Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Working the iceberg : a staffroom morality play

This play comes from a research project about how teachers understand and sustain their work in challenging secondary school classrooms. The research asked “How DO teachers work in these classrooms?” not “How SHOULD they?” In the play you meet three teachers who speak candidly about their principles, priorities and vulnerabilities to a pre-service teacher as they move between classes and staffroom. These are real people, real quotes and real feelings taken from real interview data, not idealised guidelines for ‘best practice’. Rather than templates for practice, the play offers a variety of models, issues and food for thought to discuss in teacher education programs. The project was interested in the moral dynamics of classrooms created under the Council of Australian Governments’ 2009 Compact with Young Australians, a policy move that required students to be ‘earning or learning till 17’ across all Australian states. By removing the unemployment benefit for this age group, and tying school attendance to family welfare entitlements, these policies effectively raised the minimum school-leaving age. The risk in this well-intended policy move is that a lack of suitable job opportunities will keep young people at school longer than they want to be there. The effects of this ‘earning or learning’ policy will impact some communities, schools and classrooms much harder than others. The title uses the metaphor of an iceberg to refer to the complex community-school relations that lie below classroom interactions. The idea of a morality play in the play’s title refers back to a medieval form of popular play that used characters to instruct the audience in virtues and values. In the same way, this play seeks to bring to the surface and embody the different moral principles that can inform teacher’s work. The research involved classroom ethnographies of classes for 16 to 17 years olds in non-academic pathways. Eight different teacher/ class combinations were sampled across 2 high schools, 2 TAFE colleges and I hybrid TAFE/school program in three towns experiencing chronic youth unemployment. Their timetabled lessons were observed across 3 to 4 weeks and the teachers and some students were interviewed in each site. The project was funded by an ARC Discovery Early Career Award, 2012-214.

Mandatory nap times and group napping patterns in child care: An observational study

Policy provision for naps is typical in child care settings, but there is variability in the practices employed. One practice that might modify children’s early sleep patterns is the allocation of a mandatory nap time in which all children are required to lie on their beds without alternate activity permitted. There is currently limited evidence of the effects of such practices on children’s napping patterns. This study examined the association between duration of mandatory nap times and group-level napping patterns in child care settings. Observations were undertaken in a community sample of 113 preschool rooms with a scheduled nap time (N = 2,114 children). Results showed that 83.5% of child care settings implemented a mandatory nap time (range = 15–145 min) while 14.2% provided alternate activities for children throughout the nap time period. Overall, 31% of children napped during nap times. Compared to rooms with ≤ 30 min of mandatory nap time, rooms with 31–60 min and > 60 min of mandatory nap time had a two-and-a-half and fourfold increase, respectively, in the proportion of children napping. Nap onset latency did not significantly differ across groups. Among preschool children, exposure to longer mandatory nap times in child care may increase incidence of napping.