Characteristics Of Normal Modes Research Articles

Estimates of Low-Frequency Sound Speed and Attenuation in a Surface Mud Layer Using Low-Order Modes

Whereas there have been numerous theoretical and experimental studies on the properties of marine granular sands, there are significantly fewer studies on sediments classified as muds. The validity of geoacoustic models for muddy sediments has not been successfully tested due to the lack of inverted low-frequency sound speed and attenuation values. The geoacoustic properties of a surface fine-grained mud layer, overlaying three sand transition layers, and a half-space basement within the New England Mud Patch, were studied using explosive signals from long-range along-shelf sound propagation tracks. The sound-speed profile of the mud layer in the low-frequency band (100-500 Hz) was estimated using acoustic normal mode characteristics including the mode shapes and the modal dispersion curves of low-order modes, which mainly propagated in the water column and the surface mud layer. The ambiguity of sound speed at the top of the mud layer and sound-speed gradient was approximately removed. It was found that the resultant sound-speed ratio at the water-sediment interface was close to unity and the sound-speed gradient was 1.8 1/s with a standard deviation of 1.0 1/s. The attenuation in the mud layer was inverted using the attenuation coefficient of the first mode extracted from explosive signals at three source locations. The estimated attenuation at 150 Hz had a mean of 0.006 dB/m and a standard deviation of 0.003 dB/m.

Identification of interference normal mode pairs of low frequency sound in shallow water

The interference characteristics of normal modes in low-frequency broadband sound can be applied to source localization and environmental parameter inversion in shallow water. However, the identification ambiguity of interference normal mode pairs generally occurs in practical applications due to unknown source position, some weakly-excited normal modes, mismatched environmental model, etc. For the applications of a horizontal line array, a model-based processing approach is proposed to determine the orders of the interference normal mode pairs based on the intrinsic dispersion characteristics of interference normal mode pairs in the received signals and the range-independent properties of the array beam output angles. Firstly, the normal mode pair filtering is achieved by using the WARPING transform of the signal autocorrelation function in the element domain of the horizontal line array. Then, the arrival angles of the filtered interference normal mode pairs are estimated by using array beamforming. Finally, the estimated beam output angles are matched with the replica values computed by sound field model. The approach is verified by using the explosive pulse signals received by the seafloor-deployed 32-element horizontal line array at the North Yellow Sea in 2011. Furthermore, some simulations are involved to analyze the effects of environmental parameter mismatches including water sound speed profile, sea bottom parameters and water depth on the identification performance of interference normal mode pairs. The results show that the water depth is a major factor influencing the extracted values of the beam output angles of interference normal mode pairs. The approach might fail when the water depth mismatch exceeds 14% of the practical value. However, the effects of water sound speed profile mismatch and sea bottom parameters mismatch are negligible. The effect of signal-to-noise ratio in the element domain on a horizontal line array is also simulated in order to analyze the limitation of identification performance, which shows that the required signal-to-noise ratio in the element domain should be more than 2 dB.

Analysis of mode mismatch in uncertain shallow ocean environment

The actual ocean is an uncertain acoustic propagation environment. For the localization algorithms that rely on the precise ocean environmental parameters, the environmental mismatch problems will exist and performance degradation may be very serious. In the uncertain ocean environment, the uncertainties of sound field will have different effects on different normal modes propagating in the sound field, thus analysis of the mismatch characteristics of normal modes affected by uncertain environmental parameters can provide technical guidance for practical engineering applications. Based on the shallow-water acoustic propagation model, this paper simulates and analyzes the mismatch results of the modal depth eigenfunction and the horizontal wave number of each normal mode under conditions of environmental mismatch. Research indicates that the influence of different environmental parameters on normal modes in the sound field is not exactly the same. It was found that the sound-speed profile and seawater depth affect significantly, followed by sediment sound speed, the other parameters appear to be relatively minor importance.

