions.

Modeling the tail risk of crude oil futures using a quantum approach

This study proposes a quantum approach to measure the tail risk of crude oil futures. Based on the quantum harmonic oscillator (QHO) model, we first model the log return process of crude oil futures. From the equilibrium distribution of QHO model, we calculate the well-known tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES); we confirm that this quantum approach provides precise estimates of in-sample and out-of-sample VaR and ES for crude oil futures. The findings suggest the QHO model for log return process outperforms the geometric Brownian motion for price process and the historical simulation approach. The excellence of QHO model in explaining the tail risk of crude oil futures can be attributed to its fast angular frequency and high probability allocation in excited states. Crude oil market participants can use this study’s analytical framework to precisely measure and manage potential risks in the marketplace. Regulatory authorities can evaluate the degree of crude oil market instability through the current market state of crude oil futures characterized by the QHO model parameters while devising and revising crude oil market regulations. Future research can examine quantum models with (1) different assumptions, e.g., position-dependent diffusion and time-varying equilibrium return, and (2) different potential functions, e.g., infinite and finite square well.

Strong coupling between exciton and quasi-bound state in the continuum with polarization dependence

Exciton–polaritons which are formed by the strong coupling of photon and exciton, have aroused great interest. In this work, we study the strong coupling between the exciton of WS2 monolayer (perovskite) and quasi-bound states in the continuum (QBIC) under y(x) polarization, in the perovskite metasurface with WS2 monolayer. Here, QBIC mode is achieved by introducing the asymmetric parameter. It is found that the energy of Rabi splitting can reach 41.369 meV (235.19 meV) under y-polarization (x-polarization). The dispersion-coupled oscillation model is used to illustrate the strong coupling mechanism. Besides, the influences of the asymmetric parameter and the positions of WS2 monolayer on the Rabi splitting are also discussed, which are verified by finite element method (FEM) simulations. Compared with the previous works, our method provides a way to achieve Rabi splitting with polarization dependence.

Analytical Modeling of Effluent Discharges Spreading by Tidal Oscillation Currents on a Sloping Beach

ABSTRACTAn analytical solution of the two‐dimensional advection–diffusion equation is introduced that models the spreading of effluent discharges into coastal waters affected by tidal oscillation currents on a sloping beach. It is assumed that the advection part may be expressed as a vector of fluid velocity with two components. The first component presents the longshore flow, in the direction, by a simple tidal oscillation model. The weaker second component, in the direction, reflects the cross‐shore depth‐variation velocity. By separating the variables, the equation in two dimensions is reduced to the product of two time‐dependent equations in one dimension that can be solved analytically. Some analysis and graphical plotting with discussion related to the product solution are given. Comparisons with an available analytical solution for a steady‐state case and numerical simulations are also addressed.

Giant Ultrabroadband Bulk Photovoltaic Effect Engendered by Two-Photon Absorption in α-In2Se3 for Chiral Terahertz Wave Generation.

Bulk photovoltaic effect (BPVE) can break the Shockley-Queisser limit by leveraging the inherent asymmetry of crystal lattice without a junction. However, this effect is mainly confined to UV-vis spectrum due to the wide-bandgap nature of traditional ferroelectric materials, thereby limiting the exploration of the infrared light-driven efficient BPVE. Herein, giant two-photon absorption (TPA) driven BPVE is uncovered from visible to infrared in ferroelectric α-In2Se3 utilizing wavelength-tunable terahertz (THz) emission spectroscopy. Remarkably, α-In2Se3 exhibits exceptional THz emission efficiency in the infrared region, surpassing renowned THz emitters like p-InAs and achieving an efficiency approximately eight times the magnitude of standard ZnTe. The power exponent-type pump fluence and quadruple polarization features reveal a unique TPA-driven BPVE, corroborated by a fourth-order nonlinear oscillator model. Notably, TPA-engendered BPVE efficiency approaches 68% of that observed in the single-photon absorption process. Moreover, the TPA responses display clear polarization anisotropy, with considerably relative phase and amplitude driven by synchronous in-plane and out-of-plane polarization, leading to chiral THz waves with high efficiency, tunable orientation, and controllable ellipticity. This work highlights the advantages of TPA-induced BPVE responses in narrow-bandgap ferroelectric semiconductors, enhancing spectral utilization efficiency, aiding high-performance devices based on BPVE, and guiding chiral THz wave design.

