Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Different mineralization styles in a volcanic-hosted ore deposit: the fluid and isotopic signatures of the Mt Morgan Au-Cu deposit, Australia

Quantitative laser ablation (LA)-ICP-MS analyses of fluid inclusions, trace element chemistry of sulfides, stable isotope (S), and Pb isotopes have been used to discriminate the formation of two contrasting mineralization styles and to evaluate the origin of the Cu and Au at Mt Morgan. The Mt Morgan Au-Cu deposit is hosted by Devonian felsic volcanic rocks that have been intruded by multiple phases of the Mt Morgan Tonalite, a low-K, low-Al2O3 tonalite-trondhjemite-dacite (TTD) complex. An early, barren massive sulfide mineralization with stringer veins is conforming to VHMS sub-seafloor replacement processes, whereas the high-grade Au-Cu. ore is associated with a later quartz-chalcopyrite-pyrite stock work mineralization that is related to intrusive phases of the Tonalite complex. LA-ICP-MS fluid inclusion analyses reveal high As (avg. 8850 ppm) and Sb (avg. 140 ppm) for the Au-Cu mineralization and 5 to 10 times higher Cu concentration than in the fluids associated with the massive pyrite mineralization. Overall, the hydrothermal system of Mt Morgan is characterized by low average fluid salinities in both mineralization styles (45-80% seawater salinity) and temperatures of 210 to 270 degreesC estimated from fluid inclusions. Laser Raman Spectroscopic analysis indicates a consistent and uniform array Of CO2-bearing fluids. Comparison with active submarine hydrothermal vents shows an enrichment of the Mt Morgan fluids in base metals. Therefore, a seawater-dominated fluid is assumed for the barren massive sulfide mineralization, whereas magmatic volatile contributions are implied for the intrusive related mineralization. Condensation of magmatic vapor into a seawater-dominated environment explains the CO2 occurrence, the low salinities, and the enriched base and precious metal fluid composition that is associated with the Au-Cu. mineralization. The sulfur isotope signature of pyrite and chalcopyrite is composed of fractionated Devonian seawater and oxidized magmatic fluids or remobilized sulfur from existing sulfides. Pb isotopes indicate that Au and Cu. originated from the Mt Morgan intrusions and a particular volcanic strata that shows elevated Cu background. (C) 2002 Elsevier Science B.V. All rights reserved.

Effect of ethylene vinyl acetate (EVA) closed cell foam on transmitted forces in mouthguard material

Objectives: To compare transmitted forces through ethylene vinyl acetate (EVA) mouthguard material and the same EVA material with gas inclusions in the form of a closed cell foam. Method: EVA mouthguard materials with and without foam gas inclusions and 4 mm thick were impacted with a constant force from an impact pendulum. Various porosity levels in the foam materials were produced by 1%, 5%, and 10% by weight foaming agent. The forces transmitted through the EVA after energy absorption by the test materials were measured with a force sensor and compared. Results: Only minor non-significant differences in transmitted forces through the EVA with and without foam were shown. Conclusions: The inclusion of gas in the form of a closed cell foam in 4 mm thick EVA mouthguard materials did not improve the impact performance of the EVA mouthguard material.

Simulation of the load-unload response ratio and critical sensitivity in the lattice solid model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.

On the intrinsic capacity for increase of Australian flying-foxes (Pteropus spp., Megachiroptera)

In the reproductive biology of organisms, a continuum exists from "highly reproductive species" at one end to "survivor species" at the other end. Among other factors, the position of a species along this continuum affects its sensitivity to human exploitation and its vulnerability to extinction. Flying foxes are long-lived, seasonal breeders, with a rigid, well-defined breeding season that is largely or wholly genetically determined. Unlike opportunistic, highly reproductive species, such as rabbits or mice, female flying foxes are unable to produce viable young before their second or third year of life, and are then capable of producing just one young per year. Such a breeding strategy will be successful only if flying-foxes are long-lived and suffer naturally low mortality rates. In this paper, we assess the vulnerability of flying foxes to extinction, using basic parameters of reproduction observed in the wild, and in captive breeding colonies of P. poliocephalus, P. alecto and P. scapulatus, and survival rates that are likely to apply to Australian conditions. Our models show explicitly that flying-fox populations have a very low capacity for increase, even under the most ideal conditions. The implications of our models are discussed in reference to the long-term management and conservation needs of Australian flying foxes. We conclude that current death-rates of flying-foxes in NSW and Queensland fruit orchards are putting state populations at serious risk.

Leaf water relations of Eucalyptus cloeziana and Eucalyptus argophloia in response to water deficit

Leaf water relations responses to limited water supply were determined in 7-month-old plants of a dry inland provenance of Eucalyptus argophloia Blakely and in a humid coastal provenance (Gympie) and a dry inland provenance (Hungry Hills) of Eucalyptus cloeziana F. Muell. Each provenance of E. cloeziana exhibited a lower relative water content at the turgor loss point, a lower apoplastic water content, a smaller ratio of dry mass to turgid mass and a lower bulk modulus of elasticity than the single provenance of E. argophloia. Osmotic potential at full turgor and water potential at the turgor loss point were significantly lower in E. argophloia and the inland provenance of E. cloeziana than in the coastal provenance of E. cloeziana. There was limited osmotic adjustment in response to soil drying in E. cloeziana, but not in E. argophloia. Between-species differences in water relations parameters were larger than those between the E. cloeziana provenances. Both E. cloeziana provenances maintained turgor under moderate water stress through a combination of osmotic and elastic adjustments. Eucalyptus argophloia had more rigid cell walls and reached lower water potentials with less reduction in relative water content than either of the E. cloeziana provenances, thereby enabling it to extract water from dryer soils.

Identification of intracellular calcium oxalate crystals in Chamelaucium uncinatum (Myrtaceae)

Intracellular inclusions in the pedicel and calyx-tube tissues of Chamelaucium uncinatum Schauer ( Myrtaceae) flowers are irregular in shape. They were shown, by polarised light and scanning electron microscopy, to be birefringent 8.9-29.5 mum druse (i.e. aggregate) crystals. Energy-dispersive X-ray spectroscopy showed that these crystals were predominantly composed of calcium. Histochemical and acid-solubility tests indicated that the crystals were calcium oxalate. Raman microprobe spectroscopy was used to confirm this chemical identity. The calcium oxalate crystals were located in xylem-vessel lumens and also in parenchyma cells adjacent to vascular tissues. Thus, the crystals may function to regulate soluble calcium concentrations in C. uncinatum tissues near sites where calcium is unloaded from the xylem.

Anomalous water absorption in porous materials

The absorption of fluid by unsaturated, rigid porous materials may be characterized by the sorptivity. This is a simple parameter to determine and is increasingly being used as a measure of a material's resistance to exposure to fluids (especially moisture and reactive solutes) in aggressive environments. The complete isothermal absorption process is described by a nonlinear diffusion equation, with the hydraulic diffusivity being a strongly nonlinear function of the degree of saturation of the material. This diffusivity can be estimated from the sorptivity test. In a typical test the cumulative absorption is proportional to the square root of time. However, a number of researchers have observed deviation from this behaviour when the infiltrating fluid is water and there is some potential for chemo-mechanical interaction with the material. In that case the current interpretation of the test and estimation of the hydraulic diffusivity is no longer appropriate. Kuntz and Lavallee (2001) discuss the anomalous behaviour and propose a non-Darcian model as a more appropriate physical description. We present an alternative Darcian explanation and theory that retrieves the earlier advantages of the simple sorptivity test in providing parametric information about the material's hydraulic properties and allowing simple predictive formulae for the wetting profile to be generated.