Decomposing Dynamical Couplings in Mutated scFv Antibody Fragments into Stabilizing and Destabilizing Effects

Conformational fluctuations within scFv antibodies are characterized by a novel perturbation-response decomposition of molecular dynamics trajectories. Both perturbation and response profiles are stratified into stabilizing and destabilizing conditions. The linker between the VH and VL domains exhibits the dominant dynamical response by being coupled to nearly the entire protein, responding to both stabilizing and destabilizing perturbations. Perturbations within complementarity-determining regions (CDR) induce rich behavior in dynamic response. Among many effects, stabilizing any CDR loop in the VH domain triggers a destabilizing response in all CDR loops in the VL domain and vice versa. Destabilizing residues within the VL domain are likely to stabilize all CDR loops in the VH domain, and, when these residues are not buried, the CDR loops in the VL domain are also likely to be stabilized. These effects, described by shifts in normal mode characteristics, initiate a propensity for dynamic allostery with possible functional implications in bispecific antibodies.

Sound speed and attenuation in muddy sediments from low-frequency acoustic measurements

While there have been numerous theoretical and experimental studies on the properties of marine granular sands, there are significantly fewer studies on sediments classified as muds. The validity of geoacoustic models for muddy sediments has not been successfully tested due to the lack of inverted low-frequency sound speed and attenuation from acoustic measurements. The ONR-sponsored Seabed Characterization Experiment (SBCE), conducted in a mud patch on the New England continental shelf in the spring of 2017, provides an opportunity to make substantial improvements in understanding the physical mechanisms controlling sound propagation in muddy sediments. Acoustic signals (e.g., 31g explosive and combustive source signals) detonated at various ranges, depths and azimuths were measured in SBCE. This paper utilizes these measured signals to extract the acoustic normal mode characteristics including modal dispersive curve with Airy phase structure, modal amplitude, modal attenuation coefficient, and mode depth function. These normal mode characteristics are used in geo-acoustic inversion algorithms to estimate low-frequency sound speed and attenuation in muddy sediments as a function of frequency. The performance of different inversion methods using different normal mode characteristics is discussed. [Work supported by ONR Ocean Acoustics.]

Inversion of seabed attenuation by using single mode extracted by warping transform

Seabed is an important part of the marine environment and it has a significant influence on sound propagation. Considering the fact that geoacoustic parameters are directly acquired with difficulty and complexity, a lot of researchers have focused on the inversion of them. The seabed attenuation coefficient is insensitivity to the matching field. However it has great effects on the transmission loss, mode amplitude ratios, etc. It can be inverted from measurements of these quantities. In this paper, we present an inversion scheme based on warping transform technique for estimating the seabed attenuation coefficient. It utilizes an equivalent seabed model which is constructed by using a prior and posterior knowledge. The dispersion characteristics of normal modes can be observed using the time-frequency analysis of the explosive signal recorded. The dispersion curve can be used to invert the seabed sound speed and density. The results presented by other scholars in the same circle are cited in this paper that focuses on how to obtain the seabed attenuation. Warping transform technique is used to separate and extract the normal modes. The main advantage of warping transform is that it can transform the time-frequency spectrogram into linear relationship which makes it easier to extract the normal modes. The feature of this paper lies in determining the distance normalized normal mode transmission loss. If the depths of receiving hydrophone and the explosion source are constant, the plot of normalized normal mode transmission loss versus distance is a straight line from the normal modes theory, which can be used to obtain the attenuation factor of real part of pressure. Then the seabed attenuation coefficient of the shallow water acoustic model can be calculated. In order to verify the effectiveness of this method, the warping transformation technology is used to separate and extract the first three modes from the simulated Gaussian pulse signal which is obtained in a simulated environment which is similar to the real marine environment. The extracted results are completely consistent with the numerical results. After that, the impulsive signal data collected in the Yellow Sea are analyzed according to the scheme process, and the relationship between the seabed attenuation and frequency is =0.581fk1.86(dB/m) in a range from 150 Hz to 550 Hz. The results are in good agreement with those obtained by other scholars in the same circle. On the other hand, the inversion results of seabed attenuation from different modes can be used for comparison at the same frequency, which can be a good support for the result.

Geo-acoustic parameter estimation using a multistep inversion technique based on normal mode method

The geo-acoustic parameters are of great importance in determining how the sea bottom affects sound propagation in the ocean. Many inversion techniques have been developed to estimate geo-acoustic parameters. One-step inversion algorithms using a cost function defined only by energy loss may not result in a unique solution of geo-acoustic inversion problem because of the correlation between seabed sound speed and attenuation. This paper utilizes different characteristics of normal modes to define appropriate cost functions in a two-step inversion algorithm for inferring geo-acoustic parameters. This inversion scheme is applied to the combustive sound source data obtained by two L-shaped arrays. The inverted seabed sound speed and attenuation are comparable to the results derived from measured time series and transmission loss data at the same experimental site [Knobles, Wilson, Goff, and Cho, J. Acoust. Soc. Am., 124, 2008]. [Work supported by ONR321OA].

