On the Role of Higher-Order Evanescent Modes in End-Offset Inlet and End-Centered Outlet Elliptical Flow-Reversal Chamber Mufflers

This paper deals with the role of the higher-order evanescent modes generated at the area discontinuities in the acoustic attenuation characteristics of an elliptical end-chamber muffler with an end-offset inlet and end-centered outlet. It has been observed that with an increase in length, the muffler undergoes a transition from being acoustically short to acoustically long. Short end chambers and long end chambers are characterized by transverse plane waves and axial plane waves, respectively, in the low-frequency range. The nondimensional frequency limit k(0)(D-1/2) or k(0)R(0) as well as the chamber length to inlet/outlet pipe diameter ratio, i.e., L/d(0), up to which the muffler behaves like a short chamber and the corresponding limit beyond which the muffler is acoustically long are determined. The limits between which neither the transverse plane-wave model nor the conventional axial plane-wave model gives a satisfactory prediction have also been determined, the region being called the intermediate range. The end-correction expression for this muffler configuration in the acoustically long limit has been obtained using 3-D FEA carried on commercial software, covering most of the dimension range used in the design exercise. Development of a method of combining the transverse plane wave model with the axial plane wave model using the impedance Z] matrix is another noteworthy contribution of this work.

Effect of high-temperature shock-wave compression on few-layer MoS2, WS2 and MoSe2

Exposure of few-layer MoS2, WS2 and MoSe2 to high-temperature shock waves causes morphological changes and a significant decrease in the interlayer separation between the (002) planes, the decrease being greatest in MoSe2. Raman spectra show softening of both the A(1g) and the E-2g(1) modes initially, followed by a slightly stiffening. Using first-principles density functional theoretical analysis of the response of few-layer MoS2 to shock waves, we propose that a combination of shear and uniaxial compressive deformation leads to flattening of MoS2 sheets which is responsible for the changes in the vibrational spectra. (C) 2013 Elsevier B.V. All rights reserved.

Floquet generation of Majorana end modes and topological invariants

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a p-wave superconducting term, and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the (z) over cap direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks, and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to +/- 1 for time-reversal-symmetric systems. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number, while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to + 1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical solution in frequency domain is done by discretisation in space by approximating the unknown function using spectral functions like Chebyshev polynomials, Legendre polynomials and also Normal polynomials. Different numerical methods such as Galerkin Method, Petrov- Galerkin method, Method of moments and Collocation method or the Pseudo-spectral method in frequency domain are studied and compared with the available exact solution. An approximate solution is also obtained for the Timoshenko beam with varying cross-section using Laplace Spectral Element Method (LSEM). The group speeds are computed exactly for the Cantilever beam and Timoshenko beam with uniform cross-section and is compared with the group speeds obtained numerically. The shear mode and the bending modes of the Timoshenko beam with uniform cross-section are separated numerically by applying a modulated pulse as the shear force and the corresponding group speeds for varying taper parameter in are obtained numerically by varying the frequency of the input pulse. An approximate expression for calculating group speeds corresponding to the shear mode and the bending mode, and also the cut-off frequency is obtained. Finally, we show that the cut-off frequency disappears for large in, for epsilon > 0 and increases for large in, for epsilon < 0.

Majorana modes and transport across junctions of superconductors and normal metals

We study Majorana modes and transport in one-dimensional systems with a p-wave superconductor (SC) and normal metal leads. For a system with an SC lying between two leads, it is known that there is a Majorana mode at the junction between the SC and each lead. If the p-wave pairing Delta changes sign or if a strong impurity is present at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the sub-gap conductance between the leads and the SC. We derive an analytical expression as a function of Delta and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the shifts oscillate and decay exponentially as L is increased. The energy shifts exactly match the location of the peaks in the conductance. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on Delta and the strengths of an impurity inside the SC or the barriers between the SC and the leads; this in turn affects the Majorana modes and the conductance. Finally, we propose a novel experimental realization of these systems, in particular of a system where Delta changes sign at one point inside the SC.

A model supersonic buried-nozzle jet: instability and acoustic wave scattering and the far-field sound

We consider sound source mechanisms involving the acoustic and instability modes of dual-stream isothermal supersonic jets with the inner nozzle buried within an outer shroud-like nozzle. A particular focus is scattering into radiating sound waves at the shroud lip. For such jets, several families of acoustically coupled instability waves exist, beyond the regular vortical Kelvin-Helmholtz mode, with different shapes and propagation characteristics, which can therefore affect the character of the radiated sound. In our model, the coaxial shear layers are vortex sheets while the incident acoustic disturbances are the propagating shroud modes. The Wiener-Hopf method is used to compute their scattering at the sharp shroud edge to obtain the far-field radiation. The resulting far-field directivity quantifies the acoustic efficiency of different mechanisms, which is particularly important in the upstream direction, where the results show that the scattered sound is more intense than that radiated directly by the shear-layer modes.

Wave propagation in a 2D nonlinear structural acoustic waveguide using asymptotic expansions of wavenumbers

Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger equation (NLSE). The first objective here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.

Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

Wave Dynamic Processes in Cellular Detonation Reflection from Wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H (2)/O (2) diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes.

Fission of solitary wave in stratified fluid

In this paper, we study the fission of a solitary wave in the stratified fluid with a free surface. It has been discovered that there is no difference between the fissions of the internal solitary waves in odd or even modes, and the effect of the stratification on the fission of a surface solitary wave can almost be neglected

WEMo (Wave Exposure Model): Formulation, Procedures and Validation

This report describes the working of National Centers for Coastal Ocean Service (NCCOS) Wave Exposure Model (WEMo) capable of predicting the exposure of a site in estuarine and closed water to local wind generated waves. WEMo works in two different modes: the Representative Wave Energy (RWE) mode calculates the exposure using physical parameters like wave energy and wave height, while the Relative Exposure Index (REI) empirically calculates exposure as a unitless index. Detailed working of the model in both modes and their procedures are described along with a few sample runs. WEMo model output in RWE mode (wave height and wave energy) is compared against data collected from wave sensors near Harkers Island, North Carolina for validation purposes. Computed results agreed well with the wave sensors data indicating that WEMo can be an effective tool in predicting local wave energy in closed estuarine environments. (PDF contains 31 pages)

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.