Density Driven Turbulent Mixing at Batch Interfaces

Models are developed for the turbulent mixing and growth at a batch interface. These models depend crucially on the choice of diffusion coefficient $D$. The model where $D$ is the harmonic average of the mixing coefficients of the two pure fluids is analysed in detail, since this is likely to be a good approximation when the density difference between the two fluids is small. When the density difference is large, the laminar flow regime fingering will occur and there will be a relatively sharp interface between the fluids. However, in the turbulent case, as gravity drives the denser fluid into the less dense one the invading fluid is immediately mixed by turbulent diffusion. This means that sharp interfaces do not exist. Instead there will be a finite mixing region where the volume fraction of each fluid changes from $0$ to $1$. In this case $D$ will depend upon the relative concentration of the fluids. This approach leads to a degenerate diffusion problem

Investigating the physiological underpinnings of proactive and reactive behavioural types in grey seals (Halichoerus grypus): Trial deployment of a minimally invasive data logger for recording heart rate and heart rate variability in a wild free-ranging breeding pinniped species

Individuals differ non-randomly in their responses to stressors, exhibiting consistent individual differences (CIDs) in behavioural and physiological coping mechanisms commonly referred to as coping styles. Grey seals (Halichoerus grypus) are one of the few mammal species in which CIDs in stress responses have been documented in wild populations, though evidence thus far has been purely behavioural. Physiologically, coping styles can be distinguished by differences in the autonomic regulation of cardiac activity, which can be measured using heart rate variability (HRV). The objectives of this study were two-fold. First, to assess the suitability of Polar® RS800CX monitors and H2/H3 sensors for conducting HRV analyses in grey seals. Second, to quantify inter-individual variation, repeatability, and reproductive performance correlates of baseline HRV. Polar® devices were deployed successfully during the 2013 breeding season on female grey seals (N = 15) on the Isle of May, Scotland, and were capable of recording HR patterns that characterise phocid seals at rest on land. However, artefacts were widespread and biased HRV metrics. Filtration and correction protocols were able to counteract the effects of artefacts, but severely limited the amount of data available for analysis. There were significant inter-individual differences in baseline HRV, which could not be explained by factors associated with the breeding season (e.g. percentage mass loss, day of lactation), diurnal rhythms (e.g. time of day), or stressors (e.g. days since capture). These differences in baseline HRV showed consistency across early and late lactation. Individuals appeared to separate into two groups: those with consistently lower or higher baseline HRV, characteristic of proactive and reactive coping styles, respectively. Furthermore, females with lower baseline HRV showed greater maternal transfer efficiency – though there were no associations between baseline HRV and maternal expenditure (i.e. maternal mass loss, kgday–1) or fitness outcomes (i.e. pup mass gain, kgday–1). These findings build upon previous studies on behavioural CIDs in female grey seals by providing the first preliminary evidence for physiological CIDs that are associated with maternal investment. However, due to small sample sizes, further studies are required to determine whether these findings are truly indicative of coping styles. In their current form, the use of Polar® devices requires several caveats and further studies are needed to fully realise their potential. Future research should focus on validation against simultaneously recorded ECGs to improve artefact detection and correction, and modification to minimise the occurrence of artefacts. Despite their limitations, Polar® devices have immense potential as a minimally invasive research tool for conducting HRV analyses in the field

Orthogonal free quantum group factors are strongly 1-bounded

We prove that the orthogonal free quantum group factors $\mathcal{L}(\mathbb{F}O_N)$ are strongly $1$-bounded in the sense of Jung. In particular, they are not isomorphic to free group factors. This result is obtained by establishing a spectral regularity result for the edge reversing operator on the quantum Cayley tree associated to $\mathbb{F}O_N$, and combining this result with a recent free entropy dimension rank theorem of Jung and Shlyakhtenko.Comment: v3: accepted versio

Reduced operator algebras of trace-preserving quantum automorphism groups

Let $B$ be a finite dimensional C$^\ast$-algebra equipped with its canonical trace induced by the regular representation of $B$ on itself. In this paper, we study various properties of the trace-preserving quantum automorphism group \G of $B$. We prove that the discrete dual quantum group \hG has the property of rapid decay, the reduced von Neumann algebra L^\infty(\G) has the Haagerup property and is solid, and that L^\infty(\G) is (in most cases) a prime type II$_1$-factor. As applications of these and other results, we deduce the metric approximation property, exactness, simplicity and uniqueness of trace for the reduced $C^\ast$-algebra C_r(\G), and the existence of a multiplier-bounded approximate identity for the convolution algebra L^1(\G).Comment: Section 6 removed and replaced by a more general solidity resul