Numerical study of two ill-posed one-phase Stefan problems

We treat two related moving boundary problems. The first is the ill-posed Stefan problem for melting a superheated solid in one Cartesian coordinate. Mathematically, this is the same problem as that for freezing a supercooled liquid, with applications to crystal growth. By applying a front-fixing technique with finite differences, we reproduce existing numerical results in the literature, concentrating on solutions that break down in finite time. This sort of finite-time blow-up is characterised by the speed of the moving boundary becoming unbounded in the blow-up limit. The second problem, which is an extension of the first, is proposed to simulate aspects of a particular two-phase Stefan problem with surface tension. We study this novel moving boundary problem numerically, and provide results that support the hypothesis that it exhibits a similar type of finite-time blow-up as the more complicated two-phase problem. The results are unusual in the sense that it appears the addition of surface tension transforms a well-posed problem into an ill-posed one.

Stochastic regularization method for backward Cauchy problem in Banach spaces

We consider a stochastic regularization method for solving the backward Cauchy problem in Banach spaces. An order of convergence is obtained on sourcewise representative elements.

Extended GNSS ambiguity resolution models with regularization criterion and constraints

This paper firstly presents an extended ambiguity resolution model that deals with an ill-posed problem and constraints among the estimated parameters. In the extended model, the regularization criterion is used instead of the traditional least squares in order to estimate the float ambiguities better. The existing models can be derived from the general model. Secondly, the paper examines the existing ambiguity searching methods from four aspects: exclusion of nuisance integer candidates based on the available integer constraints; integer rounding; integer bootstrapping and integer least squares estimations. Finally, this paper systematically addresses the similarities and differences between the generalized TCAR and decorrelation methods from both theoretical and practical aspects.

Geometry‐specified troposphere decorrelation for subcentimeter real‐time kinematic solutions over long baselines

Real‐time kinematic (RTK) GPS techniques have been extensively developed for applications including surveying, structural monitoring, and machine automation. Limitations of the existing RTK techniques that hinder their applications for geodynamics purposes are twofold: (1) the achievable RTK accuracy is on the level of a few centimeters and the uncertainty of vertical component is 1.5–2 times worse than those of horizontal components and (2) the RTK position uncertainty grows in proportional to the base‐torover distances. The key limiting factor behind the problems is the significant effect of residual tropospheric errors on the positioning solutions, especially on the highly correlated height component. This paper develops the geometry‐specified troposphere decorrelation strategy to achieve the subcentimeter kinematic positioning accuracy in all three components. The key is to set up a relative zenith tropospheric delay (RZTD) parameter to absorb the residual tropospheric effects and to solve the established model as an ill‐posed problem using the regularization method. In order to compute a reasonable regularization parameter to obtain an optimal regularized solution, the covariance matrix of positional parameters estimated without the RZTD parameter, which is characterized by observation geometry, is used to replace the quadratic matrix of their “true” values. As a result, the regularization parameter is adaptively computed with variation of observation geometry. The experiment results show that new method can efficiently alleviate the model’s ill condition and stabilize the solution from a single data epoch. Compared to the results from the conventional least squares method, the new method can improve the longrange RTK solution precision from several centimeters to the subcentimeter in all components. More significantly, the precision of the height component is even higher. Several geosciences applications that require subcentimeter real‐time solutions can largely benefit from the proposed approach, such as monitoring of earthquakes and large dams in real‐time, high‐precision GPS leveling and refinement of the vertical datum. In addition, the high‐resolution RZTD solutions can contribute to effective recovery of tropospheric slant path delays in order to establish a 4‐D troposphere tomography.

Super-resolved faces for improved face recognition from surveillance video advances in biometrics

Characteristics of surveillance video generally include low resolution and poor quality due to environmental, storage and processing limitations. It is extremely difficult for computers and human operators to identify individuals from these videos. To overcome this problem, super-resolution can be used in conjunction with an automated face recognition system to enhance the spatial resolution of video frames containing the subject and narrow down the number of manual verifications performed by the human operator by presenting a list of most likely candidates from the database. As the super-resolution reconstruction process is ill-posed, visual artifacts are often generated as a result. These artifacts can be visually distracting to humans and/or affect machine recognition algorithms. While it is intuitive that higher resolution should lead to improved recognition accuracy, the effects of super-resolution and such artifacts on face recognition performance have not been systematically studied. This paper aims to address this gap while illustrating that super-resolution allows more accurate identification of individuals from low-resolution surveillance footage. The proposed optical flow-based super-resolution method is benchmarked against Baker et al.’s hallucination and Schultz et al.’s super-resolution techniques on images from the Terrascope and XM2VTS databases. Ground truth and interpolated images were also tested to provide a baseline for comparison. Results show that a suitable super-resolution system can improve the discriminability of surveillance video and enhance face recognition accuracy. The experiments also show that Schultz et al.’s method fails when dealing surveillance footage due to its assumption of rigid objects in the scene. The hallucination and optical flow-based methods performed comparably, with the optical flow-based method producing less visually distracting artifacts that interfered with human recognition.

