Normal Mode Behavior Research Articles

Viscosity of the Earth's fluid core and torsional oscillations

Viscous effects on the temporal behavior and spatial structure of torsional oscillation normal modes of the Earth's fluid core are examined. If the viscosity of the fluid core is equal to that inferred from theoretical and experimental studies of liquid metals, then viscous effects on torsional oscillations are unlikely to be important; however, if the viscosity is as high as allowed from observational constraints, then Ekman layers at the fluid core boundaries may play an important role in damping torsional oscillations. The observationally inferred decay time of decadal torsional oscillations leads to an upper bound on the viscosity of the fluid core at the core‐mantle boundary of the order of 10−2 m2/s. A sufficiently large viscosity would result in torsional oscillation normal modes that undergo pure decay, as opposed to damped oscillatory motion. The viscosity value at which the temporal behavior switches between these regimes depends on the period of the normal mode. Numerical geodynamo models must reach an Ekman number of the order of 10−7 for free‐slip boundaries or 10−10 for no‐slip boundaries to accurately model the temporal behavior of decadal period torsional oscillations.

Physics of the dusty Hall plasmas

The presence of the immobile charged dust in the plasma modifies the scale over which the Hall effect becomes important. For a positively charged dusty background this scale can become arbitrarily large. It is shown that the emergence of the Hall effect in an immobile charged background is related to the presence of an electric field that operates over the plasma gyration period. The generalized flux, which is a combination of the magnetic and fluid vortex flux, can decay due to the presence of the charge or the density inhomogeneities. The normal mode behavior of such a dusty plasma could be very different for positively and negatively charged grains. Whereas for negatively charged grains the usual magnetohydrodynamic (MHD) modes are present in the system, for positively charged grains, the Alfvén mode may not exist if Znd∼ne, where Z is the charge of the dust and nd(ne) are the dust (electron) number densities. In the presence of the inhomogeneities, inertialess dusty plasma is subject to the Hall instability. It is shown that the growth rate of the Hall instability is proportional to the whistler frequency. Since Hall drift is nondissipative in nature, this instability can play important role in redistributing the magnetic energy from the large to small scales.

On the stratorotational instability in the quasi-hydrostatic semigeostrophic limit

The linear normal mode stratorotational instability (SRI) is analytically re-examined in the inviscid limit where the length-scales of horizontal disturbances are large compared their vertical and radial counterparts. Boundary conditions different from channel walls are also considered. This quasi-hydrostatic, semigeostrophic (QHSG) approximation allows one to examine the effect of a vertically varying Brunt–Vaisaila frequency, N2. It is found that the normal mode instability persists when N2 increases quadratically with respect to the disc vertical coordinate. However, we also find that the SRI seems to exist in this inviscid QHSG extreme only for channel wall conditions: when one or both of the reflecting walls are removed, there is no instability in the asymptotic limit explored here. It is also found that only exponential-type SRI modes (as defined by Dubrulle et al.) exist under these conditions. These equations also admit non-normal mode behaviour. Fixed Lagrangian pressure conditions on both radial boundaries predict there to be no normal mode behaviour in the QHSG limit. The mathematical relationship between the results obtained here and that of the classic Eady problem for baroclinic instability is drawn. We conjecture as to the mathematical/physical nature of the SRI. The general linear problem, analysed without approximation in the context of the Boussinesq equations, admits a potential vorticity-like quantity that is advectively conserved by the shear. Its existence means that a continuous spectrum is a generic feature of this system. It also implies that in places where the Brunt–Vaisaila frequency becomes dominant the linearized flow may two-dimensionalize by advectively conserving its vertical vorticity.

Vibrational Excitons in CH-Stretching Fundamental and Overtone Vibrational Circular Dichroism Spectra

A set of vibrational circular dichroism (VCD) spectra in the CH-stretching fundamental region for about twenty compounds belonging to the class of essential oils was empirically analyzed by the use of a sort of vibrational exciton mechanism, involving three centers. Through a general formula applicable to many coupled dipole oscillators, the rotational strengths of the previously identified vibrational excitons are evaluated. The results are then critically reviewed by the use of recent ab initio methodology, as applied to selected molecules of the original set. Further insight is gained by model calculations adding up the contribution of the coupling between electric dipole moments associated with normal mode behavior and that of the polarizability from polarizable groups. The former part is responsible for the excitonic behavior of the VCD spectra. For the same selected molecules we have also investigated whether some excitonic behavior is taking place in the second overtone region, and have concluded that this is not the case.

