Narrow Results

Sharp line emission spectra of the silicon phthalocyanine complex ((n-C₆H₁₃)₃SiO)₂SiPc at low temperatures are resolved in multiple sites, and the vibronic fine structure of single-site emissions is identified. DFT methods are used to calculate the complete set of normal modes of the Cl₂SiPc analogue. Geometry optimization of the excited state further yields the Franck–Condon and Jahn–Teller distortions in the emitting state. These results are combined to obtain theoretical Huang–Rhys factors for the active modes, which compare favourably with the experimental spectrum. The dominant satellites are a 675 cm⁻¹ mode, which is identified as a totally symmetric bending of the four pyrrole rings, and a 1552 cm⁻¹ mode, which is assigned to an antisymmetric stretching of the aza-nitrogens with tetragonal b_1g symmetry.

Within the framework of the dielectric-continuum model and Loudon's uniaxial crystal model, the dispersions of the quasi-confined optical phonons in arbitrary wurtzite multiplelayer heterostructures are solved by using the transfer-matrix method. The dispersion relations of the quasi-confined phonons are investigated for GaN/AlN single QW and coupled QWs. The confinement of the quasi-confined phonons leads to a quantization of q_{z, j} characterized by an integer m that defines the order of corresponding quasi-confined modes. The quasi-confined modes are more dispersive for decreasing m (i.e., for decreasing q_{z, j}, the bands formed by the dispersion curves are narrower for higher order quasi-confined modes. The strain effect of QW structures has a clear influence on the dispersion behavior of the quasi-confined phonon modes and improves the frequency of the quasi-confined phonons.

Recently q-breathers - time-periodic solutions which localize in the space of normal modes and maximize the energy density for some mode vector q₀ - were obtained for finite nonlinear lattices. We scale these solutions to arbitrarily large lattices in various lattice dimensions. We study the scaling consequence for previously obtained analytical estimates of the localization length of q-breathers for β-FPU and α-FPU lattices. The first finding is that the degree of localization depends only on intensive quantities and is size independent. Secondly, a critical wave vector k_m is identified, which depends on one effective nonlinearity parameter, q-breathers minimize the localization length at k₀ = k_m and completely delocalize in the limit k₀ → 0, π.

In this paper, the linear and nonlinear modes of the unforced coupled rotor/stator system from a general rotor/stator model, which accounts for both the dynamics of the rotor and the stator as well as the friction and the deformation at the contact surfaces, are derived. The bifurcations of the nonlinear normal modes are analyzed based on the constrained bifurcation theory with the linear normal modes as the constraints. Then, the existence boundaries and the backward whirl frequencies of dry friction backward whirl — a hazardous self-excited oscillation in rotor/stator systems — of this model are derived. It is found by analysis that many inherent characteristics of the dry friction backward whirl can be derived from the information of the interaction of the linear and the nonlinear normal modes of the coupled rotor/stator system, such as the number of existence regions and their position relationship, the minimal friction on the contact surfaces that may induce the self-excited oscillation, the upper limits of the backward whirl frequencies of the response, and more. This study has well demonstrated the dominant role of the interaction of the linear and the nonlinear normal modes in deciding the characteristics of some nonlinear dynamical behaviors.

Today's minimum requirements for ocean acoustic models are to be able to simulate broadband signal transmissions in 2D varying environments with an acceptable computational effort. Standard approaches comprise ray, normal mode and parabolic equation techniques. In this paper we compare the performance of four broadband models on a set of shallow-water test environments with propagation out to 10 km and a maximum signal bandwidth of 10–1000 Hz. It is shown that a computationally efficient modal approach as implemented in the model is much faster than standard, less optimized models such as and . However, the handling of range dependency in the adiabatic approximation is not always sufficiently accurate, and it is suggested that a mode coupling approach be adopted in . Moreover, the interpolation of modal properties in range could lead to a further significant speed-up of mode calculations in range-dependent environments. It is concluded that coupled modes with wavenumber interpolation in both frequency and range remain the most promising wave modeling approach for broadband signal simulations in range-dependent shallow water environments. At higher frequencies (> 1 kHz) there is currently no alternative to rays as a practical signal simulation tool.

The application of coupled-mode theory to ocean acoustic propagation and scattering requires that ideal boundary conditions be applied at the surface and within the seabed. The depth of the lower boundary imposes limits on the ability of coupled-mode models to treat propagation and scattering at high grazing angles. Selecting this depth to predict the contributions of the continuous spectrum in a range-independent two-layered waveguide is not practical, and other methods must be introduced to apply coupled-mode theory in the near field of a source. An example of up-slope propagation in a range-dependent waveguide in which backscatter is governed by ray steepening and reversal is also treated. With a careful choice of the depth at which the lower boundary condition is applied, an estimate of the backscattered field is obtained.

