We study the stability of steady convection rolls in two-dimensional Rayleigh–Bénard convection with free-slip boundaries and horizontal periodicity over 12 orders of magnitude in the Prandtl number $(10^{-6} \leq Pr \leq 10^6)$ and 6 orders of magnitude in the Rayleigh number $(8{\rm \pi} ^4 < Ra \leq 10^8)$. The analysis is facilitated by partitioning our modal expansion into so-called even and odd modes. With aspect ratio $\varGamma = 2$, we observe that zonal modes (with horizontal wavenumber equal to zero) can emerge only once the steady convection roll state consisting of even modes only becomes unstable to odd perturbations. We determine the stability boundary in the $(Pr,Ra)$ plane and observe remarkably intricate features corresponding to qualitative changes in the solution, as well as three regions where the steady convection rolls lose and subsequently regain stability as the Rayleigh number is increased. We study the asymptotic limit $Pr \to 0$ and find that the steady convection rolls become unstable almost instantaneously, eventually leading to nonlinear relaxation osculations and bursts, which we can explain with a weakly nonlinear analysis. In the complementary large-$Pr$ limit, we observe that the zonal modes at the instability switch off abruptly at a large, but finite, Prandtl number.

Evidence of Late Triassic large tetrapods from the UK is rare. Here, we describe a track-bearing surface located on the shoreline near Penarth, south Wales, United Kingdom. The total exposed surface is c. 50 m long and c. 2 m wide, and is split into northern and southern sections by a small fault. We interpret these impressions as tracks, rather than abiogenic sedimentary structures, because of the possession of marked displacement rims and their relationship to each other with regularly spaced impressions forming putative trackways. The impressions are large (up to c. 50 cm in length), but poorly preserved, and retain little information about track-maker anatomy. We discuss alternative, plausible, abiotic mechanisms that might have been responsible for the formation of these features, but reject them in favour of these impressions being tetrapod tracks. We propose that the site is an additional occurrence of the ichnotaxon Eosauropus, representing a sauropodomorph trackmaker, thereby adding a useful new datum to their sparse Late Triassic record in the UK. We also used historical photogrammetry to digitally map the extent of site erosion during 2009–2020. More than 1 m of the surface exposure has been lost over this 11-year period, and the few tracks present in both models show significant smoothing, breakage and loss of detail. These tracks are an important datapoint for Late Triassic palaeontology in the UK, even if they cannot be confidently assigned to a specific trackmaker. The documented loss of the bedding surface highlights the transient and vulnerable nature of our fossil resources, particularly in coastal settings, and the need to gather data as quickly and effectively as possible.

We derive an accurate estimate for the diffusive evaporation rates of multiple droplets of different sizes and arbitrary contact angles placed on a horizontal substrate. The derivation, which is based on a combination of Green's second identity and the method of reflections, simply makes use of the solution for the evaporation of a single droplet. The theoretical results can serve as a guide for future computational and experimental studies on the collective evaporation of arrays of droplets, as well as similar multi-body, diffusion-dominated transport problems.

People with neurodevelopmental disorders often present with challenging behaviours and psychiatric illnesses. Diagnosis and treatment require patients, families and healthcare professionals to work closely together in partnership, acknowledging their respective areas of expertise. Good treatment outcomes should also be underpinned by robust research evidence. Key research priorities are highlighted.

A multitude of medical products are being developed and produced as part of efforts to tackle COVID-19. They are varied in nature and range from test kits to tracing apps, protective equipment, ventilators, medicines and, of course, vaccines. The design, testing and manufacture of many of these products differs from production in normal times due to the urgency of the situation and the rapid increase in demand created by the pandemic. This article considers the legal issues arising as a result of the production of emergency products, particularly from a products liability perspective. To what extent do existing concepts under the European Product Liability Directive, such as defect, causation and the various defences, permit the pandemic to be taken into account when a Court is considering issues of liability? What is the impact on liability of the modified regulatory regime? In light of that discussion, the case for alternative responses is examined from a comparative and European perspective, including the issue of Government indemnities for the manufacturers of products, legal exemptions from liability and alternative no-fault compensation schemes.

Comprehension of predicates and reflexives was examined in children who stutter (CWS) and children who do not stutter (CWNS) who were between 9 years, 7 months and 10 years, 2 months. Demands on working memory and manual reaction time were also assessed in two experiments that employed a four-choice picture-selection sentence comprehension task. CWS were less accurate than CWNS on the attachment of predicates. For reflexives, there was no between-group difference in accuracy, but there was a difference in speed. The two constructions induced processing at different points on a speed–accuracy continuum with CWS sacrificing accuracy to respond fast with predicates, while they maintained accuracy of reflexives by responding slower relative to CWNS. Predicates made more demands on language than nonspeech motor reaction time, whereas the reverse was the case with reflexives for CWS compared to CWNS.

