Frequency Shifts Of Modes Research Articles

Complex image method for RF antenna-plasma inductive coupling calculation in planar geometry. Part II: measurements on a resonant network

Measurements and analysis of a radio-frequency planar antenna are presented for applications in inductively-coupled plasma processing. The network of inductive and capacitive elements exhibits high currents under resonance which are efficient for plasma generation. Mode frequencies and impedances are accurately calculated by accounting for the mutual partial inductances using the impedance matrix. The effect of plasma inductive coupling on mode frequency shift and mode impedance is estimated using the complex image method, giving good agreement with experiment. It is proposed that the complex image method combined with the partial inductance concept (see the accompanying paper, Part I (Howling et al 2015 Plasma Sources Sci. Technol. 24 065014)) offers a general way to calculate the impedance characteristics of inductively-coupled plasma sources in planar geometry.

Vibrational solvatochromism. III. Rigorous treatment of the dispersion interaction contribution.

A rigorous first principles theory of vibrational solvatochromism including the intermolecular dispersion interaction, which is based on the effective fragment potential method, is developed. The present theory is an extended version of our previous vibrational solvatochromism model that took into account the Coulomb, exchange-repulsion, and induction interactions. We show that the frequency shifts of the amide I mode of N-methylacetamide in H2O and CDCl3, when combined with molecular dynamics simulations, can be quantitatively reproduced by the theory, which indicates that the dispersion interaction contribution to the vibrational frequency shift is not always negligibly small. Nonetheless, the reason that the purely Coulombic interaction model for vibrational solvatochromism works well for describing amide I mode frequency shifts in polar solvents is because the electrostatic contribution is strong and highly sensitive to the relative orientation of surrounding solvent molecules, which is in stark contrast with polarization, dispersion, and exchange-repulsion contributions. It is believed that the theory presented and discussed here will be of great use in quantitatively describing vibrational solvatochromism and electrochromism of infrared probes in not just polar solvent environments but also in biopolymers such as proteins.

Effect of a variable cosmological constant on black hole quasinormal modes

Many different cosmological models have been proposed to address the cosmological constant problem and the coincidence problem. We compare here four different models that can be used to describe an effective (time-dependent) cosmological constant $\mathrm{\ensuremath{\Lambda}}(z)$. A numerical analysis of the $\mathrm{\ensuremath{\Lambda}}(z)$ evolution obtained for each model shows that it can be used for distinguishing between all four models. We calculate next the $\ensuremath{\omega}(\mathrm{\ensuremath{\Lambda}})$ frequencies for quasinormal modes of gravitational perturbations of Schwarzschild-de Sitter black holes at different redshifts. Considering that the variation of $\mathrm{\ensuremath{\Lambda}}$ happens on cosmological time scales, the combined $\ensuremath{\omega}(\mathrm{\ensuremath{\Lambda}}(z))$ could be used in principle to track the evolution of the cosmological constant. We quantify the resulting minute frequency shift in the quasinormal mode frequencies and show that the relative frequency shift grows as ${M}^{2}$. However, even in a most optimistic scenario with an extremely high mass supermassive black hole there is no prospect for the detection of this effect.

Temperature dependent phonon frequency shift and structural stability of free-standing graphene: a spectral energy density analysis

A spectral energy density based formalism is implemented to probe the temperature dependent frequency shift, linewidth, structural stability and coupling of normal modes of vibrations of free-standing graphene using a combination of lattice dynamics and molecular dynamics (MD). The in-plane lattice parameter shows a thermal contraction upto 1300 K and it expands thereafter. Frequency of the bending mode (ZA) becomes imaginary in the quasi-harmonic dispersion at higher temperatures, suggestive of a structural instability. However, the frequency of the ZA mode becomes real in the dispersion obtained from MD. Dynamical stability to the structure is restored by strong anharmonic coupling of phonon modes which is automatically incorporated in the MD simulations, whereas it is ignored in the quasi-harmonic dispersion. The mode resolved phonon spectra at Γ point show a blue-shift of degenerate longitudinal and transverse (LO/TO) optic modes. The blue-shift observed in canonical (NVT) and isobaric–isothermal (NPT) ensembles are more prominent than the shift predicted by quasi-harmonic approximation (QHA) due to the additional contribution from phonon–phonon coupling. The out-of-plane optic (ZO) mode frequencies are red-shifted in the QHA due to membrane-effect, whereas MD simulations show that the strong phonon–phonon coupling dominates the membrane effect leading to a blue-shift. The linewidth of LO/TO and ZO modes increases non-monotonically with temperature. The anharmonic coupling of normal modes at high symmetry points in the Brillouin zone is also discussed.

