Showing papers on "Normal mode published in 2000"

Fundamentals of Physical Acoustics

Abstract: Detailed Development of the Acoustical Wave Equation. Reflection and Transmission of Normally Incident Plane Waves of Arbitrary Waveform. Normal Incidence Continued: Steady-State Analysis. Transmission Phenomena: Oblique Incidence. Normal Modes in Cartesian Coordinates: Strings, Membranes, Rooms, and Rectangular Waveguides. Horns. Propagation in Stratified Media. Propagation in Dissipative Fluids: Absorption and Dispersion. Spherical Waves. Cylindrical Waves. Waveguides. Radiation from a Baffled Piston. Diffraction. Arrays. Appendices. Index.

Building‐block approach for determining low‐frequency normal modes of macromolecules

Abstract: Normal mode analysis of proteins of various sizes, ranging from 46 (crambin) up to 858 residues (dimeric citrate synthase) were performed, by using standard approaches, as well as a recently proposed method that rests on the hypothesis that low-frequency normal modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino-acid residues. Such a hypothesis is strongly supported by our results, because we show that the latter method, named RTB, yields very accurate approximations for the low-frequency normal modes of all proteins considered. Moreover, the quality of the normal modes thus obtained depends very little on the way the polypeptidic chain is split into blocks. Noteworthy, with six amino-acids per block, the normal modes are almost as accurate as with a single amino-acid per block. In this case, for a protein of n residues and N atoms, the RTB method requires the diagonalization of an n x n matrix, whereas standard procedures require the diagonalization of a 3N x 3N matrix. Being a fast method, our approach can be useful for normal mode analyses of large systems, paving the way for further developments and applications in contexts for which the normal modes are needed frequently, as for example during molecular dynamics calculations.

Nonlinear Interactions: Analytical, Computational, and Experimental Methods

Abstract: Two-To-One Internal Resonance One-To-One Internal Resonance Three-To-One Internal Resonance Combination Resonances Systems with Widely Spaced Modes Multiple Internal Resonances Nonlinear Normal Modes Bibliography Subject Index.

Vortices in a trapped dilute Bose-Einstein condensate

Abstract: We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes, and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (`anomalous') mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.

Structures, Vibrational Frequencies, and Normal Modes of Substituted Azo Dyes: Infrared, Raman, and Density Functional Calculations

Abstract: The vibrational structures of 4-nitro-azobenzene (NAB), 4-(dimethylamino)-azobenzene (DAB), and 4-nitro,$4^{\prime}$-(dimethylamino)-azobenzene (NDAB) are of interest due to their importance in optoelectronic applications as well as the unique isomerization mechanism involving the inversion process (at the nitrogen site). In this paper, we present the Fourier transform infrared (FTIR) and Raman spectral studies of NAB, DAB, and NDAB and also report their equilibrium structures, harmonic frequencies, and normal mode assignments, employing the hybrid Hartree-Fock/density functional (HF/DF) method with the 6-31G basis set. The results of the optimized molecular structure obtained on the basis of B3LYP with 6-31G basis set suggest a greater conjugation and \pi-electron delocalization for the substituted azo dyes in comparison to the parent azo molecule, viz. trans-azobenzene (TAB). It is found that the B3LYP/6-31G method is very accurate in predicting harmonic vibrational frequencies and the normal modes for the substituted azo dyes and their isotopic analogues. On the basis of the B3LYP/6-31G force field, the infrared intensities for NAB, DAB, and NDAB, and their isotopomers, are calculated and then compared with those observed experimentally. Finally, the main differences in the vibrational spectra of the substituted azobenzene derivatives are discussed from an analysis of the normal modes.

Vibration modes of giant gravitons

Abstract: We examine the spectrum of small vibrations of giant gravitons when the gravitons expand in anti\char21{}de Sitter space and when they expand on the sphere. For any given angular harmonic, the modes are found to have frequencies related to the curvature length scale of the background; these frequencies are independent of radius (and hence angular momentum) of the brane itself. This implies that the holographic dual theory must have, in a given R charge sector, low-lying non-BPS excitations with level spacings independent of the R charge.