A rare subclass of Type Ia supernovae (SNe Ia) shows evidence of strong interaction with a hydrogen-rich circumstellar medium (CSM); these objects are referred to as SNe Ia-CSM. PTF11kx began life as a SN Ia, but after a month it began to show indications of significant interaction with its CSM. This well-studied object solidified the connection between SNe Ia-CSM and more typical SNe Ia, despite their spectral similarity to Type IIn SNe (which likely come from massive star progenitors, as opposed to the white dwarf progenitors for the SNe Ia-CSM). The spectra of all ~20 known SNe Ia-CSM are dominated by Hα emission (with widths of ~2000 km s−1) and exhibit large Hα/Hβ intensity ratios; moreover, they have an almost complete lack of He I emission (see left panel of Figure 1). They also show possible evidence of dust formation through a decrease in the red wing of Hα 75–100 days past maximum brightness. The absolute magnitudes of SNe Ia-CSM are found to be -21.3 mag ≤ MR ≤ −19 mag (see right panel of Figure 1), and they also show ultraviolet emission at early times and strong infrared emission at late times (but no detected radio or X-ray emission). Finally, the host galaxies of SNe Ia-CSM imply that these objects come from a relatively young stellar population.

An enormous effort is underway worldwide to attempt to detect gravitational waves. If successful, this will open a new frontier in astronomy. An essential portion of this effort is being carried out in Australia by the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA), with research teams working at the Australia National University, University of Western Australia, and University of Adelaide involving scientists and students representing many more institutions and nations. ACIGA is developing ultrastable high-power continuous-wave lasers for the next generation interferometric gravity wave detectors; researching the problems associated with high optical power in resonant cavities; opening frontiers in advanced interferometry configurations, quantum optics, and signal extraction; and is the world's leader in high-performance vibration isolation and suspension design. ACIGA has also been active in theoretical research and modelling of potential astronomical gravitational wave sources, and in developing data analysis detection algorithms. ACIGA has opened a research facility north of Perth, Western Australia, which will be the culmination of these efforts. This paper briefly reviews ACIGA's research activities and the prospects for gravitational wave astronomy in the southern hemisphere.

Parkinson's disease (PD) has long been associated with dementia. This has been found to correlate with participant age, age at onset of PD and severity of PD. In addition, a large corpus of research points to the fact that participants with, as well as without, dementia can be impaired in a variety of cognitive tasks. Among these, set-shifting and dual-tasking skills have received particular focus. Most studies report that a reduction in attentional resources can lead to problems with these tasks. However, none have been able to determine exactly which systems are involved in these skills and which neurological impairments underlie the observed cognitive deficits. The current study set out to investigate how performance on tasks requiring set-shifting and dual tasking related to each other, as well as overall measures of cognition gained across a variety of tasks. Fifteen participants with PD and 12 control participants underwent screening tests for dementia, as well as specific tests to assess attention, set-shifting and dual tasking. The results indicate that set-shifting ability correlated well with other measures of cognitive performance, whereas dualtasking skills did not. This could suggest that set-shifting and dual tasking are not necessarily controlled by the same process, or that a particular process is involved to different degrees. In addition, many participants showed individual performance variations and dissociations between tasks that were not necessarily evident from the statistical analysis. This indicates that it can be difficult to make assumptions on overall cognitive performance from specific tasks and vice versa. This observation has implications for clinical practice as well as research methodology.

A log-coffin excavated in the early nineteenth century proved to be well enough preserved in the early twenty-first century for the full armoury of modern scientific investigation to give its occupants and contents new identity, new origins and a new date. In many ways the interpretation is much the same as before: a local big man buried looking out to sea. Modern analytical techniques can create a person more real, more human and more securely anchored in history. This research team shows how.

We study the axisymmetric stretching of a thin sheet of viscous fluid driven by a centrifugal body force. Time-dependent simulations show that the sheet radius R(t) tends to infinity in finite time. As time t approaches the critical time t*, the sheet becomes partitioned into a very thin central region and a relatively thick rim. A net momentum and mass balance in the rim leads to a prediction for the sheet radius near the singularity that agrees with the numerical simulations. By asymptotically matching the dynamics of the sheet with the rim, we find that the thickness h in the central region is described by a similarity solution of the second kind, with h ∝ (t* − t)α where the exponent α satisfies a nonlinear eigenvalue problem. Finally, for non-zero surface tension, we find that the exponent increases rapidly to infinity at a critical value of the rotational Bond number B = 1/4. For B > 1/4, surface tension defeats the centrifugal force, causing the sheet to retract rather than to stretch, with the limiting behaviour described by a similarity solution of the first kind.

Paul Thompson’s monograph on William Butterfield set out to challenge the bizarre misconceptions which had previously warped appreciation of his work. These included Sir John Summerson’s accusation of ‘purposeful sadism’, Ian Nairn’s view of him as an ‘unexpected Heathcliff, and Henry-Russell Hitchcock’s description of him as uncivilized, ‘a man who never wrote a book or an article’ and who rarely travelled. Mendacious anecdotes suggested a puritanical and antisocial character, lacking in humanity. Thompson effectively refuted such absurdities, but Butterfield’s letters — very few of which have been published, even in part — provide fascinating evidence of his character. They reveal his humour and his affection for old friends, and his strongly held, but eminently sensible, religious views, as well as his pragmatic and conscientious practice of architecture. This evidence bears out and adds much useful detail to Thompson’s depiction of the man, refining our understanding of him and allowing his personality to come to the fore.