Frequency shifts of resonant modes of the Sun due to near-surface convective scattering

AbstractMeasurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the “surface term.” The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary 3D flows, can be reduced to an effective “quiet-Sun” wave equation with altered sound speed, Brünt–Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

Effect of aft wall offset and ramp on pressure oscillation from confined supersonic flow over cavity

A study is conducted on supersonic flow of Mach number 1.65 over rectangular cavity of length to depth ratio (L/D) 3 with aft wall ramp angles of 30°, 60° and 90° for with and without aft wall offset. Unsteady pressure measurement and schlieren flow visualization is employed to gain insight into the flow physics. Schlieren visualization revealed shock train like pattern for the cavities without offset. These shock structures are unsteady and oscillated longitudinally inside the test section over the cavity. The shock pattern disappeared as the blockage produced due to cavity pressure rise and shear layer oscillation is minimized by offsetting the cavity aft wall. Experimental investigations confirmed that the size of the cavity relative to the test section could have significant effect on the nature of flow field over the cavity and also on the acoustic oscillations within the cavity. For 90° ramp angle the dominant mode frequency in pressure oscillations shifted from second to third mode as the cavity aft wall is offset; however the shift in dominant mode frequency is not observed for the 60° cavity with aft wall offset. The forward traveling acoustic wave inside the cavity is confirmed to be present for 60° and 90° ramps while it is found to be absent for 30° ramp angled cavities. Analysis of the unsteady pressure measured inside the cavity revealed that the shock train has significant effect on the nature of acoustic oscillations from within the cavity. Aft wall offset is found to be effective in avoiding the occurrence of shock train and it is also found to increase the level of cavity pressure fluctuations. The highest pressure occurred at the aft wall and static pressure at all locations inside the cavity decreased as the aft wall ramp angle is reduced.

Resonance frequency shift of strongly heated micro-cantilevers

In optical detection setups to measure the deflection of micro-cantilevers, part of the sensing light is absorbed, heating the mechanical probe. We present experimental evidences of a frequency shift of the resonant modes of a cantilever when the light power of the optical measurement set-up is increased. This frequency shift is a signature of the temperature rise and presents a dependence on the mode number. An analytical model is derived to take into account the temperature profile along the cantilever; it shows that the frequency shifts are given by an average of the profile weighted by the local curvature for each resonant mode. We apply this framework to measurements in vacuum and demonstrate that huge temperatures can be reached with moderate light intensities: a 1000 °C with little more than 10 mW. We finally present some insight into the physical phenomena when the cantilever is in air instead of vacuum.

Seismic sensitivity to sub-surface solar activity from 18 yr of GOLF/SoHO observations

