Damped Harmonic Oscillator Model Research Articles

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 coupled damped harmonic oscillator model for arbitrary arrays of floating cylinders using homotopy methods

A coupled damped harmonic oscillator model is derived for the long-time motion of an array of floating cylinders moving in heave, forced by a prescribed initial displacement. Eigenmodes of the coupled damped harmonic oscillator model are set to be the complex resonances of the corresponding linear potential theory model of the array. Thus, the solution of the coupled damped harmonic oscillator model has the same form as the singularity expansion method. The derivation of the coupled damped harmonic oscillator model is underpinned by a homotopy method to calculate the complex resonances for arbitrary arrays. A recursive homotopy method is used to study the complex resonances as one of the geometrical parameters is varied. The coupled damped harmonic oscillator model is shown to give accurate approximations of the full linear solutions, except for exceptional cases in which additional complex resonances appear.

Near-Field Coupling Effect Analysis of SMD Inductor Using 3D-EM Model

In this paper, we propose a methodology for analyzing the near-field coupling between two surface mount device (SMD) inductors using a 3-dimensional electromagnetic (3D-EM) model. To develop the 3D-EM model, we first constitute the equivalent circuit of the SMD inductor from the measured impedance and derive the loss tangent using circuit parameters. Secondly, the loss tangent using damped harmonic oscillator model is introduced to extract the effective permeability of core magnetic material in the SMD inductor. The optimization algorithm is used to compare the two loss tangents. Then the effective permeability is used in the magnetic material for the 3D-EM modeling of the SMD inductor. The validity of the proposed 3D-EM model is confirmed by comparing the impedance and S-parameters obtained from both measured and EM-simulated values for the two near-field coupled SMD inductors. Finally, the near-field coupling effects between the two adjacent SMD inductors are visualized in terms of coupling path visualization (CPV) using the proposed 3D-EM model, which demonstrates its usefulness for near-field coupling analysis.

Physics-informed machine learning for optimizing the coating conditions of blade coating

Large-scale liquid coating has been used in various industrial fields, such as the fabrication of functional panels or surfaces. Blade coating with continuous liquid supply is a cost-effective method for large-scale coatings. To coat a liquid without defects, it is essential to maintain the coating bead trapped under the blade stably. However, numerous experiments are required to obtain the optimal conditions. We developed a novel strategy for acquiring coating conditions using physics-informed neural networks (PINNs) to avoid this laborious effort. Although standard neural networks (NNs) predict the coating performance directly from the operating parameters, PINNs predict parameters related to the state of coating bead to enhance its predictive performance. Our results revealed that the PINNs performed better than the standard NNs. Furthermore, we derived a damped harmonic oscillator model that provides physical insight into the correlation between the coating performance and coating conditions. Finally, a parametric study was performed using the PINN-based model to determine the optimal coating conditional zones, and we experimentally demonstrated the stable coating with the optimized operating parameters.

The Negative Solvatochromism of Reichardt's Dye B30 - A Complementary Study.

The UV/Vis spectra of a hypothetical negative solvatochromic dye in a solvent are theoretically calculated assuming the classical damped harmonic oscillator model and the Lorentz‐Lorenz relation. For the simulations, the oscillator strength of the solvent was varied, while for the solute all oscillator parameters were kept constant. As a result, a simple change of the oscillator strength of the solute can explain the redshift and intensity increase of the UV/Vis band of the solute. Simulated results are compared with measured UV/Vis spectroscopic data of 2,6‐diphenyl‐4‐(2,4,6‐triphenylpyridinium‐1‐yl) phenolate B30 (Reichardt‘s dye) Significant correlations of the absorption energy (1/λmax) with the molar absorption coefficient ϵ as function of solvent polarity are demonstrated for several derivatives of B30. The approach presented is only applicable to negative solvatochromism. Therefore, while the approach is vital to fully understand solvatochromism, it needs to be complemented by other approaches, e. g., to describe the changes of the chemical interactions based on the nature of the solvent, to explain all its various aspects.

