For snow-avalanche hazard mapping, one needs efficient tools that nevertheless capture the essential physical processes. The code MoT-PSA (Method of Transport – Powder Snow Avalanche) described here is based on the two-layer depth-averaged formulation for mixed snow avalanches developed by Eglit and co-workers in the 1980s but is extended to 3-D terrain and uses a fast numerical scheme based on the method of transport. Compared to previous works, we introduce novel formulations for the suspension and deposition of snow from the dense core. Snow cover and air entrainment are quantified with physics-based models. A sensitivity study of the model parameters on an idealized topography shows that both the dense core and the parameters of the powder snow cloud (PSC) governing particle suspension and settling significantly affect the dynamics. As expected, we observe that snow cover entrainment favours the formation of large PSCs with long runout. The powder-snow avalanche that occurred in Lom (Norway) on 27 February 2020 is back-calculated using MoT-PSA. With plausible parameter values, the model reproduces the dense core stopping at the gully's base and the dilute PSC travelling across the frozen lake for almost 1 km.

The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free-boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume.

The putative neural pacemaker controlling circadian rhythms in mammals is contained in the suprachiasmatic nuclei of the hypothalamus. These nuclei receive a projection, the geniculo-hypothalamic tract (GHT), from neurons in the intergeniculate leaflet (IGL) and portions of the ventral lateral geniculate nucleus (vLGN) of the thalamus. We examined the responses of putative GHT neurons to diffuse illumination using extracellular electrophysiological recordings. The great majority of IGL neurons showed sustained ON responses to diffuse retinal illumination; vLGN neurons showed more variation in their responses. Discharge rates of sustained ON neurons increased monotonically as light intensity was increased and saturated over 2–3 log units of intensity changes. Many IGL neurons had binocular input, and input from the ipsilateral eye was often inhibitory. These results indicate that GHT neurons may provide information about ambient light intensity to the suprachiasmatic nuclei.

We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to meet demand, the requirement for simultaneous availability of resources means that a network may nevertheless be unstable. We show that instability occurs through poor control, and that, for a variety of network topologies, only small modifications to controls are required in order to ensure stability. For controls which possess a natural monotonicity property, we give some new results for the classification of the corresponding Markov processes, which lead to conditions both for stability and for instability.

While light is considered the dominant stimulus for entraining (synchronizing) mammalian circadian rhythms to local environmental time, social stimuli are also widely cited as ‘zeitgebers’ (time-cues). This review critically assesses the evidence for social influences on mammalian circadian rhythms, and possible mechanisms of action. Social stimuli may affect circadian behavioural programmes by regulating the phase and period of circadian clocks (i.e. a zeitgeber action, either direct or by conditioning to photic zeitgebers), by influencing daily patterns of light exposure or modulating light input to the clock, or by associative learning processes that utilize circadian time as a discriminative or conditioned stimulus. There is good evidence that social stimuli can act as zeitgebers. In several species maternal signals are the primary zeitgeber in utero and prior to weaning. Adults of some species can also be phase shifted or entrained by single or periodic social interactions, but these effects are often weak, and appear to be mediated by social stimulation of arousal. There is no strong evidence yet for sensory-specific nonphotic inputs to the clock. The circadian phase-dependence of clock resetting to social stimuli or arousal (the ‘nonphotic’ phase response curve, PRC), where known, is distinct from that to light and similar in diurnal and nocturnal animals. There is some evidence that induction of arousal can modulate light input to the clock, but no studies yet of whether social stimuli can shift the clock by conditioning to photic cues, or be incorporated into the circadian programme by associative learning. In humans, social zeitgebers appear weak by comparison with light. In temporal isolation or under weak light-dark cycles, humans may ignore social cues and free-run independently, although cases of mutual synchrony among two or more group-housed individuals have been reported. Social cues may affect circadian timing by controlling sleep-wake states, but the phase of entrainment observed to fixed sleep-wake schedules in dim light is consistent with photic mediation (scheduled variations in behavioural state necessarily create daily light-dark cycles unless subjects are housed in constant dark or have no eyes). By contrast, discrete exercise sessions can induce phase shifts consistent with the nonphotic PRC observed in animal studies. The best evidence for social entrainment in humans is from a few totally blind subjects who synchronize to the 24 h day, or to near-24 h sleep-wake schedules under laboratory conditions. However, the critical entraining stimuli have not yet been identified, and there are no reported cases yet of social entrainment in bilaterally enucleated blind subjects. The role of social zeitgebers in mammalian behavioural ecology, their mechanisms of action, and their utility for manipulating circadian rhythms in humans, remains to be more fully elaborated.