Simple Harmonic Oscillator Model Research Articles

Influence of different micro-vibrational behavior on the thermodynamic properties of SO gas

The effects of different micro-vibrational motions of sulfur oxide on its thermodynamic properties have been carried out. The theoretical full set of vibrational levels {Eυ} and the maximum vibrational quantum number υmax of the ground electronic state X3Σ− of SO molecule are obtained using the variational algebraic method (VAM) for vibrational motions. In the temperature range of 300–4000K, the molar internal energies, the molar entropy and the vibrational heat capacities are studied by implementing the VAM vibrational energies to the classical statistical thermodynamic formulae. Compared with credible experimental data, the VAM thermodynamic results are better consistent with the experiment than the traditional simple harmonic oscillator (SHO) model and the configuration interaction (CI) calculations.

Fluid forces acting on a cylinder undergoing streamwise vortex-induced vibrations

This brief communication examines the fluid forces acting on a cylinder free to move in the streamwise direction throughout its response regime. The amplitude and phase of the unsteady drag coefficient are estimated from the displacement signals and a simple harmonic oscillator model. We examine the counter-intuitive reduction in vibration amplitude observed in streamwise vortex-induced vibrations (VIV) at resonance, which has remained one of the most poorly understood aspects of VIV. Our results show that it is not caused by a change in the phase of the fluid forcing with respect to the cylinder displacement, as suggested by previous researchers; instead, we show that there is a sudden decrease in the amplitude of the unsteady drag coefficient in this region. The possible cause of this result, relating to three-dimensionality in the wake, is briefly discussed.

DFT and experimental studies on structure and spectroscopic parameters of 3,6-diiodo-9-ethyl-9H-carbazole

The first report on crystal and molecular structure of 3,6-diiodo-9-ethyl-9H-carbazole is presented. Experimental room-temperature X-ray and 13C chemical shift studies were supported by advanced theoretical calculations using density functional theory. The 13C nuclear magnetic shieldings were predicted at the non-relativistic and relativistic level of theory using the zeroth-order regular approximation. Theoretical relativistic calculations of chemical shifts of carbons C3 and C6, directly bonded to iodine atoms, produced a reasonable agreement with experiment (initial deviation from experiment of 44.3 dropped to 4.25 ppm). The changes in ring aromatic character were estimated via a simple harmonic oscillator model of aromaticity and nucleus-independent chemical shift index calculations. A good linear correlation between experimental and theoretically predicted structural and NMR parameters was observed.

Thermal transport in one-dimensional superlattice and quasicrystal chains: Fullerene phononic crystal

In order to investigate the thermal transport in one-dimensional (1D) superlattice and quasicrystal chains, the simple harmonic-oscillator model and the C60 chains model, are studied through non-equilibrium molecular dynamics simulation. In the simple harmonic-oscillator model, we construct a simple periodic harmonic-oscillator chain by using two different stiffness coefficients alternatively. It is found that its thermal conductivity is smaller than in non-periodic chains, no matter which stiffness coefficient is used in the non-periodic chains. In order to test if this is true in a real material structure, a superlattice C60 chain is constructed by connecting perfect and defective C60 alternatively. The calculation outcome of the C60 chains coincides with the results of the simple harmonic-oscillator model, that the thermal conductivity of the superlattice C60 chain is smaller than that of perfect and defective crystal C60 chains. Besides this, we also studied the thermal transport properties of the quasicrystal C60 chain, which consists of a random defective C60 molecular structure. It is found that the thermal conductivity of the quasicrystal structure is far less than that of the crystal and superlattice chains. The phonon spectra of the perfect, defective and superlattice C60 chain are provided to give corresponding supports. Our results also propose a controllable method for the thermal management in nanoscale materials.

Amplitude modulation atomic force microscopy, is acoustic driving in liquid quantitatively reliable?