Vibrational energy transfer in a protein molecule.

Abstract: Mode coupling in a protein molecule was studied by a molecular dynamics simulation of the intramolecular vibrational energy transfer in myoglobin at near zero temperature. It was found that the vibrational energy is transferred from a given normal mode to a very few number of selective normal modes. These modes are selected by the relation between their frequencies, like Fermi resonance, governed by the third order mode coupling term. It was also confirmed that the coupling coefficients had high correlation with how much the coupled modes geometrically overlapped with each other.

Acetylene at the Threshold of Isomerization

Abstract: This article reviews recent research on acetylene which is intended as a contribution to the understanding of intramolecular vibrational energy flow when it is poorly described by either statistical (i.e., RRKM) or purely separable (i.e., harmonic oscillator/normal mode) models. The experimental spectra that inform this investigation are 7c m -1 resolution dispersed fluorescence spectra of the acetylene S 1fS0 system. Above 10 000 cm -1 of vibrational energy, these spectra are extremely congested and cannot be analyzed using conventional spectroscopic assignment procedures. Instead, a numerical pattern recognition procedure is utilized to disentangle spectroscopic patterns that are associated with approximately conserved polyad quantum numbers. This pattern recognition analysis makes possible detailed modeling of the short-time (1 ps) but large-amplitude vibrational dynamics of acetylene at high energy (15 000 cm -1 ), which is demonstrated here to be dominated by regularity even for the low-frequency bending motions (22 quanta of bend excitation). That is, a few stable motions dominate the large-amplitude bending dynamics, including local bend (one hydrogen bending), which is closely related to the acetylene-vinylidene isomerization coordinate, and a new type of vibrational motion that we call counter-rotation, in which the two hydrogens undergo circular motions on opposite ends of the CC core.

Interactions of disparate scales in drift-wave turbulence

Abstract: Renormalized statistical theory is used to calculate the interactions between short scales (wave vector k) and long scales (wave vector q<

Modeling of Lamb waves generated by integrated transducers in composite plates using a coupled finite element–normal modes expansion method

Abstract: Thin piezoelectric transducers attached to or embedded within composite structures could be used for in situ structural health monitoring. For plate-shaped structures, the useful ultrasonic vibration modes are Lamb waves. Preliminary testing has already demonstrated the suitability and practical feasibility of such integrated transducers, but better control of the generation of Lamb modes seems to be necessary. Therefore, an original modeling approach has been developed, which can be used to design and optimize these “sensitive materials.” This modeling technique allows the determination of the amplitude of each Lamb mode excited in a composite plate with surface-bonded or bulk-embedded piezoelectric elements. The method consists of a coupling of the finite element method (FEM) and the normal modes expansion method. The limited finite element mesh of the transducer and its vicinity enables the computation of the mechanical field created by the transducer, which is then introduced as a forcing function int...

Shock wave instability and the carbuncle phenomenon: same intrinsic origin?

Abstract: The theoretical linear stability of a shock wave moving in an unlimited homogeneous environment has been widely studied during the last fifty years. Important results have been obtained by Dyakov (1954), Landau & Lifchitz (1959) and then by Swan & Fowles (1975) where the fluctuating quantities are written as normal modes. More recently, numerical studies on upwind finite difference schemes have shown some instabilities in the case of the motion of an inviscid perfect gas in a rectangular channel. The purpose of this paper is first to specify a mathematical formulation for the eigenmodes and to exhibit a new mode which was not found by the previous stability analysis of shock waves. Then, this mode is confirmed by numerical simulations which may lead to a new understanding of the so-called carbuncle phenomenon.

