The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Exploring complex fitness surfaces: Multiple ornamentation and polymorphism in male guppies

The sexual ornamentation used by male guppies to attract females comprises many components, each of which varies considerably among males. Although natural and sexual selection have been shown to contribute to divergence among populations in male sexual ornaments, the role of sexual selection in maintaining polymorphism within populations is less clear. We used both parametric quadratic regression and nonparametric projection pursuit regression techniques to reveal the major axes of non-linear sexual selection on male ornaments. We visualized the fitness surfaces defined by these axes using thin-plate splines to allow a direct comparison of the two methodologies. Identification of the major axes of selection and their visualization was critical in determining the form and strength of nonlinear selection. Both types of analysis revealed fitness surfaces comprising three peaks, suggesting that there is more than one way to make an attractive guppy. Disruptive selection may be an important process underlying the presence of multiple sexual ornaments and may contribute to the maintenance of the high levels of polymorphism in male sexual ornaments found in guppy populations.

Habitat choice and vigilance behaviour of brush-tailed rock-wallabies (Petrogale penicillata) within their nocturnal foraging ranges

Habitat choice by brush-tailed rock-wallabies (Petrogale penicillata) in south-east Queensland was investigated by comparing the attributes of the nocturnal foraging locations that they selected with those of random locations within a radius of 50 m. Brush-tailed rock-wallabies were shown to select foraging locations on the basis of forage quality and/or their ability to see predators, rather than protection from predators amongst vegetation that could conceal them. Habitat choice may have been affected by limited food availability, as this study was conducted in the winter dry season. The attributes of foraging locations that brush- tailed rock-wallabies perceived as increasing their predation risk were assessed by recording the proportion of time that brush- tailed rock-wallabies spent vigilant while foraging. To measure vigilance, focal animals were observed with a night- vision scope for two minutes and the proportions of time spent vigilant and feeding were recorded. No measured feature of foraging locations was related to higher vigilance levels, suggesting that brush- tailed rock-wallabies did not alter their vigilance whether sheltered amongst grass tussocks or in open habitat, or whether feeding on good quality or poorer quality vegetation. Vigilance levels significantly declined as overnight temperatures decreased, which may have resulted from higher energy requirements of brush- tailed rock-wallabies during winter. The only factors that were found to significantly increase vigilance levels were high winds and moonlit nights. On bright nights, brush- tailed rock-wallabies were very unsettled and during high winds they often did not emerge to feed. More information is needed about how macropods detect predators at night before the effects of wind and light intensity upon vigilance can be fully understood.

Discrete element modelling of the influence of lifters on power draw of tumbling mills

Crushing and grinding are the most energy intensive part of the mineral recovery process. A major part of rock size reduction occurs in tumbling mills. Empirical models for the power draw of tumbling mills do not consider the effect of lifters. Discrete element modelling was used to investigate the effect of lifter condition on the power draw of tumbling mill. Results obtained with PFC3D code show that lifter condition will have a significant influence on the power draw and on the mode of energy consumption in the mill. Relatively high lifters will consume less power than low lifters, under otherwise identical conditions. The fraction of the power that will be consumed as friction will increase as the height of the lifters decreases. This will result in less power being used for high intensity comminution caused by the impacts. The fraction of the power that will be used to overcome frictional resistance is determined by the material's coefficient of friction. Based on the modelled results, it appears that the effective coefficient of friction for in situ mill is close to 0.1. (C) 2003 Elsevier Science Ltd. All rights reserved.

Applying discrete element modelling to vertical and horizontal shaft impact crushers

The PFC3D (particle flow code) that models the movement and interaction of particles by the DEM techniques was employed to simulate the particle movement and to calculate the velocity and energy distribution of collision in two types of impact crusher: the Canica vertical shaft crusher and the BJD horizontal shaft swing hammer mill. The distribution of collision energies was then converted into a product size distribution for a particular ore type using JKMRC impact breakage test data. Experimental data of the Canica VSI crusher treating quarry and the BJD hammer mill treating coal were used to verify the DEM simulation results. Upon the DEM procedures being validated, a detailed simulation study was conducted to investigate the effects of the machine design and operational conditions on velocity and energy distributions of collision inside the milling chamber and on the particle breakage behaviour. (C) 2003 Elsevier Ltd. All rights reserved.

Discrete element modelling of power draw of tumbling mills

The power required to operate large mills is typically 5-10 MW. Hence, optimisation of power consumption will have a significant impact on overall economic performance and environmental impact. Power draw modelling results using the discrete element code PFC3D have been compared with results derived from the widely used empirical Model of Morrell. This is achieved by calculating the power draw for a range of operating conditions for constant mill size and fill factor using two modelling approaches. fThe discrete element modelling results show that, apart from density, selection of the appropriate material damping ratio is critical for the accuracy of modelling of the mill power draw. The relative insensitivity of the power draw to the material stiffness allows selection of moderate stiffness values, which result in acceptable computation time. The results obtained confirm that modelling of the power draw for a vertical slice of the mill, of thickness 20% of the mill length, is a reliable substitute for modelling the full mill. The power draw predictions from PFC3D show good agreement with those obtained using the empirical model. Due to its inherent flexibility, power draw modelling using PFC3D appears to be a viable and attractive alternative to empirical models where necessary code and computer power are available.