Solar activity has significantly changed over the last two Schwabe cycles. After a long and deep minimum at the end of Cycle 23, the weaker activity of Cycle 24 contrasts with the previous cycles. In this work, the response of the solar acoustic oscillations to solar activity is used in order to provide insights on the structural and magnetic changes in the sub-surface layers of the Sun during this on-going unusual period of low activity. We analyze 18 years of continuous observations of the solar acoustic oscillations collected by the Sun-as-a-star GOLF instrument onboard the SoHO spacecraft. From the fitted mode frequencies, the temporal variability of the frequency shifts of the radial, dipolar, and quadrupolar modes are studied for different frequency ranges which are sensitive to different layers in the solar sub-surface interior. The low-frequency modes show nearly unchanged frequency shifts between Cycles 23 and 24, with a time evolving signature of the quasi-biennial oscillation, which is particularly visible for the quadrupole component revealing the presence of a complex magnetic structure. The modes at higher frequencies show frequency shifts 30% smaller during Cycle~24, which is in agreement with the decrease observed in the surface activity between Cycles 23 and 24. The analysis of 18 years of GOLF oscillations indicates that the structural and magnetic changes responsible for the frequency shifts remained comparable between Cycle 23 and Cycle 24 in the deeper sub-surface layers below 1400 km as revealed by the low-frequency modes. The frequency shifts of the higher-frequency modes, sensitive to shallower regions, show that Cycle 24 is magnetically weaker in the upper layers of Sun.

Simulating acoustic waves in spotted stars

Acoustic modes of oscillation are affected by stellar activity, however it is unclear how starspots contribute to these changes. Here we investigate the nonmagnetic effects of starspots on global modes with angular degree $\ell \leq 2$ in highly active stars, and characterize the spot seismic signature on synthetic light curves. We perform 3D time-domain simulations of linear acoustic waves to study their interaction with a model starspot. We model the spot as a 3D change in the sound speed stratification with respect to a convectively stable stellar background, built from solar Model S. We perform a parametric study by considering different depths and perturbation amplitudes. Exact numerical simulations allow the investigation of the wavefield-spot interaction beyond first order perturbation theory. The interaction of the axisymmetric modes with the starspot is strongly nonlinear. As mode frequency increases, the frequency shifts for radial modes exceed the value predicted by linear theory, while the shifts for the $\ell=2, m=0$ modes are smaller than predicted by linear theory, with avoided-crossing-like patterns forming between the $m=0$ and $m=1$ mode frequencies. The nonlinear behavior increases with increasing spot amplitude and/or decreasing depth. Linear theory still reproduces the correct shifts for nonaxisymmetric modes. In the nonlinear regime the mode eigenfunctions are not pure spherical harmonics, but rather a mixture of different spherical harmonics. This mode mixing, together with the frequency changes, may lead to misidentification of the modes in the observed acoustic power spectra.

Raman scattering studies of the lattice dynamics in layered MoS2

We report non-resonant and resonant Raman scattering studies of layered MoS2. Owing to its reduced dimensionality, few layered MoS2 is more sensitive to the difference between inter- and intra-layer coupling, which results in unusual frequency shifts of the Raman phonon modes. In addition, relative intensities between the two Raman active phonon modes E2g1 and A1g unexpectedly depend on the laser excitation energy, which might be associated with the electronic band structure, including spin-orbit coupling and phonon dispersions. Through resonant Raman scattering measurements, the indirect-to-direct band gap behavior and electron-phonon interaction information were obtained. Raman scattering spectroscopy is seen to be very effective for studying the layer-dependent characteristics of layered MoS2.

Non-radial oscillations of the magnetized rotating stars with purely toroidal magnetic fields

We calculate non-axisymmetric oscillations of uniformly rotating polytropes magnetized with a purely toroidal magnetic field, taking account of the effects of the deformation due to the magnetic field. As for rotation, we consider only the effects of Coriolis force on the oscillation modes, ignoring those of the centrifugal force, that is, of the rotational deformation of the star. Since separation of variables is not possible for the oscillation of rotating magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We calculate magnetically modified normal modes such as $g$-, $f$-, $p$-, $r$-, and inertial modes. In the lowest order, the frequency shifts produced by the magnetic field scale with the square of the characteristic Alfv\'en frequency. As a measure of the effects of the magnetic field, we calculate the proportionality constant for the frequency shifts for various oscillation modes. We find that the effects of the deformation are significant for high frequency modes such as $f$- and $p$-modes but unimportant for low frequency modes such as $g$-, $r$-, and inertial modes.