Elastic waveguides: history and the state of the art. II

In this paper, the normal modes of an elastic rectangular waveguide are analyzed. We retrace the key aspects of the almost 150-year history of this problem. Using the superposition method, we have obtained an analytical solution of the problem for four types of symmetry of the wave field. In addition, we have established important differences of the dispersion characteristics of normal modes in a rectangle from the Rayleigh–Lamb modes for an infinite plate and the Pochhammer–Chree modes for a cylinder. We give also an estimate of a series of approximate theories for a rectangular waveguide. J. Fourier [28, Sec. 13]

Response of a harbor with two connected basins to incoming long waves

The general features of the resonant response for a given basin, including the determination of the normal modes and relative amplification of incoming long waves can be easily determined by using a numerical model. However, when the relative role of the different geometric parameters want to be studied, the use of analytical solutions becomes extremely useful. An analytical model is developed to determine the coupled oscillations between two rectangular basins connected through a gap, when only one of them is opened to the ocean. This geometry resembles the topographic features of Ciutadella inlet and its adjacent sub-basin (Cala Busquets) in Menorca, Balearic Islands. The analytical solutions show a good agreement with numerical simulations and capture well the changes induced by some hypothetical modifications of Ciutadella–Cala Busquets system. The agreement shown justifies the use of the analytical model as a basis for the discussion on the influence of the geometrical parameters in the normal mode characteristics of the coupled system.

Raman excitation profiles and excited state molecular configurations of three isomeric phenyl pyridines

Contributions of different electronic states to Raman scattering have been studied by critical analyses of Raman excitation profiles (REPs) of several normal modes of vibration of three isomeric phenyl pyridines. In this context, possible structures and other interesting properties of the three molecules in the excited electronic states have been discussed. Normal mode characteristics are also described. Most likely a singlet state, lying in the vacuum ultraviolet region with respect to the ground state, is found to be playing a very significant role in the scattering phenomena.

Molecular structures in the excited states of 2- and 4-benzylpyridine

Raman excitation profiles of several normal vibrations of 2- and 4-benzylpyridine were measured and analyzed. On the basis of the results, possible structures and other interesting properties of the two molecules in the excited electronic states are discussed. Normal mode characteristics are also described. It seems likely that a singlet state, lying in the vacuum ultraviolet region with respect to the ground state, plays a significant role in the scattering phenomena. Copyright © 1999 John Wiley & Sons, Ltd.

The influence of internal waves on signal fluctuation in the Yellow Sea

This paper studies the signal fluctuation due to the tide and internal waves in the Yellow Sea. The spread of internal waves appears to be the fluctuation of the thermocline in summer time. As a result, the characteristics of normal modes including their wave numbers and group velocities vary with this fluctuation. This leads to the signal fluctuations since the receiving signals are actually the interference results of arriving modes. The influence of internal waves on normal modes and signal fluctuation was examined in an experiment in the Yellow Sea in 1998. In the experiment, an ADCP and thermistor chain were used to observe the internal waves, while a vertical array with 32 hydrophones was used to receive CW and FM acoustic signals. The CW signals provided the measurement of amplitude fluctuation at several frequencies from 450 to 650 Hz. The FM signals were used to get the mode arriving structure by means of pulse compression and mode filtering technique. The variation of mode group delay between the 3800-Hz signal and the 450-650 Hz signal was also measured.

Coupled-mode analysis of ferrite microstrip lines

A coupled-mode analysis is presented for an axially magnetized ferrite microstrip, with a particular reference to the case of a coupled microstrip (FCL). On the basis of the gyromagnetic coupling between the basis propagating and the evanescent isotropic modes, we determine the propagation characteristics of normal modes in ferrite microstrips. The theory is also applied to define the scattering matrix of the FCL microstrip junction. The important for application behavior of FCL junction is discussed. Numerical results confirming the validity of the theory are included.

