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.

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

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

Were rivers flowing across the Sahara during the last interglacial? Implications for human migration through Africa.

Human migration north through Africa is contentious. This paper uses a novel palaeohydrological and hydraulic modelling approach to test the hypothesis that under wetter climates c.100,000 years ago major river systems ran north across the Sahara to the Mediterranean, creating viable migration routes. We confirm that three of these now buried palaeo river systems could have been active at the key time of human migration across the Sahara. Unexpectedly, it is the most western of these three rivers, the Irharhar river, that represents the most likely route for human migration. The Irharhar river flows directly south to north, uniquely linking the mountain areas experiencing monsoon climates at these times to temperate Mediterranean environments where food and resources would have been abundant. The findings have major implications for our understanding of how humans migrated north through Africa, for the first time providing a quantitative perspective on the probabilities that these routes were viable for human habitation at these times

Microbiological indicators of water quality in submerged karst caves of Wakulla Springs

22 slides in Powerpoint presentation

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

Abnormal long wave dispersion phenomena in a slightly compressible elastic plate with non-classical boundary conditions

A two parameter asymptotic analysis is employed to investigate some unusual long wave dispersion phenomena in respect of symmetric motion in a nearly incompressible elastic plate. The plate is not subject to the usual classical traction free boundary conditions, but rather has its faces fixed, precluding any displacement on the boundary. The abnormal long wave behaviour results in the derivation of non-local approximations for symmetric motion, giving frequency as a function of wave number. Motivated by these approximations, the asymptotic forms of displacement components established and long wave asymptotic integration is carried out