A bifurcated circular waveguide problem

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version A D Rawlins. A bifurcated circular waveguide problem. J.I.M.A. 54 (1995) 59-81. Oxford University press is available online at: http://imamat.oxfordjournals.org/cgi/reprint/54/1/59.pdfA rigorous and exact solution is obtained for the problem of the radiation of sound from a semi-infinite rigid duct inserted axially into a larger acoustically lined tube of infinite length. The solution to this problem is obtained by the Wiener-Hopf technique. The transmission and reflection coefficients, when the fundamental mode propagates in the semi-infinite tube, are obtained. The present results could be of use for exhaust design, and as a possible instrument for impedance measurement

A note on Wiener-Hopf matrix factorisation

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Quarterly Journal of Mechanics and Applied Mathematics following peer review. The definitive publisher-authenticated version Rawlins, A D (1985). A note on Wiener-Hopf matrix factorisation. Quarterly Journal of Mechanics and Applied Mathematics. 38 (3) 433-437 is available online at: http://qjmam.oxfordjournals.org/cgi/reprint/38/3/433.pdfIn this paper the most general class of 2 x 2 matrices is determined which permit a Wiener-Hopf factorization by the procedure of Rawlins and Williams (1). According to this procedure, the factorization problem is reduced to a matrix Hilbert problem on a half-line, where the matrix involved in the Hilbert problem is required to have zero diagonal elements

The optimum orientation of an absorbing barrier

In the following work, we solve the problem of the best orientation of a rigid noise barrier, which has one face lined with absorbent material, between a noise source and a receiver point in the shadow region of the barrier. By the ‘best orientation’, we mean that positioning of the barrier which yields the least noise level at the receiving point for a given barrier and source position

Approximate boundary conditions for diffraction by thin transmissive media

The object of this note is to describe a method that can be used to obtain useful boundary conditions to model various situations that arise in diffraction theory. In particular when wanting to apply the Wiener-Hopf technique to diffraction problems that involve thin transmissive media. Transmissive here means that the thin layer medium suffers a change in the physical quantities of density, acoustic velocity, and wave number from the surrounding medium. The present approach can be used to obtain approximate boundary conditions for other physical applications where thin strata of transmissive material arise

The method of finite-product extraction and an application to Wiener-Hopf theory

Copyright @ The Author, 2011. The publisher version of the article can be accessed at the link below.In this work we describe a simple method for finding approximate representations for special functions which are entire transcendental functions that can be represented by infinite products. This method replaces the infinite product by a finite polynomial and Gamma functions. This approximate representation is shown in the case of Bessel functions to be very accurate over a large range of parameter values. These approximate expressions can be useful for finding the roots of a transcendental equation and the Wiener-Hopf factorization of functions involving such Bessel functions.The method is shown to be potentially useful for other transcendental andWiener-Hopf problems, which involve other entire functions that have infinite product representations

On the roots of a Bessel function equation (problem)

For the abstract of this paper, please see the PDF file

A Green's function for diffraction by a rational wedge

In this paper we derive an expression for the point source Green's function for the reduced wave equation, valid in an angular sector whose angle is equal to a rational multiple of 77. This Green's function can be used to find new expressions for the field produced by the diffraction of a spherical wave by a wedge whose angle can be expressed as a rational multiple of n. The expressions obtained will be in the form of source terms and real integrals representing the diffracted field. The general result obtained is used to derive a new representation for the solution of the problem of diffraction by a mixed hard-soft half plane

A note on point source diffraction by a wedge

The object of this paper is to give new expressions for the wave field produced when a time harmonic point source is diffracted by a wedge with Dirichlet or Neumann boundary conditions on its faces. The representation of the total field is expressed in terms of quadratures of elementary functions, rather than Bessel functions, which is usual in the literature. An analogous expression is given for the three-dimensional free-space Green's function

High-frequency diffraction of an electromagnetic plane wave by an imperfectly conducting rectangular cylinder at grazing incidence

We derive new results for the electromagnetic scattered far wave field produced when a high-frequency plane E-polarized wave is at grazing incidence on an imperfectly conducting rectangular cylinder. The solution to the problem is obtained by using the geometrical theory of diffraction, multiple diffraction methods, the canonical solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with a novel analytic approach

A note on a camouflage pursuit problem

The version available is a preprint of the full and final published article which is accessible at the link below.Copyright © The author 2010. Published by Oxford University Press; all rights reserved. For Permissions, please email: [email protected] camouflage is a pursuit strategy whereby a predator moves towards a prey while appearing stationary to the prey except for the change in its perceived cross section as it approaches. If the effect of cross section size with distance is ignored then this means that the target is unable to discern that the aggressor is moving. The aggressor appears to be at its initial position or is camouflaged by a stationary object in the background. We shall derive a closed form solution to the problem of camouflage pursuit for a particular situation. Although general differential equations have already been derived for this strategy they have not been solved in closed form