Low energy excitation in liquid Sb and liquid Bi observed in inelastic x-ray scattering spectra

The dynamic structure factor S(Q, E), where Q and E are momentum and energy transfer, respectively, has been measured for liquid Sb, using inelastic x-ray scattering. A modified damped harmonic oscillator model function was applied to analyse S(Q, E) of liquid Sb and also to that of liquid Bi by Inui et al (2015 Phys. Rev. B 92, 054206). The obtained excitation energy was in fairly good agreement with that predicted by ab initio molecular dynamics simulations on these liquid semi-metals. The excitation energy of the longitudinal acoustic mode in liquid Sb and liquid Bi exhibits flat-topped Q dependence whereas the lower excitation energy below the longitudinal acoustic excitation shows Q-gap behaviour. From the viscosity estimated from the Q-gap experimentally obtained, it is inferred that the lower energy excitation arises from the transverse acoustic excitation in the liquids.

Forced Damped Harmonic Oscillator Model of the Dipole Mode of Localized Surface Plasmon Resonance

A forced damped harmonic oscillator model of the dipole plasmon mode is illustrated by the theoretical derivation and the simulation based on the metal ellipsoids. The analytical expression of the restoring force is derived. The displacement of the oscillator, which is the phenomenological relative displacement of the free negative and positive charge systems in solids, can be represented by the accumulated charges on the surface of the nanoparticles based on the derived results. With the help of the finite-difference time-domain method, the dependence of the resonance wavelengths and the surface charge distributions on the geometric parameters and the materials has been verified by the ellipsoids evolved from 10 nm radius spheres. As an essential feature of an oscillator, the phase shifts, which are between the accumulated surface charges (the displacement of the oscillator) and the electric field of the incident light, are also illustrated by the numerical simulation. For the silver nanoparticle with the radius of 10 nm, the phase shifts are consistent with the feature of a forced damped harmonic oscillator. For the large silver nanoparticle with the radius of 50 nm, the magnitudes of the phase shifts have some deviations due to the nonuniform electric field along the light propagation. By this oscillator model, we confirm that localized surface plasmon resonance arises from the collective motion of free charges modulated by the bound charges of the lattice background and the dielectric medium. The forced damped harmonic oscillator model is a clear picture for the dipole localized surface plasmon resonance.

Peculiar temperature dependence of dynamical sound speed in liquid Se50Te50 by inelastic x-ray scattering

Inelastic x-ray scattering (IXS) measurements were carried out on liquid Se50Te50 at temperatures up to 1323 K to investigate how the atomic dynamics changes with temperature through the semiconductor-metal transition. The acoustic mode was clearly observed in the dynamic structure factor and its energy was determined using a damped harmonic oscillator model. The dynamical sound speed obtained by IXS for nm−1 was found to behave similarly to the temperature dependence of ultrasonic sound velocity with a minimum near the semiconductor metal transition. The results can be explained by taking liquid Se50Te50 to be an inhomogeneous liquid consisting of metallic and semiconducting domains whose size is approximately 3 nm. The relaxation time obtained from frequency dependence of the dynamical sound speed was on a picosecond time scale.

Multiple stability switches and Hopf bifurcation in a damped harmonic oscillator with delayed feedback

This paper takes into consideration a damped harmonic oscillator model with delayed feedback. After transforming the model into a system of first-order delayed differential equations with a single discrete delay, the single stability switch and multiple stability switches phenomena as well as the existence of Hopf bifurcation of the zero equilibrium of the system are explored by taking the delay as the bifurcation parameter and analyzing in detail the associated characteristic equation. Particularly, in view of the normal form method and the center manifold reduction for retarded functional differential equations, the explicit formula determining the properties of Hopf bifurcation including the direction of the bifurcation and the stability of the bifurcating periodic solutions are given. In order to check the rationality of our theoretical results, numerical simulations for some specific examples are also carried out by means of the MATLAB software package.