Dispersive readout of ferromagnetic resonance for strongly coupled magnons and microwave photons

We demonstrate the dispersive measurement of ferromagnetic resonance in a yttrium iron garnet sphere embedded within a microwave cavity. The reduction in the longitudinal magnetization at resonance is measured as a frequency shift in the cavity mode coupled to the sphere. This measurement is a result of the intrinsic non-linearity in magnetization dynamics, indicating a promising route towards experiments in magnon cavity quantum electro-dynamics.

Experimental measurement of the frequency shifts of degenerate thickness-shear modes in a rotated Y-cut quartz resonator subject to diametrical forces.

We report the first experimental measurement of the stress-induced frequency shifts of degenerate thickness-shear modes in a rotated Y-cut quartz resonator. Two distinct but nominally degenerate modes shifted toward higher frequencies at different rates and merged into a single mode as diametrical forces were applied gradually. The single mode split into the two distinctive modes progressively as the diametrical forces were released. The experimental results are in excellent agreement with previous theoretical results and may provide an insight into mode-coupling phenomena as a possible cause of frequency jumps in quartz resonators.

Influence of the electron-phonon interaction on the temperature dependence of the phonon mode frequency in the II-VI compound solid solutions

We present an experimental investigation of the temperature dependence of the TO-phonon mode frequencies for the HgTe-based II-VI semiconductor solid solutions. In the case of the ternary Hg0.9Zn0.1Te solid solution was shown a discontinuity in the temperature dependence of the HgTe-like T0-mode and of the ZnTe-like T1-mode, similar to the Hg0.85Cd0.15Te system [Sheregii et al., Phys. Rev. Lett. 102, 045504 (2009)]. A generalization of the theoretical temperature shift of the phonon mode frequency as analytic equation is derived that includes both the anharmonic contribution and the electron-phonon e-p interaction which in this case is returnable—the electron subsystem effect on the phonon one. Data show that our equation satisfactorily describes the temperature shift of both Hg0.85Cd0.15Te and Hg0.90Zn0.10Te containing Dirac point (Eg ≡ Γ6 – Γ8 = 0) although one of the two constants describing the anharmonic shift of the HgTe-like mode should be positive what is abnormal too. In the case of the Hg0.80Cd0.20Te and Hg0.763Zn0.237Te solid solution, the role of the returnable e-p contribution is negligible but a positive temperature shift for the HgTe-like modes occurs. This result does not allow to explain the positive temperature shift of these modes merely by the contribution of the (e-p) interaction. Indeed, the relativistic contribution to the chemical bonds induces an abnormal temperature shift of the electron states in Hg-based semiconductors—the effect is expected since the Hg d spin-orbit split contribution to chemical bonds may lead to an abnormal temperature shift of the HgTe-like modes.

Anti-Islanding Detector Based on a Robust PLL

As required by international standards, the distributed energy generators, connected to the grid by an inverter, have to detect an islanding condition within a suitable time interval. In this paper, a phase-locked loop (PLL), based on a third-order prediction-correction filter, is proposed to implement an islanding detector with reduced detection time. Such a feature is obtained using the estimation of the grid angular frequency and acceleration provided by the PLL with a negligible time delay. The proposed approach is implemented on an industrial grade DSP and validated through the experimental comparison among different detection methods, such as rate of change of frequency (ROCOF) and Slip Mode frequency Shift (SMS). The combined use of ROCOF and SMS is also illustrated and discussed.

Calculation of the specific heat using the Raman frequency shifts for the solid I–II transition in benzene

The specific heat CP is calculated as a function of temperature using the observed Raman frequency shifts of the six lattice modes at constant pressures of 0 and 0.1GPa for the solid I–II transition in benzene. This calculation is performed using the volume data through the mode Grüneisen parameter of each lattice mode which we determined as functions of temperature and pressure. The specific heat CP is also calculated as a function of pressure at room temperature using the Raman frequency shifts of those phonon modes studied.The specific heat CP due to the contributions of the six lattice modes, increases with the increasing temperature at constant pressures (P=0 and 0.1GPa) and it decreases with increasing pressure (T=300K), as expected. Our calculated CP values can be compared with the experimental measurements for the solid I–II transition in benzene.