New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

Stefan problems for melting nanoscaled particles

Under certain conditions, the mathematical models governing the melting of nano-sized particles predict unphysical results, which suggests these models are incomplete. This thesis studies the addition of different physical effects to these models, using analytic and numerical techniques to obtain realistic and meaningful results. In particular, the mathematical "blow-up" of solutions to ill-posed Stefan problems is examined, and the regularisation of this blow-up via kinetic undercooling. Other effects such as surface tension, density change and size-dependent latent heat of fusion are also analysed.

Diarrhoea risk factors in enterally tube fed critically ill patients : a retrospective audit

Objective: Diarrhoea in the enterally tube fed (ETF) intensive care unit (ICU) patient is a multifactorial problem. Diarrhoeal aetiologies in this patient cohort remain debatable; however, the consequences of diarrhoea have been well established and include electrolyte imbalance, dehydration, bacterial translocation, peri anal wound contamination and sleep deprivation. This study examined the incidence of diarrhoea and explored factors contributing to the development of diarrhoea in the ETF, critically ill, adult patient. ---------- Method: After institutional ethical review and approval, a single centre medical chart audit was undertaken to examine the incidence of diarrhoea in ETF, critically ill patients. Retrospective, non-probability sequential sampling was used of all emergency admission adult ICU patients who met the inclusion/exclusion criteria. ---------- Results: Fifty patients were audited. Faecal frequency, consistency and quantity were considered important criteria in defining ETF diarrhoea. The incidence of diarrhoea was 78%. Total patient diarrhoea days (r = 0.422; p = 0.02) and total diarrhoea frequency (r = 0.313; p = 0.027) increased when the patient was ETF for longer periods of time. Increased severity of illness, peripheral oxygen saturation (Sp02), glucose control, albumin and white cell count were found to be statistically significant factors for the development of diarrhoea. ---------- Conclusion: Diarrhoea in ETF critically ill patients is multi-factorial. The early identification of diarrhoea risk factors and the development of a diarrhoea risk management algorithm is recommended.

Probiotics and diarrhoea management in enterally tube fed critically ill patients : what is the evidence?

Objective: The aim of this literature review is to identify the role of probiotics in the management of enteral tube feeding (ETF) diarrhoea in critically ill patients.---------- Background: Diarrhoea is a common gastrointestinal problem seen in ETF patients. The incidence of diarrhoea in tube fed patients varies from 2% to 68% across all patients. Despite extensive investigation, the pathogenesis surrounding ETF diarrhoea remains unclear. Evidence to support probiotics to manage ETF diarrhoea in critically ill patients remains sparse.---------- Method: Literature on ETF diarrhoea and probiotics in critically ill, adult patients was reviewed from 1980 to 2010. The Cochrane Library, Pubmed, Science Direct, Medline and the Cumulative Index of Nursing and Allied Health Literature (CINAHL) electronic databases were searched using specific inclusion/exclusion criteria. Key search terms used were: enteral nutrition, diarrhoea, critical illness, probiotics, probiotic species and randomised clinical control trial (RCT).---------- Results: Four RCT papers were identified with two reporting full studies, one reporting a pilot RCT and one conference abstract reporting an RCT pilot study. A trend towards a reduction in diarrhoea incidence was observed in the probiotic groups. However, mortality associated with probiotic use in some severely and critically ill patients must caution the clinician against its use.---------- Conclusion: Evidence to support probiotic use in the management of ETF diarrhoea in critically ill patients remains unclear. This paper argues that probiotics should not be administered to critically ill patients until further research has been conducted to examine the causal relationship between probiotics and mortality, irrespective of the patient's disease state or projected prophylactic benefit of probiotic administration.

Constitutional legitimacy : an international ill and gap in the literature?