Measuring quantitative tip–sample interaction forces in dynamic atomic force microscopy in fluids is challenging because of the strong damping of the ambient viscous medium and the fluid-mediated driving forces. This holds in particular for the commonly used acoustic excitation of the cantilever oscillation. Here we present measurements of tip–sample interactions due to conservative DLVO and hydration forces and viscous dissipation forces in aqueous electrolytes using tips with radii varying from typical 20 nm for the DLVO and hydration forces, to 1 μm for the viscous dissipation. The measurements are analyzed using a simple harmonic oscillator model, continuous beam theory with fluid-mediated excitation and thermal noise spectroscopy (TNS). In all cases consistent conservative forces, deviating less than 40% from each other, are obtained for all three approaches. The DLVO forces are even within 5% of the theoretical expectations for all approaches. Accurate measurements of dissipative forces within 15% of the predictions of macroscopic fluid dynamics require the use of TNS or continuous beam theory including fluid-mediated driving. Taking this into account, acoustic driving in liquid is quantitatively reliable.

Quantifying electrostatic force contributions in electrically biased nanoscale interactions

A study of the validity of analytical methods for calculating the electrostatic force interaction in alternating current electrostatic force microscopy is presented. Using a simple harmonic oscillator model, two analytical frameworks aimed at relating the electrostatic force between the cantilever tip and the sample with measurable parameters (amplitude and phase of the cantilever) are derived. The validity of the frameworks is examined based on two parameters that define the oscillation amplitude of the cantilever (tip voltage and tip-sample distance). Results are compared with an analytical model of the electrostatic interaction between tip and sample (tip-sample capacitance) and the range of validity of these two frameworks is provided. Our analysis confirms that the commonly used interpretation of the amplitude and the phase as a measure for the electrostatic force and for the derivative of the electrostatic force is only valid for very small oscillation amplitudes and depends on the tip geometry. Furthermore, this study demonstrates that these two techniques suffer from sensitivity limitations at large tip-sample distances. Finally, we compare the two frameworks with an alternative technique for the quantification of the tip-sample electrostatic interaction we have recently proposed and we discuss and experimentally demonstrate its advantages in terms of reliability and sensitivity, providing an example of dielectric constant measurement of a thin insulating film.

Numerical experiments on phonon properties of isotope and vacancy-type disordered graphene

We have studied phonon properties of graphene theoretically with different concentrations of 13C isotope and vacancy-type defects. The forced vibrational method, which is based on the mechanical resonance to extract the pure vibrational eigenmodes by numerical simulation, has been employed to compute the phonon density of states (PDOSs) and mode pattern of isotope-disordered graphene as well as a combined isotope and vacancy-type defective graphene structure. We observe a linear reduction of the E2g mode frequencies with an increase in 13C concentration due to the reduced mass variation of the isotope mixture. We find a downshift of the E2g mode of 65cm−1, which is a very good agreement with the experimental results, and the phonon frequencies described by the simple harmonic oscillator model. The vacancy-type defects break down the phonon degeneracy at the Г point of the LO and TO modes, distort and shift down the phonon density of states significantly. The PDOS peaks for the combined isotope and vacancy-type defects show the remarkable increase in the low-frequency region induced by their defect formations. Due to phonon scattering by 13C isotope or vacancies, some graphene phonon wave functions become localized in the real space. Our numerical experiments reveal that the lattice vibrations in the defective graphene show the remarkably different properties such as spatial localization of lattice vibrations due to their random structures from those in the perfect graphene. The calculated typical mode patterns for in-plane K point optical phonon modes indicate that the features of strongly localized state depend on the defect density, and the phonon is localized strongly within a region of several nanometers in the random percolation network structures. In particular, for in-plane K point optical phonon modes, a typical localization length is on the order of ≈7nm for isotope impurities, ≈5nm for vacancy-type defects and ≈6nm for mixed-type defects at high defect concentrations of 30%. Our findings can be useful for the interpretation of experiments on infrared, Raman, and neutron-diffraction spectra of defective graphene, as well as in the study of a wide variety of other physical properties such as thermal conductivity, specific heat capacity, and electron–phonon interaction.

