A. Rawlins - Academia.edu (original) (raw)

Papers by A. Rawlins

IEEE Transactions on Antennas and Propagation

$Research paper thumbnail of Plane-Wave Diffraction by a Rational Wedge$

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1987

In this paper, new expressions for the acoustic field produced when a plane-wave source of sound ... more In this paper, new expressions for the acoustic field produced when a plane-wave source of sound is diffracted by a soft, hard or mixed soft-hard wedge whose angle can be expressed as a rational multiple of π are given. The solution is expressed in terms of geometrical acoustic source terms and real integrals that represent the diffracted field. The expressions are in a form that allows easy calculation of the acoustic field. Uniformly valid expressions for the far field are also given for all values of the angular variable. The general result obtained includes, as special cases, Sommerfeld’s solution for diffraction by a half-plane, Reiche’s result for the diffraction by a right-angled wedge, and a new representation for the solution of the problem of diffraction by a mixed soft-hard half-plane.

$Research paper thumbnail of Diffraction of sound by a rigid screen with an absorbent edge$

Journal of Sound and Vibration, 1976

$Research paper thumbnail of The Edge Field Behaviour for the Problem of the Diffraction of a Line Source by a Soft/Hard Half Plane$

ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 1983

ABSTRACT Mathematische Bedingungen für partielle Differentialgleichungen zeigen, daß Reissnersche... more ABSTRACT Mathematische Bedingungen für partielle Differentialgleichungen zeigen, daß Reissnersche Plattenaufgaben nicht für jedes Belastungselement p(x)∈L 2 (ω) (ω : Plattenbereich) eindeutig lösbar sind [(*) der Autor, Teil I., ibid. 62, T172-T175 (1982; Zbl 0505.73035)]. In diesem Artikel wird dem in (*) diskutierten Effekt aus mechanischer Sicht nachgegangen: Als Modellproblem dient eine quadratische, längs der Berandung ∂ω gelenkig gelagerte, d.h.: (1) w(x̠)=0; M nn (x ̲)=0; M nt (x ̲)=0 ∀x ̲∈∂ω Reissnerplatte, die - im Gegensatz zu (*) - mit dem allseits bekannten Schäferschen Formelsatz beschrieben wird. Die Betrachtungen legen dar, in welcher Weise das Randbedingungssystem (1) für die Bedingungen aus (*) verletzende p(x) unzureichend wird.

The Quarterly Journal of Mechanics and Applied Mathematics, 2010

In this paper we deal with integrals whose integrand has a rapidly oscillating zeroorder Bessel f... more In this paper we deal with integrals whose integrand has a rapidly oscillating zeroorder Bessel function of the first kind with real parameters in its argument which can become large. We introduce and tabulate model integrals which depend on a single parameter, which can determine the behavior of the original integral near the zeros of the argument of the Bessel function. As an example of the uniform asymptotic analysis, we evaluate the multi-parameter integral which arises in the solution of the transition problem for an accelerating moving load on an elastically supported infinite string. Asymptotic predictions are compared with the results obtained by direct numerical integration.

$Research paper thumbnail of Grazing wave diffraction by a PEC or PMC rectangular cylinder$

2013 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2013

SIAM Journal on Mathematical Analysis, 1978

SIAM Journal on Applied Mathematics, 1986

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears... more Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.

The Quarterly Journal of Mechanics and Applied Mathematics, 2011

Motion camouflage is a pursuit strategy whereby a predator moves towards a prey while appearing s... more Motion 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.

$Research paper thumbnail of Cylindrical-Wave Diffraction by a Rational Wedge$

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1987

In this paper, new expressions for the field produced by the diffraction of a cylindrical wave by... more In this paper, new expressions for the field produced by the diffraction of a cylindrical wave by a wedge, whose angle can be expressed as a rational multiple of π, are given. The solutions are expressed in terms of source terms and real integrals that represent the diffracted field. The general result obtained includes as special cases, Macdonald’s solution for diffraction by a half plane, a solution for Carslaw’s problem of diffraction by a wedge of open angle 2/3π, and a new representation for the solution of the problem of diffraction by a mixed soft-hard half plane.

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1978

SynopsisThis paper proves some inequalities for the imaginary part of the transcendental function... more SynopsisThis paper proves some inequalities for the imaginary part of the transcendental function in a simply connected sector of the complex z-plane, where 0 < v < 1, and part of the boundary depends on v. These inequalities arose in a work of Everitt and Jones [1] which was on a general integral inequality. We give an alternative method of proving these Bessel function inequalities.

Journal of Sound and Vibration, 1983

The acoustic field of a spherical sound wave reflected from a locally reacting plane surface is e... more The acoustic field of a spherical sound wave reflected from a locally reacting plane surface is expressed as an asymptotic expansion whose terms consist of the product of Legendre polynomials and powers of the reciprocal of the distance from the image source.

Canadian Journal of Physics, 1980

In Noble's book The Wiener Hopf Technique, Pergamon, 1958, he considers the coupled system of... more In Noble's book The Wiener Hopf Technique, Pergamon, 1958, he considers the coupled system of Wiener–Hopf equations (§4.4, pp. 153–154)[Formula: see text]He shows that provided the functions L(α), M(α), Q(α), and R(α) have only simple pole singularities the solution can be reduced to two sets of infinite simultaneous linear algebraic equations. In this article a different approach is used which gives the solution in the form of a Fredholm integral equation of the second kind. This Fredholm integral equation can be reduced to infinite sets of simultaneous linear algebraic equations under the less restrictive conditions that either (i) L(α)/M(α) has no branch points in the lower α-half plane: Im(α) τ−. In the special case considered by Noble if L(α)/M(α) (or Q(α)/R(α)) only have simple poles in the lower (upper) half plane then the Fredholm integral equation reduces to one infinite set of simultaneous equations. This extends the Wiener–Hopf technique to yet a larger class of boun...

In spite of the fact that the system of equations (3)-(5) is unstable, it might still be possible... more In spite of the fact that the system of equations (3)-(5) is unstable, it might still be possible to utilize these results in a short duration impact because instabilities take time to grow. It is conceivable that a scheme could be devised in which the growth rate of the dependent variables are as slow as possible, i.e., make the positive real part of the characteristic root as small as possible so that its effects in a short duration impact are negligible.