Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions

We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce incident plane waves and measure the far field pattern of the resulting scattered field only in a finite set of directions. In this context, we say that a wavenumber is a non-scattering wavenumber if the associated relative scattering matrix has a non trivial kernel. Under certain assumptions on the physical coefficients of the inclusion, we show that the non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a second step, for a given real wavenumber and a given domain D, we present a constructive technique to prove that there exist inclusions supported in D for which the corresponding relative scattering matrix is null. These inclusions have the important property to be impossible to detect from far field measurements. The approach leads to a numerical algorithm which is described at the end of the paper and which allows to provide examples of (approximated) invisible inclusions.Comment: 20 pages, 7 figure

Micromechanical response of fibre-reinforced materials using the boundary element technique

The Boundary Element Method (BEM) and the Embedded Cell Approach (ECA) have been used to analyse the effects of constituent material properties and fibre spatial distribution on the localised behaviour of a transversely loaded, unidirectional fibre-reinforced composite. The geometrical structures examined were perfectly periodic, uniformly spaced fibre arrangements in square and hexagonal embedded cells and ten cells in which 60 fibres were randomly placed within the matrix. The models involve both elastic fibres and matrix, with the interfaces between the different phases being fully bonded. The results indicate that both the fibre packing and the material properties of the constituent phases have a significant effect on the overall stress distribution and the magnitude of localised stress concentrations within a composite. Non-periodic arrangements give rise to higher local stresses, and the magnitudes of these stress concentrations have a strong dependence on the ligament length (distance between the two neighbouring fibres that have a common high-stress region), and to a lesser extent on the angle relative to the applied load (angle between a plane containing the two fibre centres and the applied load). Furthermore, analysis of a three-phase composite, comprised of a mixture of both stiff and compliant fibres, had higher stress concentrations than the equivalent two-phase composites

Effects of dietary inclusions of oilseed meals on physical characteristics and feed intake of diets for the Nile Tilapia, Oreochromis niloticus

The present study investigated the effects of the inclusion of three oilseed by-products (soybean, copra and palm kernel meals) on some physical characteristics of pelletized feeds as well as on voluntary feed intake and faecal matter production by the Nile tilapia, Oreochromis niloticus. The dietary inclusion of soybean meal resulted in a significantly higher feed bulk density relative to the fishmeal control diet. The inclusions of copra and palm kernel meals, however, resulted in lower feed bulk densities. Sinking rates, water stabilities and nutrient retention efficiencies of feed pellets were directly related to feed bulk densities. The soybean meal diet had the fastest sinking velocities, greatest water stability and highest nutrient retention rates. The dietary inclusion of soybean meal, however, significantly impaired feed intake compared to the other three diets. Mean daily feed intakes of the control, palm kernel meal and copra meal diets corresponded to 28.88, 27.01 and 28.31 g during the experimental period and varied significantly from the mean daily intake of the soybean meal diet which corresponded to 20.01 g. Faecal matter production (g dry mass kg−1 ingested feed) was significantly higher in the tilapia groups fed the copra and palm kernel meals. The results obtained from this study show that 30% inclusions of unrefined forms of copra and palm kernel meal in Nile tilapia diets is possible, without adversely affecting feed intake or pellet nutrient losses prior to ingestion