On three-dimensional structures in relativistic hydrodynamic jets

Abstract: The appearance of wavelike helical structures on steady relativistic jets is studied using a normal mode analysis of the linearized —uid equations. Helical structures produced by the normal modes scale relative to the resonant (most unstable) wavelength and not with the absolute wavelength. The resonant wave- length of the normal modes can be less than the jet radius even on highly relativistic jets. High-pressure regions helically twisted around the jet beam may be con—ned close to the jet surface, penetrate deeply into the jet interior, or be con—ned to the jet interior. The high-pressure regions range from thin and ribbon-like to thick and tubelike depending on the mode and wavelength. The wave speeds can be sig- ni—cantly diUerent at diUerent wavelengths but are less than the —ow speed. The highest wave speed for the jets studied has a Lorentz factor somewhat more than half that of the underlying —ow speed. A maximum pressure —uctuation criterion found through comparison between theory and a set of relativistic axisymmetric jet simulations is applied to estimate the maximum amplitudes of the helical, elliptical, and triangular normal modes. Transverse velocity —uctuations for these asymmetric modes are up to twice the amplitude of those associated with the axisymmetric pinch mode. The maximum ampli- tude of jet distortions and the accompanying velocity —uctuations at, for example, the resonant wave- length decreases as the Lorentz factor increases. Long-wavelength helical surface mode and shorter wavelength helical —rst body mode generated structures should be the most signi—cant. Emission from high-pressure regions as they twist around the jet beam can vary signi—cantly as a result of angular variation in the —ow direction associated with normal mode structures if they are viewed at about the beaming angle h \ 1/c. Variation in the Doppler boost factor can lead to brightness asymmetries by factors up to 6 as long-wavelength helical structure produced by the helical surface mode winds around the jet. Higher order surface modes and —rst body modes produce less variation. Angular variation in the —ow direction associated with the helical mode appears consistent with precess- ing jet models that have been proposed to explain the variability in 3C 273 and BL Lac object AO 0235)164. In particular, cyclic angular variation in the —ow direction produced by the normal modes could produce the activity seen in BL Lac object OJ 287. Jet precession provides a mechanism for trig- gering the helical modes on multiple length scales, e.g., the galactic superluminal GRO J1655(40. Subject headings: BL Lacertae objects: individual (OJ 287) ¨ galaxies: activegalaxies: jets ¨ hydrodynamicsinstabilitiesrelativity

Dynamics of a vortex in a trapped Bose-Einstein condensate

Abstract: We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of vortex line as a function of the local gradient of the trap potential, the line curvature and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for 2D and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.

Exciton-polariton eigenmodes in light-coupled In 0.04 Ga 0.96 A s / G a A s semiconductor multiple-quantum-well periodic structures

Abstract: Features of exciton-polariton eigenmodes in a series of light-coupled ${\mathrm{In}}_{0.04}{\mathrm{Ga}}_{0.96}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ semiconductor multiple quantum wells with varying number of quantum wells $N$ from 1 to 100, and with various periodicities (Bragg, near-Bragg, and anti-Bragg), are studied in linear measurements of reflection, transmission, and absorption. At Bragg periodicity (period $d={\ensuremath{\lambda}}_{x}/2),$ a photonic band-gap mode grows in amplitude and increases linearly in linewidth with increasing $N.$ The $N$ times increased radiative damping rate is seen to arise from the light character of the eigenmode being swept out of a photonic band-gap structure. The slope of linewidth versus $N$ gives the radiative linewidth of the exciton. Away from Bragg periodicity two branches of energy levels can be resolved in absorption, corresponding to the $N$ exciton-polariton normal modes in the multiple-quantum-well structure. Signatures of individual modes becoming optically active are observed in the rich structure of reflection spectra for changing quantum-well periodicity. Antireflection coating of the samples is shown to be an effective way of thus isolating the multiple-quantum-well response.

A theoretical study of P 4 O 6 : vibrational analysis and infrared and Raman spectra

Abstract: The normal mode frequencies and the corresponding vibrational assignments of tetraphosphorus hexoxide (P 4 O 6 ) in T d symmetry are examined theoretically using the gaussian 94 set of quantum chemistry codes at the HF/6-31G ∗ , MP2/6-31G ∗ and DFT/B3LYP/6-31G ∗ levels of theory. By comparison to experimental normal mode frequencies deduced by Chapman [A.C. Chapman, Spectrochim. Acta A 24 (1968) 1687–1696] correction factors for predominant vibrational motions are determined and compared. Normal modes were decomposed into three nonredundant motions {P–O–P wag, P–O–P bend, and P–O stretch}. Standard deviations found for the DFT and MP2 corrected frequencies compared to experiment are particularly noteworthy yielding values of 15 and 11 cm −1 , respectively.

