Analysis of the evanescent field coupling between a fiber and a planar waveguide using the explicit finite difference method with a nonuniform mesh (Journal Paper)

We investigate an optical waveguide system consisting of an unclad fiber core suspended at a constant distance parallel to the surface of a planar waveguide. The coupling and propagation of light in the combined system is studied using the three-dimensional explicit finite difference beam propagation method with a nonuniform mesh configuration. The power loss in the fiber and the field distribution in the waveguide are studied as a function of various parameters, such as index changes, index profile, and propagation distance, for the combined system.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

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.

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

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.

Dynamic analysis of three point bend specimens under impact

A simple one dimensional inertial model is presented for transient response analysis of notched beams under impact, and extracting dynamic initiation toughness values. The model includes the effects of striker mass interactions, and contact deformations of the beam. Displacement time history of the striker mass is applied to the model as forcing function. The model is validated by comparison with the experimental investigation on ductile aluminium 6061 alloy and brittle polymer, PMMA.

Unsteady three-dimensional boundary layer flow due to a stretching surface

In this numerical study, the unsteady laminar incompressible boundary-layer flow over a continuously stretching surface has been investigated when the velocity of the stretching surface varies arbitrarily with time. Both the nodal and the saddle point regions of flow have been considered for the analysis. Also, constant wall temperature/concentration and constant heat/mass flux at the stretching surface have been taken into account. The quasilinearisation method with an implicit finite-difference scheme is used in the nodal point region (0 less-than-or-equal-to c less-than-or-equal-to 1) where c denotes the stretching ratio. This method fails in the saddle point region (-1 less-than-or-equal-to c less-than-or-equal-to 0) due to the occurrence of reverse flow in the y-component of velocity. In order to overcome this difficulty, the method of parametric differentiation with an implicit finite-difference scheme is used, where the values at c = 0 are taken as starting values. Results have been obtained for the stretching velocities which are accelerating and decelerating with time. Results show that the skin friction, the heat transfer and the mass transfer parameters respond significantly to the time dependent stretching velocities. Suction (A > 0) is found to be an important parameter in obtaining convergent solution in the case of the saddle point region of flow. The Prandtl number and the Schmidt number strongly affect the heat and mass transfer of the diffusing species, respectively.

Surface-ray tracing on hybrid surfaces of revolution for UTD mutual coupling analysis

An angle invariance property based on Hertz's principle of particle dynamics is employed to facilitate the surface-ray tracing on nondevelopable hybrid quadric surfaces of revolution (h-QUASOR's). This property, when used in conjunction with a Geodesic Constant Method, yields analytical expressions for all the ray-parameters required in the UTD formulation. Differential geometrical considerations require that some of the ray-parameters (defined heuristically in the UTD for the canonical convex surfaces) be modified before the UTD can be applied to such hybrid surfaces. Mutual coupling results for finite-dimensional slots have been presented as an example on a satellite launch vehicle modeled by general paraboloid of revolution and right circular cylinder.

Analysis of a long thick orthotropic circular cylindrical shell panel

An exact three-dimensional elasticity solution has been obtained for an infinitely long, thick transversely isotropic circular cylindrical shell panel, simply supported along the longitudinal edges and subjected to a radial patch load. Using a set of three displacement functions, the boundary value problem is reduced to Bessel's differential equation. Numerical results are presented for different thickness to mean radius ratios and semicentral angles of the shell panel. Classical and first-order shear deformation orthotropic shell theories have been examined in comparison with the present elasticity solution.

Flap-lag-torsion stability in hover and forward flight with three-dimensional wake

The contributions of full-wake dynamics in trim analysis are demonstrated for finding the control inputs and periodic responses simultaneously, as well as in Floquet eigenanalysis for finding the damping levels. The equations of flap bending, lag bending, and torsion are coupled with a three-dimensional, finite state wake, and low-frequency (<1/rev) to high frequency (>1/rev) multiblade modes are considered. Full blade-wake dynamics is used in trim analysis and Floquet eigenanalysis. A uniform cantilever blade in trimmed flight is investigated over a range of thrust levels, advance ratios, number of blades, and blade torsional frequencies. The investigation includes the convergence characteristics of control inputs, periodic responses, and damping levels with respect to the number of spatial azimuthal harmonics and radial shape functions in the wake representation. It also includes correlation with the measured lag damping of a three-bladed untrimmed rotor. The parametric study shows the dominant influence of wake dynamics on control inputs, periodic responses, and damping levels, and wake theory generally improves the correlation.

