Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Component wave delineation of ECG by filtering in the Fourier domain

A complete solution to the fundamental problem of delineation of an ECG signal into its component waves by filtering the discrete Fourier transform of the signal is presented. The set of samples in a component wave is transformed into a complex sequence with a distinct frequency band. The filter characteristics are determined from the time signal itself. Multiplication of the transformed signal with a complex sinusoidal function allows the use of a bank of low-pass filters for the delineation of all component waves. Data from about 300 beats have been analysed and the results are highly satisfactory both qualitatively and quantitatively.

Exact nonlinear travelling hydromagnetic wave solutions

Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.

Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers: A finite element approach

Resonant sound absorbers are used widely as anechoic coatings in underwater applications. In this paper a finite element scheme based on the Galerkin technique is used to analyze the reflection characteristics of the resonant absorber when insonified by a normal incidence plane wave. A waveguide theory coupled with an impedance matching condition in the fluid is used to model the problem. It is shown in this paper that the fluid medium encompassing the absorber can be modeled as an elastic medium with equivalent Lamé constants. Quarter symmetry conditions within the periodic unit cell are exploited. The finite element results are compared with analytical results, and with results published elsewhere in the literature. It is shown in the process that meshing of the fluid domain can be obviated if the transmission coefficients or reflection coefficients only are desired as is often the case. Finally, some design curves for thin resonant absorbers with water closure are presented in this paper.

Spectral approach for the soliton and periodic solutions of the nonlinear wave equation

A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.

Schlieren visualization of shock wave phenomena over a missile-shaped body at hypersonic Mach numbers

The flow over a missile-shaped configuration is investigated by means of Schlieren visualization in short-duration facility producing free stream Mach numbers of 5.75 and 8. This visualization technique is demonstrated with a 41 degrees full apex angle blunt cone missile-shaped body mounted with and without cavity. Experiments are carried out with air as the test gas to visualize the flow field. The experimental results show a strong intensity variation in the deflection of light in a flow field, due to the flow compressibility. Shock stand-off distance measured with the Schlieren method is in good agreement with theory and computational fluid dynamic study for both the configurations. Magnitude of the shock oscillation for a cavity model may be greater than the case of a model without cavity. The picture of visualization shows that there is an outgoing and incoming flow closer to the cavity. Cavity flow oscillation was found to subside to steady flow with a decrease in the free stream Mach number.

A simple equivalent circuit analysis of rectangular folded-waveguide slow-wave structure

A simple yet accurate equivalent circuit model was developed for the analysis of slow-wave properties (dispersion and interaction impedance characteristics) of a rectangular folded-waveguide slow-wave structure. Present formulation includes the effects of the presence of beam-hole in the circuit, which were ignored in existing approaches. The analysis was benchmarked against measurement as well as with 3D electromagnetic modeling using MAFIA for two typical slow-wave structures operating in Ka- and Q-bands, and close agreements were observed. The analysis was extended for demonstrating the effect of the variation of beam-hole radius on the RF interaction efficiency of the device. (C) 2009 Elsevier GmbH. All rights reserved.

Surface acoustic wave distribution and acousto-optic interaction in proton exchanged LiNbO3 waveguides

The efficiency of acoustooptic (AO) interaction in YZ-cut proton exchanged (PE) LiNbO3 waveguides is theoretically analysed by determining the overlap between the optical and acoustic field distributions. The present analysis takes into account the perturbed SAW field distribution due to the presence of the PE layer on the LiNbO3 substrate determined by the rigorous layered medium approach. The overlap is found to be significant upto very high acoustic frequencies of the order of 5 GHz, whereas in the earlier analysis by vonHelmolt and Schaffer [6] for diffused waveguides, it was shown that the overlap integral rolls down to nearly zero at this high frequency range.

