On the theory of complex rays

The article surveys the application of complex-ray theory to the scalar Helmholtz equation in two dimensions. The first objective is to motivate a framework within which complex rays may be used to make predictions about wavefields in a wide variety of geometrical configurations. A crucial ingredient in this framework is the role played by Sp{} in determining the regions of existence of complex rays. The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the many characterizations of Stokes surfaces, including the adaptation and application of recent developments in exponential asymptotics to the complex Wentzel--Kramers--Brilbuin expansion of these wavefields

Downsizing assessment of automotive Stirling engines

A 67 kW (90 hp) Stirling engine design, sized for use in a 1984 1440 kg (3170 lb) automobile was the focal point for developing automotive Stirling engine technology. Since recent trends are towards lighter vehicles, an assessment was made of the applicability of the Stirling technology being developed for smaller, lower power engines. Using both the Philips scaling laws and a Lewis Research Center (Lewis) Stirling engine performance code, dimensional and performance characteristics were determined for a 26 kW (35 hp) and a 37 kW (50 hp) engine for use in a nominal 907 kg (2000 lb) vehicle. Key engine elements were sized and stressed and mechanical layouts were made to ensure mechanical fit and integrity of the engines. Fuel economy estimates indicated that the Stirling engine would maintain a 30 to 45 percent fuel economy advantage comparable spark ignition and diesel powered vehicles in the 1984 period

Asymptotic solutions of the Helmholtz equation: generalised Friedlander-Keller ray expansions of fractional order

Applications of a WKBJ-type `ray ansatz' to obtain asymptotic solutions of the Helmholtz equation in the high{frequency limit are now standard, and underpin the construction of `geometrical optics' ray diagrams in many electromagnetic, acoustic and elastic reflection, transmission and other scattering problems. These applications were subsequently extended by Keller to include other types of rays - called `diffracted' rays - to provide an accessible and impressively accurate theory which is relevant in wide-ranging sets of circumstances. Friedlander and Keller then introduced a modified ray ansatz to extend yet further the scope of ray theory and its applicability to certain other classes of diffraction problems (tangential ray incidence upon an obstructing boundary, for instance), and did so by the inclusion of an extra term proportional to a power of the wavenumber within the exponent of the initial ansatz. Our purpose here is to generalise this further still by the inclusion of several such terms, ordered in a natural sequence in terms of strategically-chosen fractional powers of the large wavenumber, and to derive a systematic sequence of boundary value problems for the coefficient phase functions that arise within this generalised exponent, as well as one for the leading-order amplitude occurring as a pre-exponential factor. One particular choice of fractional power is considered in detail, and waves with specified radially-symmetric or planar wavefronts are then analysed, along with a boundary value problem typifying two-dimensional radiation whereby arbitrary phase and amplitude variations are specified on a prescribed boundary curve. This theory is then applied to the scattering of plane and cylindrical waves at curved boundaries with small-scale perturbations to their underlying profile

Stokes phenomenon and matched asymptotic expansions

This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes multipliers explicitly depend on the behaviour of the coefficients of the relevant asymptotic expansions

The SISO CSPI PDG standard for commercial off-the-shelf simulation package interoperability reference models

For many years discrete-event simulation has been used to analyze production and logistics problems in manufactur-ing and defense. Commercial-off-the-shelf Simulation Packages (CSPs), visual interactive modelling environ-ments such as Arena, Anylogic, Flexsim, Simul8, Witness, etc., support the development, experimentation and visua-lization of simulation models. There have been various attempts to create distributed simulations with these CSPs and their tools, some with the High Level Architecture (HLA). These are complex and it is quite difficult to assess how a set of models/CSP are actually interoperating. As the first in a series of standards aimed at standardizing how the HLA is used to support CSP distributed simula-tions, the Simulation Interoperability Standards Organiza-tion’s (SISO) CSP Interoperability Product Development Group (CSPI PDG) has developed and standardized a set of Interoperability Reference Models (IRM) that are in-tended to clearly identify the interoperability capabilities of CSP distributed simulations

Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions

The standard approach to applying ray theory to solving Maxwell’s equations in the large wave-number limit involves seeking solutions that have (i) an oscillatory exponential with a phase term that is linear in the wave-number and (ii) has an amplitude profile expressed in terms of inverse powers of that wave-number. The Friedlander–Keller modification includes an additional power of this wave-number in the phase of the wave structure, and this additional term is crucial when analysing certain wave phenomena such as creeping and whispering gallery wave propagation. However, other wave phenomena necessitate a generalisation of this theory. The purposes of this paper are to provide a ‘generalised’ Friedlander–Keller ray ansatz for Maxwell’s equations to obtain a new set of field equations for the various phase terms and amplitude of the wave structure; these are then solved subject to boundary data conforming to wave-fronts that are either specified or general. These examples specifically require this generalisation as they are not amenable to classic ray theory

Asymptotics of near-cloaking

This paper describes how asymptotic analysis can be used to gain new insights into the theory of cloaking of spherical and cylindrical targets within the context of acoustic waves in a class of linear elastic materials. In certain cases these configurations allow solutions to be written down in terms of eigenfunction expansions from which high-frequency asymptotics can be extracted systematically. These asymptotics are compared with the predictions of ray theory and are used to describe the scattering that occurs when perfect cloaking models are regularised

Semiclassical transmission across transition states

It is shown that the probability of quantum-mechanical transmission across a phase space bottleneck can be compactly approximated using an operator derived from a complex Poincar\'e return map. This result uniformly incorporates tunnelling effects with classically-allowed transmission and generalises a result previously derived for a classically small region of phase space.Comment: To appear in Nonlinearit

Problem gambling: a suitable case for social work?

Problem gambling attracts little attention from health and social care agencies in the UK. Prevalence surveys suggest that 0.6% of the population are problem gamblers and it is suggested that for each of these individuals, 10–17 other people, including children and other family members, are affected. Problem gambling is linked to many individual and social problems including: depression, suicide, significant debt, bankruptcy, family conflict, domestic violence, neglect and maltreatment of children and offending. This makes the issue central to social work territory. Yet, the training of social workers in the UK has consistently neglected issues of addictive behaviour. Whilst some attention has been paid in recent years to substance abuse issues, there has remained a silence in relation to gambling problems. Social workers provide more help for problems relating to addictions than other helping professions. There is good evidence that treatment, and early intervention for gambling problems, including psycho-social and public health approaches, can be very effective. This paper argues that problem gambling should be moved onto the radar of the social work profession, via inclusion on qualifying and post-qualifying training programmes and via research and dissemination of good practice via institutions such as the Social Care Institute for Excellence (SCIE). Keywords: problem gambling; addictive behaviour; socia