Plasmon resonances and plasmon‐induced charge transport in linear atomic chains

In linear hydrogen atomic chains, plasmon resonances and plasmon‐induced charge transport are studied by time‐dependent density functional theory. For the large linear chain, it is a general phenomenon that, in the longitudinal excitation, there are high‐energy resonances and a large low‐energy resonance. The energy of the large low‐energy resonance conforms to the results calculated by the classical Drude model. In order to explain the formation mechanism of the high‐energy resonances, we present a simple harmonic oscillator model. This model may reasonably account for the relationship between low‐energy and high‐energy resonances, and has a certain degree of universality. As the interatomic distance decreases, the current shows a gradual transition from insulator to metal. The current enhancement mainly depends on the local field enhancement associated with plasmon excitation, and the enhanced electron delocalization effect as a result of the decrease of the interatomic distance. © 2013 Wiley Periodicals, Inc.

Note: Curve fit models for atomic force microscopy cantilever calibration in water

Atomic force microscopy stiffness calibrations performed on commercial instruments using the thermal noise method on the same cantilever in both air and water can vary by as much as 20% when a simple harmonic oscillator model and white noise are used in curve fitting. In this note, several fitting strategies are described that reduce this difference to about 11%.

Mechanochemical reaction of TiO2 with β-alanine for the preparation of visible light active nitrogen doped titania: adsorption and kinetic studies

Nitrogen doped TiO2 (TiO2−xNx) with a homogenous anatase phase was synthesized, using β-alanine as a nitrogen precursor and ethanol as a oxygen depriving agent in the concentration range of 0.05, 0.10, 0.15 and 0.2 at% and were characterized by Powder X-ray Diffraction (PXRD), X-ray Photoelectron Spectra (XPS), Scanning Electron Microscope (SEM), Fourier Transform Infrared (FT-IR) and UV–visible Diffused Reflectance Spectroscopic (DRS) techniques. Ethanol deprives the surface oxygen, thereby generating oxygen defects whose concentration was evaluated by FTIR, Photoluminescence (PL) and Electron Spin Resonance (ESR) studies. FTIR analysis reveal that concentration of oxygen vacancies/defects (Vo) decreases as the nitrogen concentration increases leading to the reduction in the Ti–O bond length. This results in a shift of the IR absorption peak towards a low wave number as predicted by simple physical harmonic oscillator model. The Ti 2p3/2 XPS spectra of TiO2−xNx shifts to lower binding energies due to the increase in the electron densities around the Ti atoms indicating the formation of Ti3+ in the doped samples. N2 adsorption–desorption isotherms measurements show a slight increase in the Brunner–Emmet–Teller (BET) surface area, pore diameter, mesopore volume, while the crystallite size and the morphology were also effected by the nitrogen doping. The equilibrium adsorption of Toluene molecules on the photocatalyst surface follows Langmuir theory and the rate controlling step could be the surface reaction of the adsorbed Toluene molecules.

Single and Pairwise Motion of Particles near an Ideally Polarizable Electrode

Single-particle longitudinal motion and pairwise lateral motion was investigated while the particles were excited by an oscillating electric field directed normally to an electrode proximate to the particles. The electrode was polarized over a range of potential insufficient to drive electrochemical reactions, a range called the "ideally polarizable region". The particles' motion was qualitatively dependent on the choice of electrolyte despite the absence of electrochemical reactions. As when electrochemical reactions were not explicitly excluded, the phase angle θ between particle height and electric field correlated with the particles' separation or aggregation during excitation. A simple harmonic oscillator model of the particles' response, including colloidal and hydrodynamic forces and including the Basset force not previously cited in this context, showed how θ can increase from 0° at low frequencies, cross 90° at ∼100 Hz, and then increase to 180° as frequency was increased. The model captured the essence of experimental observations discussed here and in earlier works. This is the first a priori prediction of θ for this problem.