Space charge frequency shifts of the cyclotron modes in multi-species ion plasmas.

Shifts of the cyclotron frequency away from the "bare" cyclotron frequency are observed to be proportional to the total ion density through the E × B rotation frequency, and to the relative concentration of each ion species, in quantitative agreement with analytic theory. These shifts are measured at small excitation amplitudes on the typical center-of-mass m = 1 mode, and also on cyclotron modes with m = 0 and m = 2 azimuthal dependence. The frequency spacing between these modes is proportional to the rotation frequency of the ion cloud, which is controlled and measured using a "rotating wall" and laser-induced fluorescence. These cylindrical ion plasmas consist of Mg(+) isotopes, with H3 O (+) and O2 (+) impurities. It is observed that the shift in the m = 1 cyclotron frequency is larger for the minority species (25)Mg(+) and (26)Mg(+), than for the majority species (24)Mg(+). A simple center-of-mass model is presented, which is in quantitative agreement with these results. It is also shown that this model interprets and expands the intensity dependent calibration equation, (M/q) = A/f + B/f (2) + CI/f (2).

Performance Assessment of Slip Mode Frequency Shift (SMS) Islanding Detection Methods

The awareness concerning the grid connected Photovoltaic (PV) has become vital and a major concern nowadays. Islanding detection is one of the most dominant challenges for distributed generation system connected to the utility grid. In addition, islanding has not been a preferable option as it may pose safety hazard and may cause damage to power generation and power supply facilities as a result of unsynchronized re-closer. Therefore, the islanding detection techniques are needed to ensure safe and reliable system operation. One of the established islanding prevention methods is the Slip Mode Frequency Shift (SMS) islanding method, which has numerous advantages over the other techniques. This paper investigates the active islanding detection methods and specifically focused on the SMS islanding method. The results show that the SMS islanding method successfully detected an unintentional fault and managed to isolate the system within the prescribed time range.

Atomic transitions of Rb, D2 line in strong magnetic fields: Hyperfine Paschen–Back regime

An efficient λ/2-method (λ is the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium is implemented to study the splitting of hyperfine transitions of 85Rb and 87Rb D2 lines in an external magnetic field in the range of B=3–7kG. It is experimentally demonstrated that at B>3kG from 38 (22) Zeeman transitions allowed at low B-field in 85Rb (87Rb) spectra in the case of σ+ polarized laser radiation there remain only 12 (8) which is caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen–Back regime). Note that at B>4.5kG these 20 atomic transitions are regrouped into two completely separate groups of 10 atomic transitions each. Their frequency positions and fixed (within each group) frequency slopes, as well as the probability characteristics, are determined. A unique behavior of two atomic transitions is stressed: one transition belongs to 85Rb, the other to 87Rb and for low magnetic fields they could be presented as transitions Fg=3,mF=+3→Fe=4,mF=+4 and Fg=2,mF=+2→Fe=3,mF=+3, correspondingly. The experimental results of the atomic transition frequency shifts and the modification of their probabilities agree well with the theory. A comparison of the behavior of the D1 and D2 atomic transitions is presented. Possible applications are described.

Modal evaluation of fluid volume in spacecraft propellant tanks

A novel, real-time method of determining the volume of propellant present in a spacecraft tank in reduced gravity is presented. In the experiment reported here, modal analysis techniques are applied to detect shifts in resonant mode frequencies of a fluid-loaded tank as fluid is drained from the tank. These experiments are conducted in the weightless environment of parabolic flights through participation in the NASA Systems Engineering Exploration Discovery (SEED) program. Ground testing of the experimental methods is compared with the flight data, and the resolution of the analysis is estimated to be better than 10% of actual fill-fraction. Comparison with existing direct and indirect techniques for assessing propellant volume in reduced gravity suggests that the modal analysis method may prove to be more cost effective and afford better resolution than existing methods.Â