Broadband and narrowband time-domain asymptotics are proposed for pulse propagation in range-independent ocean environments. The broadband approximation results by applying the stationary-phase method to the Fourier transform of the Green's function, expressed in terms of normal modes. The narrowband approximation is obtained by incorporating the shape function of the emitted signal — assumed Gaussian — into the phase term and applying the steepest-descent method. The roots of the frequency-derivative of the phase are located in the complex plane by using a second-order expansion of the eigenvalues. The performance of the two approximations is studied numerically. While the broadband approximation improves with increasing bandwidth, the narrowband approximation improves when the bandwidth decreases. Both approximations improve with increasing range, and they can be used for delivering time-domain results more efficiently than with standard Fourier synthesis.

This paper is concerned with the use of the reassigned wavelet transform for mode identification in shallow water acoustic propagation. Mode identification is important for inverse procedures in underwater acoustics. An efficient way to recognize the modal structure of the acoustic field when a single hydrophone is available is to refer to the time frequency analysis of the recorded signal using wavelet transform. However, the standard wavelet transform in some cases may result in an obscure representation of the dispersion curves. Thus, a reassigned process is proposed which brings important improvements in the time frequency representation of the signal. This is achieved by moving the calculation point of the scalogram in the center of gravity of the energy concentration, associated with each one of the propagating modes. This argument is supported by two illustrative examples corresponding to propagation of low frequency tomographic signals, in shallow water.

For ducted propagation in a waveguide when the source and receiver are placed close to the depth of the waveguide axis, there exist cusped caustics repeatedly along the axis. In neighborhoods of these cusped caustics, the interference of the wave fields that correspond to near-axial rays occurs. This results in the formation of a coherent structure (the axial wave) that propagates along the waveguide axis like a wave. In this paper, for the two-dimensional reference point source problem with the parabolic index of refraction squared the axial wave is represented in the form of a sum of the first normal modes and a remainder field. The mathematical framework is provided by two different representations of the acoustic field. The first one was obtained by Grigorieva et al.¹ It includes a sum of ray summands and the axial wave. The second representation including ray summands, a sum of the first normal modes, and a remainder field is derived in the present paper. For the remainder a simple formula including a special function is obtained. Numerical simulations are carried out for parameters corresponding to long-range ocean acoustic propagation experiments.

A coupled-mode formalism based on complex Airy layer mode solutions is presented. It is an extension into the complex horizontal wavenumber plane of the companion article [Stotts, J. Acoust. Soc. Am.111 (2002) 1623–1643], referred to here as the real horizontal wavenumber version, which accounted for general ocean environments but was restricted to normal modes on the real horizontal wavenumber axis. A formulation of the expressions for both trapped and continuum complex coupling coefficients is developed to dramatically reduce computer storage requirements and to make the calculation more practical. The motivation of this work is to demonstrate the numerical implementation of the derivations and to apply the method to an example benchmark. Differences from the real horizontal wavenumber formalism are highlighted. The coupled equations are solved using the Lanczos method [Knobles, J. Acoust. Soc. Am.96 (1994) 1741–1747]. Comparisons of the coupled-mode solution to a parabolic equation solution for the ONR shelf break benchmark validate the results.

Solution of wide-band underwater acoustic problems with the classical Normal Mode method in the frequency domain needs to solve the problem repeating for every frequency component of the wide-band source signal. In this paper, a direct and causal analytical Time Domain Normal Mode Method is presented for arbitrary time-dependent acoustic sources for a single layered isovelocity waveguide. An incomplete separation of variables technique is used to solve the inhomogeneous wave equation, directly in the time domain. Therefore, it becomes possible to calculate the time domain acoustic pressure in a single run.

The paper describes the theory and implementation issues of modeling of the acoustic field scattered by an air-filled spherical elastic shell immersed in a shallow-water waveguide over a homogeneous, fluid half-space. The normal mode evaluation is applied to the source contribution and to the scattering coefficients. The arising branch cut integrals are simplified and expressed via the probability integral. Two cases are analyzed: when a source frequency differs from the critical frequency of a normal mode and when they coincide. The formalism is applied to evaluate the effect of coupling between propagation and scattering on transmission loss.

Acoustic radiation modes (ARMs) and normal modes (NMs) are calculated at the surface of a fluid-filled domain around a solid structure and inside the domain, respectively. In order to compute the exterior acoustic problem and modes, both the finite element method (FEM) and the infinite element method (IFEM) are applied. More accurate results can be obtained by using finer meshes in the FEM or higher-order radial interpolation polynomials in the IFEM, which causes additional degrees of freedom (DOF). As such, more computational cost is required. For this reason, knowledge about convergence behavior of the modes for different mesh cases is desirable, and is the aim of this paper. It is shown that the acoustic impedance matrix for the calculation of the radiation modes can be also constructed from the system matrices of finite and infinite elements instead of boundary element matrices, as is usually done. Grouping behavior of the eigenvalues of the radiation modes can be observed. Finally, both kinds of modes in exterior acoustics are compared in the example of the cross-section of a recorder in air. When the number of DOF is increased by using higher-order radial interpolation polynomials, different eigenvalue convergences can be observed for interpolation polynomials of even and odd order.

