Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Rover autonomous integrity monitoring of GNSS RTK positioning solutions with multi-constellations

This paper studies receiver autonomous integrity monitoring (RAIM) algorithms and performance benefits of RTK solutions with multiple-constellations. The proposed method is generally known as Multi-constellation RAIM -McRAIM. The McRAIM algorithms take advantage of the ambiguity invariant character to assist fast identification of multiple satellite faults in the context of multiple constellations, and then detect faulty satellites in the follow-up ambiguity search and position estimation processes. The concept of Virtual Galileo Constellation (VGC) is used to generate useful data sets of dual-constellations for performance analysis. Experimental results from a 24-h data set demonstrate that with GPS&VGC constellations, McRAIM can significantly enhance the detection and exclusion probabilities of two simultaneous faulty satellites in RTK solutions.

Use of hydrotalcites for the removal of toxic anions from aqueous solutions

The removal of toxic anions has been achieved using hydrotalcite via two methods: (1) coprecipitation and (2) thermal activation. Hydrotalcite formed via the coprecipitation method, using solutions containing arsenate and vanadate up to pH 10, are able to remove more than 95% of the toxic anions (0.2 M) from solution. The removal of toxic anions in solutions with a pH of >10 reduces the removal uptake percentage to 75%. Raman spectroscopy observed multiple A1 stretching modes of V−O and As−O at 930 and 810 cm−1, assigned to vanadate and arsenate, respectively. Analysis of the intensity and position of the A1 stretching modes helped to identify the vanadate and arsenate specie intercalated into the hydrotalcite structure. It has been determined that 3:1 hydrotalcite structure predominantly intercalate anions into the interlayer region, while the 2:1 and 4:1 hydrotalcite structures shows a large portion of anions being removed from solution by adsorption processes. Treatment of carbonate solutions (0.2 M) containing arsenate and vanadate (0.2 M) three times with thermally activated hydrotalcite has been shown to remove 76% and 81% of the toxic anions, respectively. Thermally activated hydrotalcite with a Mg:Al ratio of 2:1, 3:1, and 4:1 have all been shown to remove 95% of arsenate and vanadate (25 ppm). At increased concentrations of arsenate and vanadate, the removal uptake percentage decreased significantly, except for the 4:1 thermally activated hydrotalcite. Thermally activated Bayer hydrotalcite has also been shown to be highly effective in the removal of arsenate and vanadate. The thermal activation of the solid residue component (red mud) removes 30% of anions from solution (100 ppm of both anions), while seawater-neutralized red mud removes 70%. The formation of hydrotalcite during the seawater neutralization process removes anions via two mechanisms, rather than one observed for thermally activated red mud.

Quantitative evaluation of route allocation solutions at large-scale passenger stations

Routing trains within passenger stations in major cities is a common scheduling problem for railway operation. Various studies have been undertaken to derive and formulate solutions to this route allocation problem (RAP) which is particularly evident in mainland China nowadays because of the growing traffic demand and limited station capacity. A reasonable solution must be selected from a set of available RAP solutions attained in the planning stage to facilitate station operation. The selection is however based on the experience of the operators only and objective evaluation of the solutions is rarely addressed. In order to maximise the utilisation of station capacity while maintaining service quality and allowing for service disturbance, quantitative evaluation of RAP solutions is highly desirable. In this study, quantitative evaluation of RAP solutions is proposed and it is enabled by a set of indices covering infrastructure utilisation, buffer times and delay propagation. The proposed evaluation is carried out on a number of RAP solutions at a real-life busy railway station in mainland China and the results highlight the effectiveness of the indices in pinpointing the strengths and weaknesses of the solutions. This study provides the necessary platform to improve the RAP solution in planning and to allow train re-routing upon service disturbances.

Comparison of the binding stoichiometries of positively charged DNA-binding drugs using positive and negative ion electrospray ionization mass spectrometry

Positive and negative ion electrospray ionization (ESI) mass spectra of complexes of positively charged small molecules (distamycin, Hoechst 33258, [Ru(phen)2dpq]Cl2 and [Ru(phen)2dpqC]Cl2) have been compared. [Ru(phen)2dpq]Cl2 and [Ru(phen)2dpqC]Cl2 bind to DNA by intercalation. Negative ion ESI mass spectra of mixtures of [Ru(phen)2dpq]Cl2 or [Ru(phen)2dpqC]Cl2 with DNA showed ions from DNA-ligand complexes consistent with solution studies. In contrast, only ions from freeDNAwere present in positive ion ESI mass spectra of mixtures of [Ru(phen)2dpq]Cl2 or [Ru(phen)2dpqC]Cl2 with DNA, highlighting the need for obtaining ESI mass spectra of non-covalent complexes under a range of experimental conditions. Negative ion spectra of mixtures of the minor groove binder Hoechst 33258 with DNA containing a known minor groove binding sequence were dominated by ions from a 1:1 complex. In contrast, in positive ion spectra there were also ions present from a 2:1 (Hoechst 33258: DNA) complex, suggesting an alternative binding mode was possible either in solution or in the gas phase. When Hoechst 33258 was mixed with a DNA sequence lacking a high affinity minor groove binding site, the negative ion ESI mass spectra showed that 1:1 and 2:1 complexes were formed, consistent with existence of binding modes other than minor groove binding. The data presented suggest that comparison of positive and negative ion ESI-MS spectra might provide an insight into various binding modes in both solution and the gas phase.