A MOSFET power supply clamp with feedback enhanced triggering for ESD protection in advanced CMOS technologies

A novel power supply protection clamp is presented which incorporates feedback techniques to improve ESD and normal operational mode behavior. The design uses a short duration RC trigger, which enables the clamp to tolerate very fast power supply ramp rates and exhibit reduced area and leakage. The design is built in a 90 nm CMOS technology with fully salicided source/drain regions.

Full-field imaging of Gigahertz film bulk acoustic resonator motion.

A full-field view laser ultrasonic imaging method has been developed that measures acoustic motion at a surface without scanning. Images are recorded at normal video frame rates by using dynamic holography with photorefractive interferometric detection. By extending the approach to ultra high frequencies, an acoustic microscope has been developed that is capable of operation at Gigahertz frequency and micron length scales. Both acoustic amplitude and phase are recorded, allowing full calibration and determination of phases to within a single arbitrary constant. Results are presented of measurements at frequencies of 800-900 MHz, illustrating a multitude of normal mode behavior in electrically driven thin film acoustic resonators. Coupled with microwave electrical impedance measurements, this imaging mode provides an exceptionally fast method for evaluation of electric-to-acoustic coupling of these devices and their performance. Images of 256 x 240 pixels are recorded at 18 fps rates synchronized to obtain both in-phase and quadrature detection of the acoustic motion. Simple averaging provides sensitivity to the subnanometer level at each pixel calibrated over the image using interferometry. Identification of specific acoustic modes and their relationship to electrical impedance characteristics show the advantages and overall high speed of the technique.

Raman Spectroscopy of Ferroelectric Thin Films

ABSTRACTDuring a ferroelectric phase transition or domain rearrangement, ions or molecules in a ferroelectric material move in a highly cooperative manner from their initial lattice positions into the final positions they occupy and the collective response results into a “soft” lattice vibrational mode. Moreover, the structural changes are always accompanied by at least a few other changes in the normal mode behavior of the material. In the present work, Raman spectroscopy is conveniently employed to study such vibrational modes and other related phenomena in ferroelectric materials at the sub-microscale levels. We have investigated ferroelectric thin films of various lead and barium based perovskites prepared by sol-gel technique. The effect of processing conditions, A- and B- site substitutions, and size dependence on their Raman spectra were analyzed in terms of the structure-property correlations.

Basic physics of xylophone and marimba bars

The frequency-dependent wave velocity and nonsinusoidal spatial dependence found for transverse waves in finite vibrating bars stands in stark contrast to the solutions to the one-dimensional wave equation, for example for the idealized vibrating string. The difference is particularly important when the resulting vibrations are used to produce music. Here, the appropriate approximate equations for transverse vibrations on a uniform bar are developed and compared to measurements using wooden bars. The results are extended using a simple finite element model to provide a means to predict normal mode behavior in nonuniform wooden bars such as those used for xylophones, marimbas, and related musical instruments.

Basic physics of colloidal plasmas

Colloidal plasma is a distinct class of the impure plasmas with multispecies ionic composition. The distinction lies in the phase distribution of the impurity-ion species. The ability to tailor the electrostatic interactions between these colloidal particles provides a fertile ground for scientists to investigate the fundamental aspects of the Coulomb phase transition behavior. The present contribution will review the basic physics of the charging mechanism of the colloidal particles as well as the physics of the collective normal mode behavior of the general multi-ion species plasmas. Emphasis will be laid on the clarification of the prevailing confusing ideas about distinct qualities of the various acoustic modes, which are likely to exist in colloidal plasmas as well as in normal multi-ion species plasmas. Introductory ideas about the proposed physical models for the Coulomb phase transition in colloidal plasma will also be discussed.