The central argument of this work is that “democratic constitutional legitimacy”[2] probably does not currently exist in the politics of any country internationally. This inherent problem in constitutionalism is an endemic governance problem most citizenries should be dealing with, only that we are not in a large extent doing so and haven’t been historically. This position was ascertained using a form of Beck and Grande’s (2010) cosmopolitan methodology in my doctoral thesis (which we shall return to). It is argued that every constitution is in need of considerable rethinking so as to bring its statutes in line with the interests of the plurality of individuals it oversees. Finally, this work attempts to show that research in this area of democratic constitutional legitimacy is lacking in the literature as only a few scholars presently engage the issue (namely Simone Chambers).

Trans digital storytelling : everyday activism, mutable identity and the problem of visibility

Mainstream representations of trans people typically run the gamut from victim to mentally ill and are almost always articulated by non-trans voices. The era of user-generated digital content and participatory culture has heralded unprecedented opportunities for trans people who wish to speak their own stories in public spaces. Digital Storytelling, as an easy accessible autobiographic audio-visual form, offers scope to play with multi-dimensional and ambiguous representations of identity that contest mainstream assumptions of what it is to be ‘male’ or ‘female’. Also, unlike mainstream media forms, online and viral distribution of Digital Stories offer potential to reach a wide range of audiences, which is appealing to activist oriented storytellers who wish to confront social prejudices. However, with these newfound possibilities come concerns regarding visibility and privacy, especially for storytellers who are all too aware of the risks of being ‘out’ as trans. This paper explores these issues from the perspective of three trans storytellers, with reference to the Digital Stories they have created and shared online and on DVD. These examplars are contextualised with some popular and scholarly perspectives on trans representation, in particular embodied and performed identity. It is contended that trans Digital Stories, while appearing in some ways to be quite conventional, actually challenge common notions of gender identity in ways that are both radical and transformative.

Enhancing opportunities to feed forward ; developing problem solving skills using web based scenarios

Universities often struggle to satisfy students’ need for feedback. This is an area where student satisfaction with courses of study can be low. Yet it is clear that one of the properties of good teaching is giving the highest quality feedback on student work. The term ‘feedback’ though is most commonly associated with summative assessment given by a teacher after work is completed. The student can often be a passive participant in the process. This paper looks at the implementation of a web based interactive scenario completed by students prior to summative assessment. It requires students to participate actively to develop and improve their legal problem solving skills. Traditional delivery of legal education focuses on print and an instructor who conveys the meaning of the written word to students. Today, mixed modes of teaching are often preferred and they can provide enhanced opportunities for feeding forward with greater emphasis on what students do. Web based activities allow for flexible delivery; they are accessible off campus, at a time that suits the student and may be completed by students at their own pace. This paper reports on an online interactive activity which provides valuable formative feedback necessary to allow for successful completion of a final problem solving assignment. It focuses on how the online activity feeds forward and contributes to the development of legal problem solving skills. Introduction to Law is a unit designed and introduced for completion by undergraduate students from faculties other than law but is focused most particularly on students enrolled in the Bachelor of Entertainment Industries degree, a joint initiative of the faculties of Creative Industries, Business and Law at the Queensland University of Technology in Australia. The final (and major) assessment for the unit is an assignment requiring students to explain the legal consequences of particular scenarios. A number of cost effective web based interactive scenarios have been developed to support the unit’s classroom activities. The tool commences with instruction on problem solving method. Students then view the stimulus which is a narrative produced in the form of a music video clip. A series of questions are posed which guide students through the process and they can compare their responses with sample answers provided. The activity clarifies the problem solving method and expectations for the summative assessment and allows students to practise the skill. The paper reports on the approach to teaching and learning taken in the unit including the design process and implementation of the activity. It includes an evaluation of the activity with respect to its effectiveness as a tool to feed forward and reflects on the implications for the teaching of law in higher education.

Drugs, labels and (p)ill-fitting boxes : ADHD and children who are hard to teach

In offering a critical review of the problem we call “ADHD” this paper progresses in three stages. The first two parts juxtapose the dominant voices emanating from the literature in medicine and psychology, highlighting some interdependency between these otherwise competing interest groups. In part three, the nature of the relationship between these groups and the institution of the school is considered, as is the role that the school may play in the psycho-pathologisation of fidgety, distractible, active children who prove hard to teach. In so doing, the author provides an insight as to why the problem we call “ADHD” has achieved celebrity status in Australia and what the effects of that may be for children who come to be described in these ways.

Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.