Resonant Raman spectroscopy on enriched 13C carbon nanotubes

Isotopically enriched single-wall carbon nanotubes with different 13C concentrations were investigated by resonant Raman spectroscopy. Linear reductions of the Raman frequencies with an increase of 13C concentration are observed for the different nanotube Raman modes, and the effect of the reduced mass variation of the isotope mixture on the phonon frequencies is described through a simple harmonic oscillator model. In addition to the frequency dependence, the Raman linewidths as a function of the 13C concentration were also investigated and an expression describing this is presented. We observe an increase in the G band linewidth, as the 13C: 12C ratio approaches unity. Measurements with different excitation energies were performed and the frequency dispersions of the D and G′ bands with laser energy were observed to be the same for 12C and 13C nanotubes, suggesting no changes in the electronic structure after isotope enrichment. Through analysis of the radial breathing modes in the Raman spectra obtained with different excitation energies, a relation between these modes frequency and the 13C nanotubes diameter was also established.

Plasmonic Nickel Nanoantennas

The fundamental optical properties of pure nickel nanostructures are studied by far-field extinction spectroscopy and optical near-field microscopy, providing direct experimental evidence of the existence of particle plasmon resonances predicted by theory. Experimental and calculated near-field maps allow for unambiguous identification of dipolar plasmon modes. By comparing calculated near-field and far-field spectra, dramatic shifts are found between the near-field and far-field plasmon resonances, which are much stronger than in gold nanoantennas. Based on a simple damped harmonic oscillator model to describe plasmonic resonances, it is possible to explain these shifts as due to plasmon damping.

A Reconstruction of Madden–Julian Oscillation Variability from 1905 to 2008

AbstractThe most widely accepted characterization of the Madden–Julian oscillation (MJO) is the bivariate index developed by Wheeler and Hendon. This index relies in part on satellite-based observations of outgoing longwave radiation and thus is not defined for the presatellite era. The MJO is known to have a strong signature in surface pressure, and daily measurements of this variable are available as far back as the late nineteenth century. This study undertakes a statistical reconstruction of the Wheeler and Hendon MJO index from 1905 to 2008 based on tropical surface pressures estimated recently by the twentieth-century reanalysis project. The temporal and spectral properties of the reconstructed index are first shown to be consistent with the Wheeler and Hendon index over the common period (1979–2008). The reconstructed index is then validated over the earlier period (1905–1978) by examining its relationship with cloud cover, surface wind, precipitation, and sea level. These relationships are shown to be consistent with corresponding results obtained from the Wheeler and Hendon index over the shared period and stable over the earlier period. Finally, a simple damped harmonic oscillator model is used to gain new insights into the predictability of the MJO index and also demonstrate consistency between the reconstructed index and the Wheeler and Hendon index. These results give confidence in the validity of the historical reconstruction of the MJO index over the last century.

Absorption Ångström coefficient, brown carbon, and aerosols: basic concepts, bulk matter, and spherical particles

Abstract. The concept of wavelength-dependent absorption Ångström coefficients (AACs) is discussed and clarified for both single and two-wavelengths AACs and guidance for their implementation with noisy absorption spectra is provided. This discussion is followed by application of the concept to models for brown carbon bulk absorption spectra including the damped simple harmonic oscillator model, its Lorentzian approximation, and the band-gap model with and without Urbach tail. We show that the band-gap model with Urbach tail always has an unphysical discontinuity in the first derivative of the AAC at the band-gap – Urbach-tail matching wavelength. Complex refractive indices obtained from the bulk damped simple harmonic oscillator model are used to calculate absorption spectra for spherical particles, followed by a discussion of their features. For bulk material and small particles, this model predicts a monotonic decrease of the AAC with wavelength well above the resonance wavelength; the model predicts a monotonic increase for large particles.