Dynamo transformation of the collisional R–T in a weakly ionized plasma

Theoretical prediction of a new kind of normal mode behaviour of electro-mechanical nature was first time reported by Dwivedi and Das in 1992 in the context of mesospheric modeling of observed neutral induced turbulence. Local dynamo action (due to relative neutral flow) governs the basic physical principle for linear excitation of the neutral induced low frequency instability (NILF) in mesospheric plasma, which comprises of weakly ionized inhomogeneous gas confined by the external gravity and ambient magnetic field. The present contribution offers physical explanation in terms of dynamo transformation of neutral drag effect as a source to understand complete suppression of the usual collisional R-T and in turn linear driving of the NILF. It is therefore emphasized, worth calling it as the dynamo instability.

Millimeter-wave semiconductor two-port network at 77K

The gyromagnetic properties of magnetized ferrites are widely used in many novel rf and microwave devices. According to the Drude model, similar principles should also be applicable to magnetized semiconductors due to its gyroelectric properties. In this study, an axially magnetized semiconductor resonator is characterized in terms of bias field and signal frequency. The resonance and loss regions are identified at 77K. The affect of changing material and geometrical properties of the resonator on the splitting and tuning behavior of normal modes are illustrated. Green's Function approach is used to derive the S-parameters of a two port semiconductor network. The network response and the material properties can be used to calibrate the semiconductor material before measuring the millimeter-wave properties of the resonator. This theoretical analysis may prove to be vital in realizing miniaturized and broadband semiconductor junction circulators and filters for high-Tc superconductive circuits.

A discrete-particle formulation of the equations of motion for planar electrodynamic systems

The fundamental properties of a planar electrodynamic system are investigated analytically. The electrically charged particle's motion is conservative and governed by a set of nonlinear ordinary differential equations. Linearization about static equilibrium admits normal mode behavior. As examples, the dynamics of a fixed-charge electroscope and an electrostatic string are considered. This paper suggests that a surface charge, when appropriately controlled, can be turned from a liability into an asset.

Collective vibrational dynamics of simple liquids

Instantaneous normal mode investigations of molecular liquids are presented for coupled translational and rotational coordinates as well as for vibrational coordinates. Illustrative examples are chosen so as to demonstrate the influence of structural and dynamical properties on the normal mode behaviour. It is demonstrated that among the structural properties characterising a liquid system the normal mode spectrum is uniquely well suited for being related to the dynamics. The theoretical derivation of the normal mode spectrum for molecular systems starting from configurational distributions is shown to be an ill-behaving problem. Normal mode spectral shapes for strongly infrared active vibrational modes are presented and correlated with transition dipole moment and liquid structure. Finally a perturbational procedure is proposed to quantify the motional narrowing effect of molecular dynamics on inhomogeneously broadened vibrational bands.

Mesoscopic model for the primary response of magnetic materials (invited)

A model for the relaxation of thermal fluctuations is applied to the dynamical response of magnetic materials. Systems investigated include paramagnets, spin glasses, and ferromagnets. The key feature which distinguishes the model is that it describes the behavior of localized normal modes (e.g., magnons), not barrier hopping or domain-wall motion. Mathematical approximations to the model reproduce several previously used empirical formulas, such as the stretched exponential, power-law, and logarithmic time dependences, but the unapproximated model gives generally better agreement with observed response. Data of sufficient quality and range allow quantitative confirmation of all assumptions of the model. The model provides a common physical basis for observed magnetic after-effects, the magnitude and distribution of Landau–Lifshitz damping parameters, and 1/f noise.

Geodynamic models of fault‐controlled extension

Results from geodynamic models for lithospheric extension that includes one or two large‐scale upper crustal faults are presented. The study does not address the origin of these faults, but the consequences if they exist. Model components include a solid mechanical lithosphere composed of thermoelastic‐plastic material with viscous creep that is subject to extension, buoyant supporting forces and sedimentary loads, and a coincident, but thicker, thermal lithosphere that includes the effect of sediment blanketing and radiogenic heating. We have chosen for comparison purposes a “standard” reference model which minimizes creep in the crust; consequently, our results depend strongly on plastic deformation. Our models show that large faults can control the position and growth history of the mantle instabilities that can lead to rupture. We observe that these instabilities have secondary, “normal mode”‐like character. Models with two faults show that the normal mode behavior can interact and create an enhancement to the necking process, provided the faults are an ideal distance apart. We compare models with two rates of extension, 1.2 cm yr−1 (“fast”) and 0.038 cm yr−1 (“slow”), which show remarkably little difference. We compare our reference model with models using “wet” and “dry” rheologies and observe that flow in the crust can attenuate the propagation effect created by the faults.

