Axisymmetric Radiation from a Finite Gap in an Infinite, Rigid, Circular Duct

The axisymmetric radiation of sound from a finite gap in anotherwise infinite rigid, hollow, cylindrical duct is examinedusing a method which, whilst equivalent to, has several advantagesover the modified Wiener-Hopf technique. The total sound fieldis expressed as the sum of that for a semi-infinite duct (whichis known exactly) plus two interaction potentials (which mustbe determined). In this way the problem is reformulated as twocoupled Wiener-Hopf-type problems which are then solved forthe unknown interaction potentials. Asymptotic results are presentedfor the case when the separation distance between the duct edgesis large.     

Scattering of fluid loaded elastic plate waves at the vertex of a wedge of arbitrary angle, I: analytic solution

This article is the first part of an investigation into thescattering of fluid coupled structural waves by an angular discontinuityat the junction of two plates of different material properties.These two thin elastic plates are semi-infinite in extent thereforeforming the faces of an infinite wedge, the interior of whichcontains a compressible fluid. A plane unattenuated structuralwave is incident along the lower face of the wedge and is scatteredat the apex. The edges of the elastic plates may be joined ina variety of different ways, for example, they may be pin-jointedto an external structure or welded to each other. In the formercase, the plates will experience only the usual flexural vibrationswhereas in the latter case longitudinal (in-plane) disturbanceswill be generated and will propagate away from the wedge apex. An exact explicit solution is sought in terms of a Sommerfeldintegral representation for the fluid velocity potential. Thispermits the boundary-value problem to be recast as a functionaldifference equation which is easily solved in terms of the Maliuzhinetsspecial function (Maliuzhinets, Soviet Phys. Dokl. 3 1958).The chosen ansatz for the solution is of a different form fromthat used previously by the authors for the less complicatedmembrane wedge problem. The new ansatz has several analyticand numerical advantages which enable the reflection and transmissioncoefficients to be expressed explicitly in a compact form thatis ideal for computation. In the second part of this study a full numerical investigationof the reflection and transmission coefficients will be presentedfor a variety of interesting parameter ranges and edge conditions.     

A METHOD FOR SIMPLIFYING LARGE ECOSYSTEM MODELS

Abstract Simplifying large ecosystem models is essential if we are to understand the underlying causes of observed behaviors. However, such understanding is often employed to achieve simplification. This paper introduces two model simplification methods that can be applied without requiring intimate prior knowledge of the system. Their utility is measured by the resulting values of given model diagnostics relative to those of the large model. The first method is a simple automated procedure for nondimensionalizing large ecosystem models, which identifies and eliminates terms that have little effect on model diagnostics. Some of its limitations are then addressed by the rate elimination method, which measures the relative importance of model terms using least‐squares regression. The methods are applied to a model of the nitrogen cycle in Port Phillip Bay, Victoria, Australia. The rate elimination method provided more insights into the causal relationships built into the model than the nondimensionalizing method. It also allowed the reduction of the model's dimension. Thus it is a useful first step in model simplification.