Stability Implications of Bendixson’s Criterion

This note presents a proof that the omega limit set of a solution to a planar system satisfying the Bendixson criterion is either empty or is a single equilibrium. The proof involves elementary techniques which should be accessible to senior undergraduates and graduate students

An Sveir Model for Assessing Potential Impact of an Imperfect Anti-SARS Vaccine

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv \u3e 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv \u3e 1

Nano-Thermal Transport Array: An Instrument for Combinatorial Measurements of Heat Transfer in Nanoscale Films

The nano-Thermal Transport Array is a silicon-based micromachined device for measuring the thermal properties of nanoscale materials in a high-throughput methodology. The device contains an array of thermal sensors, each one of which consists of a silicon nitride membrane and a tungsten heating element that also serves as a temperature gauge. The thermal behavior of the sensors is described with an analytical model. The assumptions underlying this model and its accuracy are checked using the finite element method. The analytical model is used in a data reduction scheme that relates experimental quantities to materials properties. Measured properties include thermal effusivity, thermal conductivity, and heat capacity. While the array is specifically designed for combinatorial analysis, here we demonstrate the capabilities of the device with a high-throughput study of copper multi-layer films as a function of film thickness, ranging from 15 to 470 nm. Thermal conductivity results show good agreement with earlier models predicting the conductivity based on electron scattering at interfaces.Engineering and Applied Science

Toxicity of Carbon Nanotubes in the Lungs of Mice 7 and 90 Days After Intratracheal Instillation

Single-walled carbon nanotubes have many potential applications in the electronic, computer, and aerospace industries. Because unprocessed nanotubes could become airborne and potentially reach the lungs, their pulmonary toxicity was investigated. The three products studied were made by different methods, and contained different types and amounts of residual catalytic metals. Mice were each intratracheally instilled once with 0,0.1 or 0.5 mg of nanotubes, a carbon black negative control, or a quartz positive control, and killed for histopathological study 7 d or 90 d after the treatment. All nanotube products induced epithelioid granulomas and, in some cases, interstitial inflammation in the animals of the 7 -d groups. These lesions persisted and were worse in the 90-d groups. We found that, if nanotubes reach the lung, they can be more toxic than quartz, which is considered a serious occupational health hazard in chronic inhalation exposures

Research into the diversification of university careers in learning and teaching and intentionally closing-the-loop on graduate employability

Universities are both a source of employable graduates and careers. This paper examines universities as developers and employers of their own graduates from the perspective of employees and recruited positions. Research questions were: what do learning and teaching careers look like at universities, and; what are the occupational patterns, satisfactions and concerns of the staff in those careers? An autoethnographic account of employees’ career journeys (all of whom were employed in learning and teaching or closely related areas) from five different universities were shared, compared and contrasted. Two of these universities are profiled as having a large proportion of students from target equity groups and therefore have intentionally recruited learning and teaching staff to widen student participation. A desktop review of six months of university employment vacancies from these two universities was conducted. A consistent theme across the autoethnographic stories was a feeling of being an outsider. The authors’ hypothesis is that this is related to haphazard preparation for learning and teaching positions. Of the 322 university vacancies, 84% were for professional staff, 23% of which were in learning and teaching, with the most prevalent role being Coordinator. Fourteen per cent were for academic staff, 64% of which involved learning and teaching, and the most prevalent title was Lecturer/Senior Lecturer. Key takeaways include recommendations for universities to intentionally enhance the employability of graduates who pursue learning and teaching positions within universities, and for prospective university learning and teaching staff to enhance their employability