Linear and Nonlinear Optical Characteristics of Basic Fuchsin-Doped Polyvinyl Alcohol Films for Flexible Optoelectronics

Abstract Polyvinyl alcohol (PVA) containing different levels of basic fuchsine (BF) was prepared using the solution casting method. Characterization via Fourier-transform infrared spectroscopy detailed changes in functional groups within the PVA/BF composites, indicates the hydrogen bonding between OH group of PVA and BF molecules. Optical investigations spanning the 190-2500 nm range demonstrated UV blocking properties in prepared PVA/BF composites (fromn 2.05 to 2.56 eV and from 4.08 to 6.32 eV). Moreover, the studies on optical band gap indicated a decrease with increased BF concentrations, reflecting altered electronic transitions within the prepared composites. The study also employed the single oscillator model provided by Wemple-DiDomenico to elucidate refractive index variations. After incorporating BF dye into the PVA polymer, the values of the dielectric constant as the frequency approaches infinity (ε∞), the dielectric constant of lattice (εL), dispersion energy (Ed), and oscillator energy (Eo) in PVA/BF composite samples showed an increase. Moreover, the nonlinear optical properties, including optical susceptibility and nonlinear refractive index were investigated and discussed. These findings underscore the versatility of PVA doped with BF for various applications including optical filters, and solar cell devices.

Coupled in-line and cross-flow vortex-induced vibration responses of a fluid-conveying riser with variable tension in shear flow

When seawater streams around risers, it causes vortex-induced vibrations (VIV), which occur in two forms: in-line (IL) and cross-flow (CF). Accurate prediction of coupled IL and CF VIV behaviors is essential for designing risers. To investigate the VIV of marine risers used in deep-sea oil and gas transportation, this study analyzed the coupled CF and IL VIV characteristics of the riser with axially time-varying tension under the combined effects of internal flow and oceanic linear shear flow. The work established the vibration control equation for the riser considering internal flow velocity, axial top tension, and bending stiffness, which is based on Euler-Bernoulli beam theory. The double Van der Pol diffusion wake oscillator model was used to simulate the vortex-induced forces from the ocean currents, and the internal fluid was considered as a single-phase incompressible liquid. Using the Generalized Integral Transform Technique (GITT), the coupled system of nonlinear partial differential equations was further transformed into a system of nonlinear ordinary differential equations for numerical solution. A parametric study was conducted to analyze the impact of current velocity, internal flow velocity, and diffusion term on the VIV responses, including structural displacement, structural frequency, displacement envelope, and displacement evolution. Numerical results indicate that the vibration modes of the riser are influenced by both CF and IL directions, and the effect of IL can not be ignored. The diffusion term has a significant impact on the vibrations of the riser. The number of vibration modes of the riser is mainly influenced by the increasing current velocity, and for a given current velocity, the vibration of the riser becomes chaotic when the dimensionless internal fluid velocity increased within a certain range.

Relationship between Φ4-matrix model and N-body harmonic oscillator or Calogero-Moser model

Abstract We study some Hermitian Φ4-matrix model and some real symmetric Φ4-matrix model whose kinetic terms are given by Tr(EΦ2), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition functions of these matrix models correspond to zero-energy solutions of a Schödinger type equation with N-body harmonic oscillator Hamiltonian and Calogero-Moser Hamiltonian, respectively. The first half of this paper is primarily a review of previous work of us. The discussion of the properties of zero-energy solutions and the discussion of systems of differential equations satisfied by partition functions derived from the Virasoro algebra in the latter half of this paper contain novel material.

Mathematical Model for Oscillations in an Electric Drive with a Two-Stage Cylindrical Gear Reducer

Mathematical Model for Oscillations in an Electric Drive with a Two-Stage Cylindrical Gear Reducer

On the construction of the coherent states of the semiconfined harmonic oscillator with a position-dependent effective mass

Abstract We present details of the method for constructing the coherent states of the quantum harmonic oscillator model that exhibits the semiconfinement effect due to a specific change of its mass by position. Its energy spectrum completely overlaps with the Hermite oscillator energy spectrum, whereas the wavefunctions of the stationary states are expressed via the generalized Laguerre polynomials. Two different methods have been applied to compute the coherent states. They are generalized and Barut-Girardello coherent states methods. In both cases, the exact expressions have been obtained. We also analyzed some limit cases, under which the constructed coherent states completely recover the coherent states of the Hermite oscillator.

Generalized exponential time differencing for fractional oscillation models

Generalized exponential time differencing for fractional oscillation models