Parameter exploration of optically trapped liquid aerosols

When studying the motion of optically trapped particles on the microsecond time scale, in low-viscosity media such as air, inertia cannot be neglected. Resolution of unusual and interesting behavior not seen in colloidal trapping experiments is possible. In an attempt to explain the phenomena we use power-spectral methods to perform a parameter study of the Brownian motion of optically trapped liquid aerosol droplets concentrated around the critically damped regime. We present evidence that the system is suitably described by a simple harmonic oscillator model which must include a description of Faxén's correction, but not necessarily frequency dependent hydrodynamic corrections to Stokes' law. We also provide results describing how the system behaves under several variables and discuss the difficulty in decoupling the parameters responsible for the observed behavior. We show that due to the relatively low dynamic viscosity and high trap stiffness, it is easy to transfer between over- and underdamped motion by experimentally altering either trap stiffness or damping. Our results suggest stable aerosol trapping may be achieved in underdamped conditions, but the onset of deleterious optical forces at high trapping powers prevents the probing of the upper stability limits due to Brownian motion.

Cooper pair sizes in superfluid nuclei in a simplified model

Cooper pair sizes are evaluated in a simple harmonic oscillator model reproducing the values of sophisticated Hartree-Fock-Bogoliubov calculations. Underlying reasons for the very small sizes of 2.0--2.5 fm of Cooper pairs in the surface of nuclei are analyzed. It is shown that the confining properties of the nuclear volume is the dominating effect. It is argued that for Cooper pair sizes the local-density approximation idea is particularly inadapted.

A simple model of energy expenditure in human locomotion

A simple harmonic oscillator model is proposed to describe the mechanical power involved in human locomotion. In this framework, by taking into account the anthropometric parameters of a standard individual, we are able to calculate the speed-power curves in human walking. The proposed model accounts for the well known Margaria's law in which the cost of human running (independent from the speed) is fixed to 1 kcal/(kg km). The model includes the effects of a gentle slope (either positive or negative) and the effect due to the mechanical response of the walking surface. The model results obtained in the presence of a slope are in qualitative agreement with the experimental data obtained by A. Leonardi et al.

Femtosecond response in rare gas matrices doped with NO impurities: A stochastic approach

The femtosecond response of NO-doped rare gas matrices is studied within a stochastic Langevin theoretical framework. As is shown, a simple damped harmonic oscillator model can describe properly the absorption and emission line shapes associated with the NO ( A 2 Σ + ↔ X 2 Π ) electronic transitions inside these media as well as the matrix first solvation shell response in a process with two timescales, finding a fairly good agreement with available experimental data. This approach thus constitutes an alternative and complementary way to analyze the structural relaxation dynamics of systems in liquids and solids, leading to a better understanding of the underlying physics.

Simulations of impulsive laser scattering of biological protein assemblies: Application to M13 bacteriophage

We develop a theoretical framework, based on a bond-polarizability model, for simulating the impulsive force experienced on a protein or an assembly of proteins from a pulsed light source by coupling the laser electric field to an atomic distortion. The mechanism is impulsive stimulated Raman scattering (ISRS) where mechanical distortions produce variation in the electronic polarization through atomic displacements similar to vibrational Raman scattering. The magnitude of the impulsive force is determined from the empirical two-body bond-polarizability model and the intensity of the incident light. We apply the method to the M13 bacteriophage protein capsid system by performing several classical molecular-dynamics simulations that include the additional impulsive laser scattering force at various light intensities and pulse widths. The results of the molecular-dynamics simulations are then qualitatively interpreted with a simple harmonic oscillator model driven by ISRS. The intensity of light required to produce damage to the capsid in the simulations was found to be far higher than what was found in recent pulsed laser scattering experiments of M13 phage, suggesting that the observed inactivation of viruses with ultrashort laser pulses involves processes and/or mechanisms not taken into account in the present simulations.