Numerical algorithms are formulated for the prediction of seiche modes (eigen frequencies and mode shapes) in elongated natural basins. Confirmation is provided by an analytical solution for a basin with a linear variation in surface width and a parabolic variation in cross-section. Spatial variations in geometry are shown to have a significant influence on modal frequencies and especially modal shapes. In particular, local modal amplitudes are significantly enhanced by extensive regions of shallower water. Applications are given to the Caspian Sea and the Adriatic Sea.

Properties of discrete breathers are discussed from two points of view: (I) the ab initio modeling in graphene and (II) classical molecular dynamics simulations in the ace-centered cubic (fcc) Ni. In the first (I) approach, the possibility of exciting breathers depends on the strain applied to the graphene sheet. The uniaxial strain leads to opening the gap in the phonon band and, therefore, the existence of breathers with frequencies within the gap. In the second (II) approach, the structure of fcc Ni supports breathers of another kind, which possess a hard nonlinearity type. It is shown that particular high frequency normal mode can be used to construct the breather by means of overlaying a spherically symmetrical function, the maximum of which coincides with the breather core. The approach of breathers excitation based on nonlinear normal modes is independent of the level of approximation. Even though breathers could be obtained both in classical and first-principles calculations, each case has advantages and shortcomings, that are compared in the present work.

Problem of long-range sound propagation in the randomly-inhomogeneous deep ocean is considered. We examine a novel approach for modeling of wave propagation, developed by Hegewisch and Tomsovic. This approach relies on construction of a wavefield propagator using the random matrix theory (RMT). We study the ability of the RMT-based propagator to reproduce properties of the propagator corresponding to direct numerical solution of the parabolic equation. It is shown that mode coupling described by the RMT-based propagator is basically consistent with the direct Monte-Carlo simulation. The agreement is worsened only for relatively short distances, when long-lasting cross-mode correlations are significant. It is shown that the RMT-based propagator with properly chosen range step can reproduce some coherent features in spectral statistics.

The Helmholtz equation for exterior acoustic problems can be solved by the finite element method in combination with conjugated infinite elements. Both provide frequency-independent system matrices, forming a discrete, linear system of equations. The homogenous system can be understood as a quadratic eigenvalue problem of normal modes (NMs). Knowledge about the only relevant NMs, which — when doing modal superposition — still provide a sufficiently accurate solution for the sound pressure and sound power in comparison to the full set of modes, leads to reduced computational effort. Properties of NMs and criteria of modal reduction are discussed in this work.

An inversion scheme based on time-warping is presented for estimating the attenuation coefficient of a sediment bottom using a single vector sensor, restricted to shallow water and using low-frequency impulsive sources. The attenuation information is extracted from the modal phase difference between pressure and vertical velocity. The method is derived from Pekeris waveguide theoretical equations and the eigen values are obtained using the normal mode model Kraken. Some changes are made to the time-warping process to mitigate the inherent interference between adjacent modes, which improves the phase extraction capabilities. Results are presented for a two-layer, homogeneous environment using the RAM propagation model for depth-dependent sound speed profile simulations. This version of RAM was updated to provide radial and vertical velocities. For additional generality, the technique is evaluated in the presence of white noise.

The normal mode method is widely used in ocean acoustic propagation. Usually, finite difference and finite element methods are used in its solution. Recently, a method has been proposed for heterogeneous layered waveguides where the depth eigenproblem is solved using the classical Rayleigh–Ritz approximation. The method has high accuracy for low to high frequency problems. However, the matrices that appear in the eigenvalue problem for radial wavenumbers require numerical integration of the matrix elements since the sound speed and density profiles are numerically defined. In this paper, a technique is proposed to reduce the computational cost of the Rayleigh–Ritz method by expanding the sound speed profile in a Fourier series using nonlinear least square fit so that the integrals of the matrix elements can be computed in closed form. This technique is tested in a variety of problems and found to be sufficiently accurate in obtaining the radial wavenumbers as well as the transmission loss in a waveguide. The computational savings obtained by this approach is remarkable, the improvements being one or two orders of magnitude.

A waveguide consisting of an isospeed water layer overlying a halfspace with a sound speed gradient is considered. The dependence of horizontal wavenumbers of normal modes in such a waveguide on the sound frequency, water depth and geoacoustic parameters of the bottom are investigated. It is shown that these dependencies are described by ordinary differential equations that can be solved numerically at very low computational cost providing a substantial increase in the efficiency of broadband modelling of sound propagation. The explicit formulae for the derivatives of horizontal wavenumbers with respect to the bottom parameters can be also used in dispersion-based geoacoustic inversion methods. This approach can be extended to the case of a waveguide consisting of several layers of Airy-type media. We also propose a new and concise proof that the spectrum of the Sturm-Liouville problem from which the modes are found for this waveguide is purely discrete.