A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

The fluorescence of Nd3+ in lead borate and bismuth borate glasses with large stimulated emission cross section

The stimulated emission cross section σp for the 1060 nm transition of Nd3+ in lead borate and bismuth borate glasses has been determined from fluorescence measurements. The compositional dependence of σp, which has been evaluated using radiative transition probability, refractive index of the host glass, effective fluorescence linewidth, and position of the band, with PbO/Bi2O3 content is investigated. The σp values of the 1060 nm band of Nd3+ for lead borate and bismuth borate glasses are found to be in the range 2.6–5.7×10−20 cm2 at 298 K and 3.0–6.3×10−20 cm2 at 4.2 K. The σp values are comparatively large suggesting the possible utilization of these materials in laser applications.

A deep‐level spectroscopic technique for determining capture cross‐section activation energy of Si‐related DX centers in AlxGa1-xAs

A deep‐level transient spectroscopy (DLTS) technique is reported for determining the capture cross‐section activation energy directly. Conventionally, the capture activation energy is obtained from the temperature dependence of the capture cross section. Capture cross‐section measurement is often very doubtful due to many intrinsic errors and is more critical for nonexponential capture kinetics. The essence of this technique is to use an emission pulse to allow the defects to emit electrons and the transient signal from capture process due to a large capture barrier was analyzed, in contrast with the emission signal in conventional DLTS. This technique has been applied for determining the capture barrier for silicon‐related DX centers in AlxGa1−xAs for different AlAs mole fractions.

Surrogate based design optimisation of composite aerofoil cross-section for helicopter vibration reduction

Design optimisation of a helicopter rotor blade is performed. The objective is to reduce helicopter vibration and constraints are put on frequencies and aeroelastic stability. The ply angles of the D-spar and skin of the composite rotor blade with NACA 0015 aerofoil section are considered as design variables. Polynomial response surfaces and space filling experimental designs are used to generate surrogate models of the objective function with respect to cross-section properties. The stacking sequence corresponding to the optimal cross-section is found using a real-coded genetic algorithm. Ply angle discretisation of 1 degrees, 15 degrees, 30 degrees and 45 degrees are used. The mean value of the objective function is used to find the optimal blade designs and the resulting designs are tested for variance. The optimal designs show a vibration reduction of 26% to 33% from the baseline design. A substantial reduction in vibration and an aeroelastically stable blade is obtained even after accounting for composite material uncertainty.

QCD mini-jets contribution to the total cross-section for pions and protons and expectations at LHC

We describe our kt-resummation model for total cross-sections and show its application to pp and ¯pp scattering. The model uses mini-jets to drive the rise of the cross-section and soft gluon resummation in the infrared region to transform the violent rise of the mini-jet cross-section into a logarithmic behaviour in agreement with the Froissart bound.

Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.

Controlling the cross-section of waveguides inscribed on bulk chalcogenide glasses using fast laser

Waveguides have been fabricated on melt-quenched, bulk chalcogenide glasses using the femto-second laser inscription technique at low repetition rates in the single scan regime. The inscribed waveguides have been characterized by butt-coupling method and the diameter of the waveguide calculated using the mode-field image of the waveguide. The waveguide cross-section symmetry is analyzed using the heat diffusion model by relating the energy and translation speed of the laser. The net-fluence and symmetry of the waveguides are correlated based on the theoretical values and experimental results of guiding cross-section.

Cross-section fluctuations in open microwave billiards and quantum graphs: The counting-of-maxima method revisited

The fluctuations exhibited by the cross sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Gamma(corr) of the cross-section correlation function. Brink and Stephen Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as a function of the parameter under consideration. They stated that the product of the average number of maxima per unit energy range and Gamma(corr) is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances.

Pulsatile flow in tubes of varying cross-sections

The pulsatile flow of an incompressible viscous fluid in a cylindrical tube of varying cross section is investigated for small Reynolds numbers. The solutions consist of a stedy and an oscillatory part. The shear stress distribution on the wall is evaluated and discussed in detail for special geometries like tapered tubes, locally constricted tubes and peristaltic tubes. The existence of separation in the flow field is noticed.

QCD and total cross-sections : photons and hadrons

In this contribution, we discuss a total cross-section model which can be applied to both photon and purely hadronic processes. We find that the model can reproduce photo-production cross-sections, as well as extrapolation of gamma*p processes to gamma p using Vector Meson Dominance models, with minimal modifications from the proton case.

QCD and total cross-sections : photons and hadrons

In this contribution, we discuss a total cross-section model which can be applied to both photon and purely hadronic processes. We find that the model can reproduce photo-production cross-sections, as well as extrapolation of gamma*p processes to gamma p using Vector Meson Dominance models, with minimal modifications from the proton case.

Steady flow of couple stress fluid through tubes of slowly varying cross-sections--application to blood flows

Steady laminar flow of a non-Newtonian fluid based on couple stress fluid theory, through narrow tubes of varying cross-sections has been studied theoretically. Asymptotic solutions are obtained for the basic equations and the expressions for the velocity field and the wall shear stress are derived for a general cross-section. Computation and discussions are carried out for the geometries which occur in the context of physiological flows or in particular blood flows. The tapered tubes and constricted tubes are of special importance. It is observed that increase in certain parameters results in erratic flow behaviour proximal to the constricted areas which is further enhanced by the increase in the geometric parameters. This elucidates the implications of the flow in the development of vascular lesions.

Minijets,soft gluon resummation and photon cross-sections

We compare the high energy behaviour of hadronic photon-photon cross-sections in different models. We find that the photon-photon cross-section appears to rise faster than the purely hadronic ones (proton-proton and proton-antiproton).

Zero momentum gluons and the total pp and pbarp cross-sections

We describe a QCD motivated model for total cross-sections which uses the eikonal representation and incorporates QCD mini-jets to drive the rise with energy of the cross-section, while the impact parameter distribution is obtained through the Fourier transform of the transverse momentum distribution of soft gluons emitted in the parton-parton interactions giving rise to mini-jets in the final state. A singular but integral expression for the running coupling constant in the infrared region is part of this model.