Support vector machine for evaluating seismic-liquefaction potential using shear wave velocity

The use of the shear wave velocity data as a field index for evaluating the liquefaction potential of sands is receiving increased attention because both shear wave velocity and liquefaction resistance are similarly influenced by many of the same factors such as void ratio, state of stress, stress history and geologic age. In this paper, the potential of support vector machine (SVM) based classification approach has been used to assess the liquefaction potential from actual shear wave velocity data. In this approach, an approximate implementation of a structural risk minimization (SRM) induction principle is done, which aims at minimizing a bound on the generalization error of a model rather than minimizing only the mean square error over the data set. Here SVM has been used as a classification tool to predict liquefaction potential of a soil based on shear wave velocity. The dataset consists the information of soil characteristics such as effective vertical stress (sigma'(v0)), soil type, shear wave velocity (V-s) and earthquake parameters such as peak horizontal acceleration (a(max)) and earthquake magnitude (M). Out of the available 186 datasets, 130 are considered for training and remaining 56 are used for testing the model. The study indicated that SVM can successfully model the complex relationship between seismic parameters, soil parameters and the liquefaction potential. In the model based on soil characteristics, the input parameters used are sigma'(v0), soil type. V-s, a(max) and M. In the other model based on shear wave velocity alone uses V-s, a(max) and M as input parameters. In this paper, it has been demonstrated that Vs alone can be used to predict the liquefaction potential of a soil using a support vector machine model. (C) 2010 Elsevier B.V. All rights reserved.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part I. Theory

Time-domain-finite-wave analysis of the engine exhaust system is usually done using the method of characteristics. This makes use of either the moving frame method, or the stationary frame method. The stationary frame method is more convenient than its counterpart inasmuch as it avoids the tedium of graphical computations. In this paper (part I), the stationary-frame computational scheme along with the boundary conditions has been implemented. The analysis of a uniform tube, cavity-pipe junction including the engine and the radiation ends, and also the simple area discontinuities has been presented. The analysis has been done accounting for wall friction and heat-transfer for a one-dimensional unsteady flow. In the process, a few inconsistencies in the formulations reported in the literature have been pointed out and corrected. In the accompanying paper (part II) results obtained from the simulation are shown to be in good agreement with the experimental observations.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part II. Computed results and experimental corroboration thereof

Time-domain-finite-wave analysis of engine exhaust systems is usually carried out by means of the method of characteristics. The theory and the computational details of the stationary-frame method have been worked out in the accompanying paper (part I). In this paper (part II), typical computed results are given and discussed. A setup designed for experimental corroboration is described. The results obtained from the simulation are found to be in good agreement with experimental observations.

Strong nonlocalization induced by small scale parameter on terahertz flexural wave dispersion characteristics of a monolayer graphene

This paper presents the strong nonlocal scale effect on the flexural wave propagation in a monolayer graphene sheet. The graphene is modeled as an isotropic plate of one atom thick. Nonlocal governing equation of motion is derived and wave propagation analysis is performed using spectral analysis. The present analysis shows that the flexural wave dispersion in graphene obtained by local and nonlocal elasticity theories is quite different. The nonlocal elasticity calculation shows that the wavenumber escapes to infinite at certain frequency and the corresponding wave velocity tends to zero at that frequency indicating localization and stationary behavior. This behavior is captured in the spectrum and dispersion curves. The cut-off frequency of flexural wave not only depend on the axial wavenumber but also on the nonlocal scaling parameter. The effect of axial wavenumber on the wave behavior in graphene is also discussed in the present manuscript. (C) 2010 Elsevier B.V. All rights reserved.

Analysis of serpentine folded-waveguide slow-wave structure using elliptical conformal transformation

Elliptical conformal transformation was used to derive closed form expressions for the equivalent circuit series inductance and shunt capacitance per period of a serpentine folded-waveguide slow-wave structure including the effects of the beam-hole. The lumped parameters were subsequently interpreted for the dispersion and interaction impedance characteristics of the structure. The analysis was benchmarked for two typical millimeter-wave structures operating in Ka- and W-bands, against measurement, 3D electromagnetic modeling using CST Microwave Studio, parametric analysis and equivalent circuit analysis. (C) 2010 Elsevier GmbH. All rights reserved.

Transverse plane wave analysis of short elliptical chamber mufflers: An analytical approach

Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations. (C) 2010 Elsevier Ltd. All rights reserved.

Exact N-Wave Solutions for the Non-Planar Burgers Equation

An exact representation of N-wave solutions for the non-planar Burgers equation u(t) + uu(x) + 1/2ju/t = 1/2deltau(xx), j = m/n, m < 2n, where m and n are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for Absolute value of x < square-root (2Q0 t), where Q0 is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as t tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all j = m/n, m < 2n, and are rather involved; explicit results are written out for j = 0, 1, 1/2, 1/3 and 1/4. The case of spherical symmetry j = 2 is found to be 'singular' and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are compared with those of Crighton & Scott (1979).