Nonlinear evolution of double tearing modes

Abstract: The linear and nonlinear behaviors of the tearing mode is systematically studied for nonmonotonic q-profiles on the basis of the reduced magnetohydrodynamics (MHD) equations in cylindrical geometry, and some new features about the double tearing mode are revealed. The linear eigenmode scales as a resistive internal mode for a small distance between two rational surfaces with the same q-value, Δrs, and as the tearing one for large Δrs. New nonlinear phenomena appear in the tearing mode regime and for shorter Δrs. The linear eigenfunction shows sharply localized fluid motion at both resonant surfaces and small but global convective motion between the resonant surfaces; consequently the mode goes through a Rutherford-type regime. When the islands have grown enough, the mode shows explosive growth. This results from the nonlinear coupling among the higher harmonics, so that the inner and outer magnetic islands interact with each other leading to an internal disruption.

Dynamics of a vortex in a trapped Bose-Einstein condensate

Abstract: We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of vortex line as a function of the local gradient of the trap potential, the line curvature and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for 2D and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.

Generalized weak turbulence theory

Abstract: In this article we present the derivation of a generalized weak turbulence kinetic equation for unmagnetized collisionless plasmas in a uniform medium. For the sake of simplicity the present formulation assumes longitudinal electrostatic interaction only, and the effects of spontaneous thermal fluctuations are ignored. In spite of these simplifications, the present formalism represents a generalization of the existing weak turbulence theory in that a nonlinear eigenmode excited in a turbulent plasma with frequency close to twice the plasma frequency is incorporated into the discussion. Traditional weak turbulence theory emphasizes various linear and nonlinear interactions among wave modes in quiescent plasmas (i.e., Langmuir and ion-sound waves). In contrast, the present formalism describes linear and nonlinear interactions among Langmuir, ion-sound, and the new nonlinear eigenmode. Nonlinear wave kinetic equations for these modes are systematically derived, and the particle kinetic equation which generalizes the well known quasilinear diffusion equation, is also derived.

Interferometric coherency determination of wavelength or what are broadband ELF waves

Abstract: To determine the wavelength of waves within a random, isotropic wave field, we introduce the observable of wave coherency measured with plasma wave interferometers. We show generally that within a random direction wave field, wavelengths large compared to the interferometer length produce large coherency (nearly 1), but wavelengths the order of a few times the interferometer length, or smaller, produce small coherency (close to zero). We apply this principle first to examining auroral hiss and lower hybrid waves measured by the Physics of Auroral Zone Electrons (PHAZE) 2 and Topside Probe of the Auroral Zone (TOPAZ) 3 experiments and show that the implied wavelengths are consistent with the expected dispersion relations and with other, different estimates of wavelength for these modes. Next, we apply the principle to broadband extra low frequency (BB-ELF) electric fields observed in both experiments and conclude that the wavelengths are small. In one case we calculate the coherency of BB-ELF electric fields, using an ensemble average of 7889 data samples, and demonstrate that the coherency near the oxygen gyrofrequency is very small (≅0.15), corresponding to wavelengths of 10 m and the order of the ion gyroradius. We conclude that because of the short wavelengths, previous satellite measurements of BB-ELF electric fields may have underestimated the electric field amplitudes, unless ion gyroradii are substantially larger than the case for these rocket measurements. Although the wavelengths and frequencies of BB-ELF electric fields are now known, we are unable to assign the wave to a known, normal mode of homogeneous plasmas. This suggests that inhomogeneities may be essential for describing BB-ELF electric fields.

Instantaneous normal mode analysis of supercooled water

Abstract: We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by mode-coupling theory. We find that the diffusion constant depends on the fraction of directions in configuration space connecting different local minima, supporting the hypothesis that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find a relation between the number of basins accessed in equilibrium and the connectivity between them.

