An asymptotic membrane-like theory for long-wave motion in a pre-stressed elastic plate

An asymptotically consistent two-dimensional theory is developed to help elucidate dynamic response in finitely deformed layers. The layers are composed of incompressible elastic material, with the theory appropriate for long-wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function. Leading-order and refined higher-order equations for the mid-surface deflection are derived. In the case of zero normal initial static stress and in-plane tension, the leading-order equation reduces to the classical membrane equation, with its refined counterpart also being obtained. The theory is applied to a one-dimensional edge loading problem for a semi-infinite plate. In doing so, the leading- and higher-order governing equations are used as inner and outer asymptotic expansions, the latter valid within the vicinity of the associated quasi-front. A solution is derived by using the method of matched asymptotic expansions

Products Liability, Consumer Misperceptions, and Market Power

This paper compares alternative liability rules for allocating losses from defective products when consumers under- estimate these losses and producers may have some market power. If producers do not have any market power, the rule of strict liability .leads to both the first-best accident probability and industry output. If producers do have some market power, strict liability still leads to the first-best accident probability, but there will now be too little output of the industry. It is shown that if market power is sufficiently large, a negligence rule is preferable. Under this rule, firms can still be induced to choose the first-best accident probability, but now the remaining damages are borne by consumers. Since consumers underestimate these damages, they buy more than under strict liability. However, there is a limit to how much the negligence rule can encourage extra consumption. It is shown that if market power is sufficiently large, the rule of no liability may then be preferred to the negligence rule. Without any liability imposed, producers will not choose the first-best accident probability. However, this may be more than compensated for by the increased output of the industry.

Non-principal surface waves in deformed incompressible materials

The Stroh formalism is applied to the analysis of infinitesimal surface wave propagation in a statically, finitely and homogeneously deformed isotropic half-space. The free surface is assumed to coincide with one of the principal planes of the primary strain, but a propagating surface wave is not restricted to a principal direction. A variant of Taziev’s technique [R.M. Taziev, Dispersion relation for acoustic waves in an anisotropic elastic half-space, Sov. Phys. Acoust. 35 (1989) 535–538] is used to obtain an explicit expression of the secular equation for the surface wave speed, which possesses no restrictions on the form of the strain energy function. Albeit powerful, this method does not produce a unique solution and additional checks are necessary. However, a class of materials is presented for which an exact secular equation for the surface wave speed can be formulated. This class includes the well-known Mooney–Rivlin model. The main results are illustrated with several numerical examples

Holographic mensuration of suspended particles in aquatic systems

The distribution and dynamics of aggregates in the aquatic environment play an important role in the modelling of biogeochemical processes. Previous work on aggregates in the ocean (e.g. sedimentary 'marine snow' particles), which vary in size from tens of microns to several millimetres, has used electronic counting or conventional photography coupled with image analysis. Here we describe a non-destructive in situ approach by use of holographic mensuration, hologrammetry, that affords greater scope and higher accuracy for the enumeration, sizing, and spatial distribution determination of aggregate particles. By means of two complimentary techniques, in-line and offaxis transmission holography, we present the initial experiments conducted in our laboratory and discuss the preliminaiy results from real image analysis

Off-axis transmission holographic system for recording aquatic particles

We describe a holographic system for recording particles suspended in water. The hologram plate is located in air, separated from the test tank by an air/glass/water boundary. The holographic emulsion is therefore unaffected by adverse aquatic conditions within the tank (i.e. surface contamination, non-uniform swelling). The design geometry is intended to minimise the aberrations that arise from recording subjects located in water and replaying their hologram image in air. Third order aberrations, most crucially spherical aberration and astigmatism, are suppressed to give an experimental resolution of 7 lp/mm using USAF 1951 target in water 600mm from the boundary. Particles (plankton species) in the sub-millimeter to several millimeters size range are observed at planar sections within the recording volume by visual inspection of the hologram replayed in real image mode

In situ off-axis holography of marine plankton

We present an off-axis transmission holographic technique for recording marine plankton in situ within a test tank of 36,000 ml with a pulsed laser in a 40 ns interval. The holographic plate is located in air and is therefore unaffected by aquatic conditions that may cause emulsion degradation (e.g. non-uniform swelling and surface contamination). The reference beam traverses a path in air only, and thus remains unaffected by dense concentrations of plankton. Third order aberrations, notably spherical aberration and astigmatism, are suppressed to yield an experimental resolution of 7 lp/mm (70 micrometres) with a USAF 1951 target located 600 mm in water from the observation window. Plankton particle counts examined by real image reconstruction show a strong correlation with duplicate samples examined under a microscope

A shallow-water model for hydraulically transcritical flows

This document describes a numerical model that was developed to study two-dimensional, reduced-gravity, shallow-water flows. When the dynamics of these flows is strongly nonlinear, the flow may become hydraulically supercritical and discontinuities in the flow field may arise. The presence of discontinuities in the flow field requires a special numerical treatment in order to maintain both accuracy and stability in the numerically-approximated solution. In this model, a shock-capturing scheme called the Essentially Non-Oscillatory (ENO) scheme is implemented. The ENO scheme is a high-order, adaptive-stencil, finite-difference, characteristic-based scheme for hyperbolic equations that has been applied widely to flows governed by the Euler equations of gas dynamics. The model described in this document was developed for geophysical applications, and therefore includes the effects of rotation (constant Coriolis parameter), forcing (time dependent and/or spatially varying), and bottom drag (linear or nonlinear). The presentation includes the mathematical formulation of the model as well as instructions on how to prepare and execute model runs.Funding was provided by the Office of Naval Research under Grant Number N00014-93-1-1369

Managing storm water flow in the Neridup Creek catchment

The Department of Agriculture and Food, Western Australia (DAFWA) was commissioned by the Esperance Regional Forum to investigate opportunities for managing storm flow, erosion and sedimentation in large storm events through Neridup Creek catchment. This report details the findings of the investigation and also provides some recommendations for managing farm-scale drainage issues and catchment water flow