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.

Thermomechanical behaviour of pin joints subjected to sheet loads

An important problem regarding pin joints in a thermal environment is addressed. The motivation emerges from structural safety requirements in nuclear and aerospace engineering. A two-dimensional model of a smooth, rigid misfit pin in a large isotropic sheet is considered as an abstraction. The sheet is subjected to a biaxial stress system and far-field unidirectional heat flow. The thermoelastic analysis is complex due to non-linear load-dependent contact and separation conditions at the pin-hole interface and the absence of existence and uniqueness theorems for the class of frictionless thermoelastic contact problems. Identification of relevant parameters and appropriate synthesis of thermal and mechanical variables enables the thermomechanical generalization of pin-joint behaviour. This paper then proceeds to explore the possibility of multiple solutions in such problems, especially interface contact configuration.

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).

PVU and wave-particle splitting schemes for Euler equations of gas dynamics

A new way of flux-splitting, termed as the wave-particle splitting is presented for developing upwind methods for solving Euler equations of gas dynamics. Based on this splitting, two new upwind methods termed as Acoustic Flux Vector Splitting (AFVS) and Acoustic Flux Difference Splitting (AFDS) methods are developed. A new Boltzmann scheme, which closely resembles the wave-particle splitting, is developed using the kinetic theory of gases. This method, termed as Peculiar Velocity based Upwind (PVU) method, uses the concept of peculiar velocity for upwinding. A special feature of all these methods that the unidirectional and multidirectional parts of the flux vector are treated separately. Extensive computations done using these schemes demonstrate the soundness of the ideas.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Effect of open joint on stress wave propagation

Stress wave characteristics are drastically altered by joints and other inhomogenities. This paper addresses the effect of an open joint on stress wave transmission. An elastodynamic analysis is developed to supplement and explain some recent observations by Fourney and Dick(1995) on open as well as filled joints. The analytical model developed here assuming spherical symmetry can be extended to filled joints between dissimilar media, but results are presented only for open joints separating identical materials. As a special case, stress wave transmission across a joint with no gap is also addressed.