Bending and torsional vibration control of a flexible plate structure using H/sub /spl infin//-based robust control law

Abstract: This paper presents a method of controlling the bending and torsional vibration modes of a flexible plate structure (theoretically which has infinite number of vibration modes) using H/sub /spl infin//-based robust control. For this purpose, a three degree of freedom (DOF) reduced order lumped mass model of a plate structure is derived by considering first three vibration modes and neglecting the all other high-frequency modes. These neglected modes constitute the unstructured uncertainties of the system and taken care of in the time of design process. An idea is proposed to reduce the unmodeled system uncertainties by placing actuators in the node points of a neglected mode. As a result, it is possible to avoid the spillover instability (avoid the influence of a neglected mode) without affecting the control of lower order modes. Then a static state feedback controller is designed based on the reduced order model and the approximate knowledge of unmodeled uncertainties. The efficacy of feedback controller is shown through simulation and experimental studies.

Theoretical study of collective modes in DNA at ambient temperature

Abstract: The instantaneous normal modes corresponding to radial hydrogen bonds vibrations, torsion, and axial compression fluctuations of a DNA molecule model at ambient temperature are theoretically investigated. Due to thermal disorder, normal modes are not plane waves with a single wave number q but have a finite and frequency dependent damping width. The density of modes ρ(ν), the average dispersion relation ν(q), as well as the coherence length ξ(ν) are analytically calculated. The Gibbs averaged resolvent is computed using a replicated transfer matrix formalism and variational wave functions for the ground and first excited state. Our results for the density of modes are compared to Raman spectroscopy measurements of the collective modes for DNA in solution and show a good agreement with experimental data in the low frequency regime ν<150 cm−1. Radial optical modes extend over frequencies ranging from 50 to 100 cm−1. Torsional and compressional acoustic modes are limited to ν<25 cm−1. Normal modes are highly...

Franck−Condon Simulation of the S1 → S0 Spectrum of Phenol

Abstract: In this paper, a Franck−Condon simulation of the S1 → S0 transition of phenol is given including all normal modes. The geometries of phenol in its S0 and S1 states are obtained from CASSCF calculations. The calculated scaled harmonic frequencies are in good agreement with the experimental values. To calculate the Franck−Condon factors, Duschinsky rotations between the S0 and S1 states are taken into account. A very strong Duschinsky rotation is observed between modes 1 and 18a and modes 9b, 14, and the OH-bending vibration. To get good agreement between experimental and theoretical intensities, the calculated geometry of the S1 state is fitted by reducing the C−O bond length and elongating the molecule along mode 6a. Thus, the most significant changes in geometry in the S1 state can be deduced from the experimentally observed intensity pattern. The program developed to calculate the Franck−Condon factors is described and tested for the well-known spectrum of the benzene molecule. It is shown how the use o...

Combinations for the Free-Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions

Abstract: The free-vibration behavior of rectangular plates constitutes an important field in applied mechanics, and the natural frequencies are known to be primarily affected by the bound-ary conditions as well as aspect and thickness ratios. Any one of the three classical edge conditions, i.e., free, simply supported, and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations the present paper introduces the Polya counting theory in combinatorial mathematics, Formulas are derived for counting the exact numbers, A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three classical edge conditions and is used to numerically verify the numbers. In this numerical study the number of combinations in the free-vibration behavior is determined for some plate models by using the derived formulas. Results are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the modified Ritz method.

An object transport system using flexural ultrasonic progressive waves generated by two-mode excitation

Abstract: An object transport system using low amplitude and high frequency progressive waves generated by two-mode excitation is presented. A theoretical model for the system was developed using normal mode expansion and the modal participation factor. To identify the factors that affect the transport speed, the changes with the mass of objects on the beam, the input power, the phase difference, and the excitation frequency were experimentally investigated. With a power input of 40 W, a transport speed of 10 cm/s was obtained for an object weighing 30 g. The tests indicate that, not only the phase difference but also the excitation frequency, were the dominant factors in determining the transport speed and direction. Specifically, when the excitation frequency was chosen to be at the exact midpoint of the two modes, the object stopped moving. A slight change of frequency in either direction resulted in change of object transport direction. For actual factory application, a simple stop-go and tracking control using the General Purpose Interface Bus (GPIB) were implemented.