Plane wave analysis of conical and exponential pipes with incompressible mean flow

The general equation for one-dimensional wave propagation at low flow Mach numbers (M less-than-or-equals, slant0·2) is derived and is solved analytically for conical and exponential shapes. The transfer matrices are derived and shown to be self-consistent. Comparison is also made with the relevant data available in the literature. The transmission loss behaviour of conical and exponential pipes, and mufflers involving these shapes, are studied. Analytical expressions of the same are given for the case of a stationary medium. The mufflers involving conical and exponential pipes are shown to be inferior to simple expansion chambers (of similar dimensions) at higher frequencies from the point of view of noise abatement, as was observed earlier experimentally.

Origin of a trend in ECMWF wind analysis and its objective removal

The suitability of the European Centre for Medium Range Weather Forecasting (ECMWF) operational wind analysis for the period 1980-1991 for studying interannual variability is examined. The changes in the model and the analysis procedure are shown to give rise to a systematic and significant trend in the large scale circulation features. A new method of removing the systematic errors at all levels is presented using multivariate EOF analysis. Objectively detrended analysis of the three-dimensional wind field agrees well with independent Florida State University (FSU) wind analysis at the surface. It is shown that the interannual variations in the detrended surface analysis agree well in amplitude as well as spatial patterns with those of the FSU analysis. Therefore, the detrended analyses at other levels as well are expected to be useful for studies of variability and predictability at interannual time scales. It is demonstrated that this trend in the wind field is due to the shift in the climatologies from the period 1980-1985 to the period 1986-1991.

Parallel computing concepts and methods for floquet analysis of helicopter trim and stability

Floquet analysis is widely used for small-order systems (say, order M < 100) to find trim results of control inputs and periodic responses, and stability results of damping levels and frequencies, Presently, however, it is practical neither for design applications nor for comprehensive analysis models that lead to large systems (M > 100); the run time on a sequential computer is simply prohibitive, Accordingly, a massively parallel Floquet analysis is developed with emphasis on large systems, and it is implemented on two SIMD or single-instruction, multiple-data computers with 4096 and 8192 processors, The focus of this development is a parallel shooting method with damped Newton iteration to generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct, The eigenvalues and eigenvectors of the FTM are computed by a parallel QR method, and thereby stability results are generated, For illustration, flap and flap-lag stability of isolated rotors are treated by the parallel analysis and by a corresponding sequential analysis with the conventional shooting and QR methods; linear quasisteady airfoil aerodynamics and a finite-state three-dimensional wake model are used, Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition numbers of the eigenvalues and the residual errors of the eigenpairs, and reliability figures are comparable in both the parallel and sequential analyses, Compared to the sequential analysis, the parallel analysis reduces the run time of large systems dramatically, and the reduction increases with increasing system order; this finding offers considerable promise for design and comprehensive-analysis applications.

Halogen Bonding in 2,5-Dichloro-1,4-benzoquinone: Insights from Experimental and Theoretical Charge Density Analysis

Experimental charge density distribution in 2, 5-dichloro-1, 4-benzoquinone has been carried out using high resolution X-ray diffraction data at 90 K to quantitatively evaluate the nature of C-Cl center dot center dot center dot O=C halogen bond in molecular crystals. Additionally, the halogen bond is studied from geometrical point of view and the same has been visualized using Hirshfeld surface analysis. The obtained results from experimental charge density analysis are compared with periodic quantum calculations using B3LYP 6-31G(d,p) level of theory. The topological values at bond critical point, three-dimensional static deformation density features and electrostatic potential isosurfaces unequivocally establish the attractive nature of C-Cl center dot center dot center dot O=C halogen bond in crystalline lattice.

Analysis of laminates with ply drops

Thickness tapered laminates obtained by terminating a certain number of plies contain resin-rich areas called ‘resin pockets’ near ply drops, where high stress concentrations exist. Study of the effects of ply drops and resin pockets on the tensile behaviour of tapered laminates considering certain important parameters like taper angle, the number of plies dropped, and the fiber orientation is reported here. Estimation of the tensile strength of tapered laminates necessitates accurate determination of the state of stress near the ply-drop region, which is, in general, three-dimensional (3-D) in nature. Recognising the fact that full 3-D finite-element analysis becomes computationally exorbitant, special layered 3-D finite-element analysis is carried out. Laminates with ply drops along only one direction are analysed to elicit the nature of the local bending effects occurring near the ply drops. Complete 3-D Tsai–Wu criterion considering all the six stress components is used to obtain a quick and comparative assessment of the tensile strength of these laminates. High stress concentration zones are identified and the effects of number of plies dropped at a station and resin pocket geometry are illustrated. The mechanism of load transfer near ply drops and the local bending that occurs are described. Susceptibility of ply drop zones to the onset and subsequent growth of delaminations is also brought out.