The effect of wave energy trapping in inhomogeneous elastic structure

In contrast to an acoustical waveguide the distribution of characteristics of normal modes with respect to the cross section in elastic waveguides is strongly dependent on frequency. Such dependence gives rise to several interesting wave phenomena, which take place in inhomogeneous structures. One of them, namely, energy trapping, is quantitatively and qualitatively considered in this report. In terms of the theory of elastic waveguides, this phenomenon manifests itself in an anomaly of the frequency functions of the reflection (transmission) coefficients of energy in the composite waveguides. These functions are calculated for both in-plane and flexural motions in waveguides consisting of two semi-infinite layers with equal thickness. The results are systematized with respect to the ratio of wave impedances of the layers. The frequency bands where the energy trapping is effective are determined. The dependence of these bands on the mechanical characteristics of materials is different for the in-plane and flexural waves. The mechanism of redistribution of energy among the incident and reflected waves is shown. The function of the normal mode with opposite signs of phase and group velocities is illustrated.

Qy-Excitation Resonance Raman Spectra of Chlorophyll a and Related Complexes. Normal Mode Characteristics of the Low-Frequency Vibrations

Qy-excitation resonance Raman (RR) spectra are reported for film aggregates of chlorophyll (Chl) a and a series of related complexes. The latter include Mg(II) octaethylporphyrin (MgOEP), Mg(II) trans-octaethylchlorin (MgOEC), methyl-9-desoxomesopyrochlorophyllide (DMPChl) a, and methylpyrochlorophyllide (MPChl) a. These complexes represent a series in which the structural complexities of Chl a (saturated pyrrole ring, isocyclic ring, C9-keto group, C2-vinyl group, and C10-carbomethoxy group) are systematically added to the basic tetrapyrrole architecture. On the basis of comparison of the RR scattering characteristics of the different complexes and the predictions of semiempirical normal coordinate calculations, a self-consistent set of vibrational assignments has been developed for all the RR active modes in the low-frequency regime (100−1000 cm-1). The studies indicate that the low-frequency vibrations encompass a diverse set of motions that include both the ring skeleton and peripheral substituent groups. However, modes in the very low-frequency regime (<250 cm-1) are primarily due to deformations of the substituent groups. Collectively, the normal mode characteristics of Chl a and the other Mg(II) complexes provide insights into the nature of the vibrational modes that are coupled to the photophysically important, lowest energy excited states of natural photosynthetic assemblies.

Three-dimensional vibration of rectangular plates : Variance of simple support conditions and influence of in-plane inertia

Plate models developed on the basis of the three-dimensional elasticity theory are crucial to the correct solutions in dynamics problems. In a three-dimensional setting, there exist numerous possible definitions of boundary conditions. This paper attempts to identify the variance of three-dimensional simple support conditions existing in practice. The hard simple support condition assumes vanishing normal stresses at the edges and zero transverse and tangential displacement at the peripheries. The soft simple support, on the other hand, imposes zero transverse displacement with vanishing normal and shear stresses at the boundaries. To quantify the relative effects of each boundary condition on the vibratory responses of thick plates, a global three-dimensional Ritz formulation is employed for analysis. This technique uses sets of finite polynomial series in Cartesian co-ordinates to approximate the global normal mode variations of the plate. These separable one-dimensional polynomials are orthogonally generated within the plate domain such that all the essential edge conditions are identically satisfied. The accuracy of the proposed three-dimensional Ritz method is assured from the convergence and comparison studies. Numerical experiments have been conducted to study firstly, the effects of geometric parameters on the overall normal mode characteristics of simply supported plates ; and secondly, the effects of in-plane inertia on the vibration frequencies of plates with different thicknesses. The three-dimensional deformed mode shapes for selected cases have also been computed. These have served to describe more vividly the normal mode characteristics of different types of simply supported rectangular plates.

Numerical Investigations with a Hybrid Isentropic–Sigma Model. Part I: Normal-Mode Characteristics

In a validation experiment of a hybrid isentropic–sigma coordinate primitive equation model developed at the University of Wisconsin (the UW θ−σ model), an initial value technique is used to investigate numerically the normal-mode characteristics of baroclinically amplifying disturbances over a spectrum of meteorologically significant wavelength. The experiments are designed to determine the impact of coupling an isentropic-coordinate free atmospheric domain to a sigma-coordinate planetary boundary layer (PBL) on the normal-mode characteristics. The growth rate and phase speed spectra of the most unstable normal modes are obtained for an analytically prescribed zonal flow field. The evolution and vertical structure of the kinetic energy, energy conversions, growth rates, and geopotential fields are investigated. Several modifications have been made to earlier versions of the UW θ−σ model to overcome noise introduced by adjustments associated with emerging and submerging grid volumes at the sigma–isentropic interface. With these modifications, the hybrid model accurately simulates the evolution and structure of normal-mode baroclinic disturbances for all wavenumbers considered except for wavenumber two. The normal-mode growth rate and phase speed spectra compare well with previous studies using standard sigma coordinate models. There is no evidence of aliasing the baroclinic normal-mode characteristics due to the coupling of isentropic and sigma domains.