What are the health needs, familial and social problems of Thai migrants in a local community in Australia? A focus group study

This study explored the health needs, familial and social problems of Thai migrants in a local community in Brisbane, Australia. Five focus groups with Thai migrants were conducted. The qualitative data were examined using thematic content analysis that is specifically designed for focus group analysis. Four themes were identified: (1) positive experiences in Australia, (2) physical health problems, (3) mental health problems, and (4) familial and social health problems. This study revealed key health needs related to chronic disease and mental health, major barriers to health service use, such as language skills, and facilitating factors, such as the Thai Temple. We concluded that because the health needs, familial and social problems of Thai migrants were complex and culture bound, the development of health and community services for Thai migrants needs to take account of the ways in which Thai culture both negatively impacts health and offer positive solutions to problems.

The human cost of change : tales from the campus about personal change fatigue, resistance, and resilience

For the last decade, one question has haunted me: what helps people to cope with large-scale organisational change in their workplace? This study explores the construct of personal change resilience, and its potential for identifying solutions to the problems of change fatigue and change resistance. The thesis has emerged from the fields of change management, leadership, training, mentoring, evaluation, management and trust within the context of higher education in Australia at the beginning of the twenty-first century. In this thesis I present a theoretical model of the factors to consider in increasing peoples’ personal change resilience as they navigate large-scale organisational change at work, thereby closing a gap in the literature on the construct of change resilience. The model presented is based on both the literature in the realms of business and education, and on the findings of the research. In this thesis, an autoethnographic case study of two Australian university projects is presented as one narrative, resulting in a methodological step forward in the use of multiple research participants’ stories in the development of a single narrative. The findings describe the experiences of workers in higher education and emphasise the importance of considerate management in the achievement of positive experiences of organisational change. This research makes a significant contribution to new knowledge in three ways. First, it closes a gap in the literature in the realm of change management around personal change resilience as a solution to the problem of change fatigue by presenting models of both change failure and personal change resilience. Second, it is methodologically innovative in the use of personae to tell the stories of multiple participants in one coherent tale presented as a work of ethnographic fiction seen through an autoethnographic lens. By doing so, it develops a methodology for giving a voice to those to whom change is done in the workplace. Third, it provides a perspective on organisational change management from the view of the actual workers affected by change, thereby adding to the literature that currently exists, which is based on the views of those with responsibility for leading or managing change rather than those it affects. This thesis is intended as a practical starting point for conversations by actual change managers in higher education, and it is written in such a way as to help them see how theory can be applied in real life, and how empowering and enabling the actual working staff members, and engaging with them in a considerate way before, during and even after the change process, can help to make them resilient enough to cope with the change, rather than leaving them burned out or disengaged and no longer a well-functioning member of the institution. This thesis shows how considerately managed large-scale organisational change can result in positive outcomes for both the organisation and the individuals who work in it.

Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.

Predicting positive and negative impacts of cancer among long-term endometrial cancer survivors

OBJECTIVE Although the survival outcomes among women diagnosed with endometrial cancer are very favorable, little is known about the long-term impact of their cancer experience. This study identifies the extent of positive and negative impacts of cancer and factors associated with this, amongst long-term survivors of endometrial cancer. METHODS Australian women diagnosed with endometrial cancer (N=632) were sent questionnaires at the time of diagnosis and 3-5 years later. Hierarchical multiple regression models were used to examine whether a range of variables at diagnosis/treatment predicted subsequent scores on the Impact of Cancer Scale, which examines positive (e.g. health awareness) and negative (e.g. appearance concerns) impacts amongst cancer survivors. RESULTS Overall, women had a higher mean score for the positive than negative impact scales (M=3.5 versus M=2.5, respectively). An intermediate grade of endometrial cancer, a prior diagnosis of cancer and lower levels of education were significant, but weak, predictors of higher scores on the positive impact scale. Higher scores on the negative impact scale were predicted by a higher grade of cancer, poor physical and mental health, a younger age, being single or having lower levels of education. CONCLUSIONS The study demonstrates that factors that predict positive impact in cancer survivors differ to those that predict negative impact, suggesting that interventions to optimize cancer survivors' quality of life will need to be multi-dimensional, and this supports the need for tailored intervention.