Structure and dynamical properties of hydrated F-actin investigated by X-ray scattering

Structure and dynamical properties of hydrated actin filament (F-actin) are revealed by X-ray diffraction and inelastic X-ray scattering (IXS) in a temperature range of 180–298 K, respectively. We assigned the peaks in the radial distribution functions of the hydrated F-actin by molecular dynamics (MD) simulation for F-actin in water. Although the hydration water of F-actin does not freeze in the temperature range measured, the hydrogen-bonded network where hydration water molecules mediate the hydrophilic groups of F-action becomes enhanced with decreasing temperature, as previously seen for many hydrated proteins. By applying a damped harmonic oscillator model to the dynamical structure factor obtained from the IXS spectra of hydrated F-actin, we investigated the intensity and energy of the phonon excitation as a function of temperature. The phonon excitation energy decreased and the phonon population which is proportional to the intensity of the phonon excitation increased with increasing temperature as previously reported for hydrated lysozyme and could be related to the conformational flexibility of the protein regarding the intraprotein short-time collective vibrational motions. In contrast to hydrated lysozyme, these phenomena for hydrated F-actin were observed at ~11 nm−1 of momentum transfer, Q, indicating that they arise from water dimer mediating the hydrophilic parts of F-actin.

Lattice dynamics and electronic Grüneisen parameters of femtosecond laser-excited bismuth

In this study, we probed the lattice dynamics of bismuth subjected to femtosecond laser irradiation by ultrafast electron diffraction. The changes in the diffraction intensity and angle were determined. The lattice exhibited compression upon laser excitation, followed by expansion with damped vibrations. Coherent acoustic phonons were observed as oscillations in the lattice spacing. The results were analyzed using a damped harmonic oscillator model where the hot electrons caused the blast compressive force, which resulted in lattice-spacing oscillation for the expanded lattice following the compression. We obtained the rate of electron–phonon coupling, its anisotropy, and the Grüneisen parameters of the electronic subsystem.

Gold Nanorod Plasmon Resonance Damping Effects on a Nanopatterned Substrate

Substrate properties might significantly influence the scattering spectra of supported plasmonic nanoparticles because of different damping mechanisms. In this work, indium tin oxide substrates are modified by the combination of nanosphere lithography and ion-bombardment to create a nanopattern with sharp boundaries between the irradiated and masked regions. The single-particle scattering spectra of gold nanorods distributed over the nanopattern are investigated in detail. For nanorods located purely on either the masked or implanted areas, the spectra can be adequately interpreted in terms of a classical damped harmonic oscillator model, taking the chemical interface damping into account. When the particles overlap the masked and irradiated areas, however, markedly a different behavior is found depending on the actual arrangement. For the rods experiencing a symmetric inhomogeneity (i.e., by bridging between two masked regions), damping varies smoothly with the extent of substrate inhomogeneity. For the ...

Propagative and diffusive regimes of acoustic damping in bulk amorphous material.

In amorphous solids, a non-negligible part of thermal conductivity results from phonon scattering on the structural disorder. The conversion of acoustic energy into thermal energy is often measured by the dynamical dtructure factor (DSF) thanks to inelastic neutron or x-ray scattering. The DSF is used to quantify the dispersion relation of phonons, together with their damping. However, the connection of the dynamical structure factor with dynamical attenuation of wave packets in glasses is still a matter of debate. We focus here on the analysis of wave-packet propagation in numerical models of amorphous silicon. We show that the damped harmonic oscillator model fits of the dynamical structure factors give a good estimate of the wave packets mean free path, only below the Ioffe-Regel frequency. Above the Ioffe-Regel frequency and below the mobility edge, a pure diffusive regime without a definite mean free path is observed. The high-frequency mobility edge is characteristic of a transition to localized vibrations. Below the Ioffe-Regel frequency, a mixed regime is evidenced at intermediate frequencies, with a coexistence of propagative and diffusive wave fronts. The transition between these different regimes is analyzed in detail and reveals a complex dynamics for energy transport, thus raising the question of the correct modeling of thermal transport in amorphous materials.

