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.

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.

Socialising across channels : group multichannel communication

People increasingly communicate over multiple channels, such as SMS, email and IM. Choosing the channel for interaction is typically a considered action and shapes the message itself. In order to explore how people make sense of communication mediums and more generally, social group behaviour, we developed a multichannel communication prototype. Preliminary results indicate that multichannel communication was considered very useful in the group context even considering the increased quantity of messages while it was little used for person-to-person interaction.

Leveraging mundane technologies for group mobile social communication

This paper outlines results from the long-term deployment of a system for mobile group socialization which utilizes a variety of mundane technologies to support cross-media notifications and messaging. We focus here on the results as they pertain to usage of mundane technologies, particularly the use of such technologies within the context of a cross-media system. We introduce “Rhub”, our prototype, which was designed to support coordination, communication and sharing amongst informal social groups. We also describe and discuss the usage of the “console,” a text-based syntax to enable consistent use across text messaging, instant messaging, email and the web. The prototype has been in active use for over 18 months by over 170 participants, who have used it on an everyday basis for their own socializing requirements.