A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

Smooth Path Planning for Passages with Heading and Curvature Discontinuities

The problem of continuous curvature path planning for passages is considered. This problem arises when an autonomous vehicle traverses between prescribed boundaries such as corridors, tunnels, channels, etc. Passage boundaries with curvature and heading discontinuities pose challenges for generating smooth paths passing through them. Continuous curvature half-S shaped paths derived from the Four Parameter Logistic Curve family are proposed as a prospective path planning solution. Analytic conditions are derived for generating continuous curvature paths confined within the passage boundaries. Zero end curvature highlights the scalability of the proposed solution and its compatibility with other path planners in terms of larger path planning domains. Various scenarios with curvature and heading discontinuities are considered presenting viability of the proposed solution.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Optimization Problem in a Class of Linear System. Application to Multiple Drug Administration

2000 Mathematics Subject Classification: 62H15, 62P10.

Maintaining nutrition in aged care residents with a train-the-trainer intervention and nutrition coordinator

Objective: To investigate the impact of a train-the-trainer program on the nutritional status of older people in residential care. ----- Design: Prospective, randomized controlled study. Setting: Eight nursing homes in Southeast Queensland, Australia. ----- Participants: A total of 352 residents participated - 245 were female (69.6%). The mean age was 84.2 years and the majority (79.4%) were classified as high dependency. ----- Intervention: Residents from four nursing homes were randomly selected for a nutrition education program coordinated by Nutrition Coordinators. Residents from the other four nursing homes (control) received usual care. ----- Measurements: The Subjective Global Assessment was used to determine prevalence of malnutrition at baseline and six months post intervention. The Resident Classification Scale measured functional dependency. Prescribed diet, fluids, oral hygiene status and allied health referrals were obtained by chart audit. ----- Results: Approximately half the residents were well nourished with 49.4% moderately or severely malnourished. Residents in the intervention group were more likely to maintain or improve their nutritional status compared with the control group who were more likely to experience a deterioration (P=0.027). The odds of the control group being malnourished post test was 1.6 times more likely compared with the intervention group but this did not reach statistical significance (P=0.1). ----- Conclusion: The results of the study encourage the implementation of a Nutrition Coordinator program to maintain nutritional status of aged care residents. Nevertheless, malnutrition rates continue to be unacceptably high. In a rapidly aging society, the aged care sector needs to confront malnutrition and provide better resources for staff to take measures against this problem.

Women are people too : the problem of designing for gender

Cultural theory breaks with Modern analysis by rejecting traditional notions of race, gender, class and sexuality. In doing so, alternative frameworks such as Post-Feminism emerge which are useful for thinking about culture, technology and what our interactions with it mean. From a Post-Feminist perspective it can be seen how in our multi-cultural, post-industrial, digitized world, there is space to move beyond traditional ways of dividing up society such as ‘male’ and ‘female’. We are then free to re-construct our identity in light of a rich diversity of individually relevant experiences. Therefore, in order to get a better understanding of the highly nuanced cultural interactions that characterize our use of technology, this paper argues against using the inherently stereotyped lens of gender and allowing a new set of user needs to emerge.

Comparing exercise prescribed with exercise completed : effects of gender and mode of exercise

The purpose of this study was to compare the amount of exercise prescribed with the amount completed between two different modes of training intervention and between the sexes. Thirty-two men (mean age = 39.1 years, body mass index = 32.9 kg · m-2) and women (mean age = 39.6 years, body mass index = 32.1 kg · m-2) were prescribed traditional resistance training or light-resistance circuit training for 16 weeks. Lean mass and fat mass were determined by dual-energy X-ray absorptiometry at weeks 1 and 16. A completion index was calculated to provide a measure of the extent to which participants completed exercise training relative to the amount of exercise prescribed. The absolute amount of exercise completed by the circuit training group was significantly greater than the amount prescribed (P < 0.0001). The resistance training group consistently under-completed relative to the amount prescribed, but the difference was not significant. The completion index for the circuit training group (26 ± 21.7%) was significantly different from that of the resistance training group (-7.4 ± 3.0%). The completion index was not significantly different between men and women in either group. These data suggest that overweight and obese individuals participating in light-resistance circuit training complete more exercise than is prescribed. Men and women do not differ in the extent to which they over- or under-complete prescribed exercise.

Validation of the Chinese version of the Problem Areas in Diabetes (PAID-C) scale

OBJECTIVE To examine the psychometric properties of a Chinese version of the Problem Areas In Diabetes (PAID-C) scale. RESEARCH DESIGN AND METHODS The reliability and validity of the PAID-C were evaluated in a convenience sample of 205 outpatients with type 2 diabetes. Confirmatory factor analysis, Bland-Altman analysis, and Spearman's correlations facilitated the psychometric evaluation. RESULTS Confirmatory factor analysis confirmed a one-factor structure of the PAID-C (χ2/df ratio = 1.894, goodness-of-fit index = 0.901, comparative fit index = 0.905, root mean square error of approximation = 0.066). The PAID-C was associated with A1C (rs = 0.15; P < 0.05) and diabetes self-care behaviors in general diet (rs = −0.17; P < 0.05) and exercise (rs = −0.17; P < 0.05). The 4-week test-retest reliability demonstrated satisfactory stability (rs = 0.83; P < 0.01). CONCLUSIONS The PAID-C is a reliable and valid measure to determine diabetes-related emotional distress in Chinese people with type 2 diabetes.

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Investigating the mediating effects of emotional intelligence and coping on problem behaviours in adolescents

This study explored the mediating effect of emotional intelligence (EI) and coping strategies on problem behaviours in Australian adolescents. One hundred and forty-five adolescents (60 boys and 85 girls with a mean age of 12.02 years) completed self-report instruments of EI, stress coping strategies, and problem behaviours. The relationships between Emotional Management and Control and engagement in internalising and externalising behaviours were found to be mediated by the use of non-productive coping strategies. Mediation models of the relationship between problem behaviours and the Understanding Emotions and Emotional Recognition and Expression dimensions were found to be only partially mediated by the engagement in problem-focused and non-productive coping strategies. The results are discussed in regards to how coping strategies utilised in adolescence may produce more or less adaptive patterns of coping during adulthood. The development of emotional abilities may be required to improve coping outcomes for adolescents, which in turn may produce better psychological outcomes for adolescents in the long term.