Piezoresponse force and electrochemical strain microscopy in dual AC resonance tracking mode: Analysis of tracking errors

Contact-resonance atomic force microscopy allows the quantitative mapping of local viscoelastic and electromechanical properties. Excitation and amplification are generally described by the damped harmonic oscillator (DHO) model. The dual AC resonance tracking technique measures the amplitude and phase at two probing frequencies close to the resonance frequency and calculates the parameters of the DHO model from the amplitudes and phases. However, real systems show contact-resonance curves with slight deviations from the DHO model. In this work, we analyze how these deviations influence the obtained DHO parameters. We show that for a piezoelectric sample and for a mixed ion-electron conducting sample, the drive amplitude increases with increasing tracking error, while the opposite is observed for the amplification factor. Thus, in electrochemical strain microscopy experiments, the influence of the tracking error on the DHO parameters can be analyzed by calculating a tracking error image and studying correlations with the DHO parameter images.

Temperature dependent Raman scattering and electronic transitions in rare earth SmFeO3

Emerging interdisciplinary fields of multiferroics and spin-optronics demand for new oxide materials that unfolds significant coupling between electric and magnetic order at room temperature, preferably with controlled optical properties. Rare-earth orthoferrites (RFeO3) have received much attention due to their coupled electric, magnetic and optic properties. Here we report structural, optical, temperature-dependent (83–800K) Raman spectroscopy, electronic transition analysis and electric poling induced magnetic modulation in nanostructured SmFeO3 (SFO). Rietveld refinement of SFO confirmed the orthorhombic phase (space group D2h16, Pbnm) with expanded lattice parameters (ao = 5.3979Å < bo = 5.5922 Å < co = 7.7104Å). Microstructural analysis revealed the formation of uniformly distributed spherical grains of 40 ± 2nm size. First-order 18 Raman active vibrational phonon modes identified using damped harmonic oscillator model suggested the main activity in SFO lies between 100 and 650cm−1. Above 483K, clear fading of high frequency mode (~ 632cm−1) due to spin-reorientation and fusion in low frequency modes (~132cm−1) around 673K is considered as direct evidence of possible phase transition from antiferromagnetic to paramagnetic order. Optical response in studied spectral range from 200 to 800nm is dominated by two (p-d) and (d-d) charge transfer transitions, which favors strong exchange interaction as well as high magnetic transition temperatures. Large observed bandgap Eg of 5.21eV, determined from diffuse reflectance Uv–visible spectroscopy in combination with the electric poling induced magnetic modulation establish SFO, a suitable oxide material for future power efficient microelectronic and spin-optoelectronic devices.

Spectral curve fitting of dielectric constants

Optical constants are important properties governing the response of a material to incident light. It follows that they are often extracted from spectra measured by absorbance, transmittance or reflectance. One convenient method to obtain optical constants is by curve fitting. Here, model curves should satisfy Kramer-Kronig relations, and preferably can be expressed in closed form or easily calculable. In this study we use dielectric constants of three different molecular ices in the infrared region to evaluate four different model curves that are generally used for fitting optical constants: (1) the classical damped harmonic oscillator, (2) Voigt line shape, (3) Fourier series, and (4) the Triangular basis. Among these, only the classical damped harmonic oscillator model strictly satisfies the Kramer-Kronig relation. If considering the trade-off between accuracy and speed, Fourier series fitting is the best option when spectral bands are broad while for narrow peaks the classical damped harmonic oscillator and the Triangular basis fitting model are the best choice.