Comparison of DEM and experiment for a scale model SAG mill

Predictions of flow patterns in a 600-mm scale model SAG mill made using four classes of discrete element method (DEM) models are compared to experimental photographs. The accuracy of the various models is assessed using quantitative data on shoulder, toe and vortex center positions taken from ensembles of both experimental and simulation results. These detailed comparisons reveal the strengths and weaknesses of the various models for simulating mills and allow the effect of different modelling assumptions to be quantitatively evaluated. In particular, very close agreement is demonstrated between the full 3D model (including the end wall effects) and the experiments. It is also demonstrated that the traditional two-dimensional circular particle DEM model under-predicts the shoulder, toe and vortex center positions and the power draw by around 10 degrees. The effect of particle shape and the dimensionality of the model are also assessed, with particle shape predominantly affecting the shoulder position while the dimensionality of the model affects mainly the toe position. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.

Potential role of head lice, Pediculus humanus capitis, as vectors of Rickettsia prowazekii

Since the pioneering work of Charles Nicolle in 1909 [see Gross (1996) Proc Natl Acad Sci USA 93:10539-10540] most medical officers and scientists have assumed that body lice are the sole vectors of Rickettsia prowazekii, the aetiological agent of louse-borne epidemic typhus (LBET). Here we review the evidence for the axiom that head lice are not involved in epidemics of LBET. Laboratory experiments demonstrate the ability of head lice to transmit R. prowazekii, but evidence for this in the field has not been reported. However, the assumption that head lice do not transmit R. prowazekii has meant that head lice have not been examined for R. prowazekii during epidemics of LBET. The strong association between obvious (high) infestations of body lice and LBET has contributed to this perception, but this association does not preclude head lice as vectors of R. prowazekii. Indeed, where the prevalence and intensity of body louse infections may be high (e.g. during epidemics of LBET), the prevalence and intensity of head louse infestations is generally high as well. This review of the epidemiology of head louse and body louse infestations, and of LBET, indicates that head lice are potential vectors of R. prowazekii in the field. Simple observations in the field would reveal whether or not head lice are natural vectors of this major human pathogen.

Ultraviolet signals in birds are special

Recent behavioural experiments have shown that birds use ultraviolet (UV)-reflective and fluorescent plumage as cues in mate choice. It remains controversial, however, whether such UV signals play a special role in sexual communication, or whether they are part of general plumage coloration. We use a comparative approach to test for a general association between sexual signalling and either UV-reflective or fluorescent plumage. Among the species surveyed, 72% have UV colours and there is a significant positive association between UV reflectance and courtship displays. Among parrots (Psittaciformes), 68% of surveyed species have fluorescent plumage, and again there is a strong positive association between courtship displays and fluorescence. These associations are not artefacts of the plumage used in courtship displays, being generally more 'colourful' because there is no association between display and colours lacking UV reflectance or fluorescence. Equally, these associations are not phylogenetic artefacts because all results remain unchanged when families or genera, rather than species, are used as independent data points. We also find that, in parrots, fluorescent plumage is usually found adjacent to UV-reflective plumage. Using a simple visual model to examine one parrot, the budgerigar Melopsittacus undulatus, we show that the juxtaposition of UV-reflective and fluorescent plumage leads to a 25-fold increase in chromatic contrast to the budgerigar's visual system. Taken together, these results suggest that signals based on UV contrast are of special importance in the context of active sexual displays. We review briefly six hypotheses on why this may be the case: suitability for short-range signalling; high contrast with backgrounds; invisibility to predators; exploitation of pre-existing sensory biases; advertisement of feather structure; and amplification of behavioural signals.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Surface stickiness of drops of carbohydrate and organic acid solutions during convective drying: Experiments and modeling

Drying kinetics of low molecular weight sugars such as fructose, glucose, sucrose and organic acid such as citric acid and high molecular weight carbohydrate such as maltodextrin (DE 6) were determined experimentally using single drop drying experiments as well as predicted numerically by solving the mass and heat transfer equations. The predicted moisture and temperature histories agreed with the experimental ones within 6% average relative (absolute) error and average difference of +/- 1degreesC, respectively. The stickiness histories of these drops were determined experimentally and predicted numerically based on the glass transition temperature (T-g) of surface layer. The model predicted the experimental observations with good accuracy. A nonsticky regime for these materials during spray drying is proposed by simulating a drop, initially 120 mum in diameter, in a spray drying environment.

Opening windows into the mind: mothers' preferences for mental state explanations and children's theory of mind

A new questionnaire, the Maternal Mental State Input Inventory (MMSII) was created to measure mothers' preferences for introducing and elaborating on mental states in conversation with their young children. In two studies, the questionnaire was given to mothers of young children, and the children's theory of mind (ToM) development was assessed with standard tasks. In both studies, the questionnaire exhibited good internal reliability, and significant correlations emerged between mothers' self-reported preferences for elaborated, explanatory talk about the mental states and children's theory of mind performance. Further, mothers' conversational preferences, as measured by the MMSII, were the best predictors of children's theory of mind development when relevant control variables were included in the analyses. These results converge with naturalistic observational research that has demonstrated links between mothers' conversational styles and their children's theory of mind. They go further in suggesting that mothers' tendencies toward elaborated, explanatory talk about a range of mental states is particularly beneficial to children's theory of mind development. (C) 2003 Elsevier Inc. All rights reserved.

Physical activity and sedentary behavior: A population-based study of barriers, enjoyment, and preference

The associations of physical activity and sedentary behavior with barriers, enjoyment, and preferences were examined in a population-based mail survey of 1,332 adults. Respondents reporting high enjoyment and preference for physical activity were more likely to report high levels of activity. Those reporting cost, the weather, and personal barriers to physical activity were less likely to be physically active. Preference for sedentary behavior was associated with the decreased likelihood of being physically active, and the weather as a barrier to physical activity was associated with the increased likelihood of sedentary behavior. These constructs can be used to examine individual and environmental influences on physical activity and sedentary behavior in specific populations and could inform the development of targeted interventions.

Optical experiments beyond the quantum limit: Squeezing entanglement and teleportation

Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.