Intramolecular vibrational redistribution in alkylbenzenes. I. Normal modes and their energy distribution

Normal modes for the ground and first excited singlet state are computed for ethylbenzene, pentylbenzene, and hexylbenzene and are assigned in terms of zero-order mode descriptors. The energy distribution, i.e., the partitioning of energy between the ring and chain, is computed for the normal modes and the concept of ‘‘system modes,’’ i.e., modes localized on the ring, is examined. Several of the basic assumptions made in traditional interpretations of intramolecular vibrational redistribution in molecules with a ‘‘ring+tail’’ structure are examined in light of the computed normal mode characteristics.

A Complete Formalism For the Inversion of Post-Glacial Rebound Data: Resolving Power Analysis

SUMMARY A formal inverse theory for mantle viscosity based upon the data of glacial isostatic adjustment is here formulated and applied to synthetic data. In this theory full account has been taken of the normal mode nature of the forward problem for realistic viscoelastic (Maxwell) models of the planet. Since it is impossible to accurately infer the excitation and decay constants of the individual normal modes from the observations, the formalism is cast in terms of the observed gross Earth data in the time domain. In this analysis expressions are required for the first-order perturbations in both the modal amplitudes and relaxation times that are induced by an arbitrary radial perturbation to the starting viscosity profile. A numerical technique is developed which enables us to accurately determine differential kernels for the modal amplitudes. the analogous kernels for the modal decay times are derived analytically (Peltier 1976), and the complete set of kernels is shown to satisfy the physical constraint imposed by the uniqueness of the state of isostatic equilibrium for the viscously incompressible Maxwell models that we employ. When the problem is parametrized in terms of the logarithm of viscosity, the kernels are capable of accurately predicting shifts in the normal mode characteristics for at least an order of magnitude variation in mantle viscosity. Using Bayesian statistics a formal inversion is applied to a set of synthetically generated data. These data, chosen to reproduce the space-time coverage of the actual observables, include a subset related to the global gravity field and a large sequence of idealized relative sea level (RSL) curves. It is found that even very weak a priori constraints can provide a stable and accurate inversion. A resolving power analysis indicates a spatial resolution of approximately 1200km near the core-mantle boundary (CMB) with a gradual improvement to better than 350km in the middle of the upper mantle. Subsets of the synthetic data are inverted in order to examine conditions on stability and accuracy, and to determine their relative contributions to the spatial resolution. Data from progressively older beaches are shown to contribute most to the spatial resolution at all depths, though the improvement in lower mantle resolution converges for data obtained from beaches formed within the last 5000 yr. Furthermore, the RSL curves in the vicinity of the peripheral bulge of the ancient Laurentide ice sheet are significant contributors to lower mantle resolution (as demonstrated in previous analyses of the forward problem). the inversion of this subset of the data also appears to be encouragingly stable.

Mode theory of electromechanical energy conversion in piezoelectric materials

The method of eigenfunctions is generalized to the problem of dynamic electroelasticity /1/, which allows of a larger variety of physically realisable boundary conditions. Using the method of eigenfunctions a so-called mode theory of electromagnetic energy conversion is developed. Its basic idea is the establishment of a connection between the dynamic electromechanical coupling coefficient of the specified displacement field and the mode or partial electromechanical coupling coefficients of the individual modes of oscillation. The latter, being non-linear integral characteristics of normal modes, play the same fundamental role with respect to the first as the eigenfunctions (normal modes) play with respect to the overall solution of the electro-elasticity problem. The coefficients of the expansion in eigenfunctions of the displacement field which gives a maximum permissible value of the electromechanical coupling coefficient for a given geometry, position of the electrodes, and method of supplying and removing the electrical energy.