Orographic Modification of Cyclone Development

Abstract The orographic modification of cyclone development is examined by means of primitive equation model simulations. When a mature baroclinic wave impinges on an east—west oriented mountain ridge, a relatively intense cyclone forms on the south side of the ridge. This cyclone extends throughout the depth of the troposphere and possesses relatively small vertical tilts, large velocities, and strong temperature perturbations compared to classical baroclinic eddies. The vorticity growth in the orographic cyclone center is larger than that of baroclinic eddies that grow over flat terrain. However, there is no absolute instability associated with this orographic enhancement. A longer ridge produces a more intense eddy. The behavior of small-amplitude normal modes on a zonally symmetric mountain ridge shows that baroclinic development is enhanced where the topography slopes in the same direction as the isentropes. This is consistent with earlier studies using uniform slopes that show that the heat flux for...

Light impulsive damping of spacecraft exhibiting normal mode behavior

This paper develops an impulsive damping control algorithm suitable for spacecraft. The fuel optimal solutions to the problem of damping the motion of spacecraft consists of impulsive control forces applied at repeated instances in time. The instances in time occur when the spacecraft undergoes maximum absolute velocities and minimum absolute displacements. This paper approximates impulses by short duration pulses. Maximum absolute velocities and minimum absolute displacements are then approximated by transient values of their respective standard deviations. Impulsive damping is achieved by applying either a large single pulse or smaller repeated pulses. A near fuel optimal mode preserving impulsive damping control algorithm is developed next. The algorithm exhibits the following properties: 1) the impulsive damping control algorithm is independent of spacecraft stiffness, 2) the associated control forces are proportional to spacecraft inertia, and 3) the impulsive damping control algorithm is decentralized. The impulsive damping of a cantilever beam demonstrates the results.

An analytic semiclassical model for local and normal stretching modes in AB 2 molecules

We present a simple, analytic model for the normal and local mode behavior of the stretching vibrations in AB 2 molecules. Starting with a zeroth-order description of degenerate, harmonic normal modes, we introduce a quartic perturbation and employ first-order secular perturbation theory to obtain a closed-form expression for the Poincaré surface of section for the action-angle variable pair corresponding to the vibrational angular momentum. Local modes correspond to pairs of levels trapped below a dynamical barrier along this angle variable; normal modes, to levels above the barrier. Uniform semiclassical quantization completely lifts the degeneracy of the zeroth-order states, and predicts the appropriate trends in the ordering of the various modes and the splitting between local mode pairs.

Normal oscillation modes of a conjugate resonator with an array-type controlled transparency

An analysis is made of the configuration of the field and losses experienced by normal oscillation modes of a conjugate resonator with an array-type controlled transparency. It is shown that the presence of gaps between the active areas of a transparency results in deformation of the normal modes in such a resonator, compared with a resonator which has a continuous aperture. Computer calculations are reported of the distribution of the field of normal modes on a resonator mirror and of the dependence of the losses experienced by the modes on the Fresnel number of the resonator. It is shown that the dependence has certain singularities corresponding to qualitative changes in the structure of normal modes, resulting in a considerable increase of the angular divergence. These features of the behavior of normal oscillation modes are supported by experiments carried out as part of the present study.

The identification of normal mode behavior in the resonance picture of local mode dynamics: normal mode splitting, stability of periodic orbits and energy transfer rates for coupled morse oscillators

The resonance model of coupled anharmonic local mode oscillators is extended to include second-order variations of the Fourier amplitude. Using this extension, all of the usual normal mode behavior including normal mode splittings, stability of periodic motions, and the energy transfer rate for degenerate stretching modes is recovered. A method is developed to predict the identity and energy of fundamental periodic orbits which become unstable. This method is more accurate and more general than previous analytic methods. These results may be of use in fitting or interpreting vibrational spectra and in studies of intramolecular vibrational energy flow.