Computational and quantum chemical study on high-frequency dielectric function of tert-butylmethyl ether in mid-infrared and near-infrared regions

Complex dielectric function of tert-butylmethyl ether (TBME) was determined and analyzed in a broad spectral region covering mid-infrared (MIR) and near-infrared (NIR) regions (6500–560cm−1). Spectra of the complex electric permittivity and complex molecular polarizability have been derived from complex refractive index spectra. The molar vibrational polarization (Pvib) corresponding to individual modes has been estimated based on the data derived from fitting damped harmonic oscillator model to the experimental complex permittivity spectrum. Factors determining the dielectric functions due to vibrational resonance absorptions corresponding to fundamental and non-fundamental (overtones and combination modes) modes were taken into account. Direct comparison of contributions to total Pvib value stemming from corresponding fundamental and non-fundamental modes has been carried out and discussed for the first time. In order to identify overtones and binary combination modes, quantum chemical calculation of the vibrational spectrum of tert-butylmethyl ether was performed for MIR and NIR regions. Fully anharmonic approach by means of generalized second-order vibrational perturbation theory (GVPT2) was applied on DFT-B2PLYP/SNST level. An accurate reproduction of experimental data was achieved with subsequent assignment of fundamental and non-fundamental bands, which enabled detailed discussion of relations between dielectric contributions of fundamental and non-fundamental modes of tert-butylmethyl ether.

Foam on troubled water: Capillary induced finite-time arrest of sloshing waves

Interfacial forces exceed gravitational forces on a scale small relative to the capillary length—two millimeters in the case of an air-water interface—and therefore dominate the physics of sub-millimetric systems. They are of paramount importance for various biological taxa and engineering processes where the motion of a liquid meniscus induces a viscous frictional force that exhibits a sublinear dependence in the meniscus velocity, i.e., a power law with an exponent smaller than one. Interested in the fundamental implications of this dependence, we use a liquid-foam sloshing system as a prototype to exacerbate the effect of sublinear friction on the macroscopic mechanics of multi-phase flows. In contrast to classical theory, we uncover the existence of a finite-time singularity in our system yielding the arrest of the fluid’s oscillations. We propose a minimal theoretical framework to capture this effect, thereby amending the paradigmatic damped harmonic oscillator model. Our results suggest that, although often not considered at the macroscale, sublinear capillary forces govern the friction at liquid-solid and liquid-liquid interfaces.

On optimization of absorption–dispersion spectra

A modified approach to the analysis of spectra of the complex electric permittivity of liquids in the Infrared region is presented. These spectra are derived from experimental spectra of the complex refractive index. Subsequently they are used to determine important secondary quantities, e.g. spectra of complex molecular polarizabilities and an integral property – the molar vibrational polarization. The accuracy of these quantities depends essentially on the accuracy of both components of the complex electric permittivity spectrum.In the proposed procedure, the spectra of the complex electric permittivity are approximated using the Classical Damped Harmonic Oscillator (CDHO) model for the description of individual bandshapes. The CDHO model defines both the real and imaginary part of the complex permittivity. The fitting procedure includes a simultaneous optimization of both the real and imaginary parts of the complex permittivity spectrum. A comparison of absorption-only curve fitting and the novel absorption-dispersion double curve fitting is presented; advantages of the new approach in accuracy, reliability and convergence time are pointed out.Due to the complexity of the problem, the choice was restricted to non-gradient methods of optimization. The performance of several gradientless algorithms was tested. Among numerous procedures the Powell General Least Squares Method Without Derivatives was found to be the most efficient. The reliability of obtained results of the band separatiovn process was tested on several simulated spectra of increasing complexity.The applicability of the developed approach to the analysis of exemplary experimental data was evaluated and discussed.

Lattice dynamics of femtosecond laser-excited antimony

Ultrafast electron diffraction is used to probe the lattice dynamics of femtosecond laser-excited antimony thin film. The temporal hierarchies of the intensity and position of diffraction orders are monitored. The femtosecond laser excitation of antimony film was found to lead to initial compression after the laser pulse, which gives way to tension vibrating at new equilibrium displacement. A damped harmonic oscillator model, in which the hot electron-blast force contributes to the driving force of oscillations in lattice spacing, is used to interpret the data. The electron–phonon energy-exchange rate and the electronic Grüneisen parameter were obtained.