Asymptotic expansions of the Gauss hypergeometric function with large parameters, $F(\unicode[STIX]{x1D6FC}+\unicode[STIX]{x1D716}_{1}\unicode[STIX]{x1D70F},\unicode[STIX]{x1D6FD}+\unicode[STIX]{x1D716}_{2}\unicode[STIX]{x1D70F};\unicode[STIX]{x1D6FE}+\unicode[STIX]{x1D716}_{3}\unicode[STIX]{x1D70F};z)$ as $|\unicode[STIX]{x1D70F}|\rightarrow \infty$, are known for many special cases, but not for one that the author encountered in recent work on fluid mechanics: $\unicode[STIX]{x1D716}_{2}=0$ and $\unicode[STIX]{x1D716}_{3}=\unicode[STIX]{x1D716}_{1}z$. This paper gives the leading term for that case if $\unicode[STIX]{x1D6FD}$ is not a negative integer and $z$ is not on the branch cut $[1,\infty )$, and it shows how subsequent terms can be found.

The discovery of the first electromagnetic counterpart to a gravitational wave signal has generated follow-up observations by over 50 facilities world-wide, ushering in the new era of multi-messenger astronomy. In this paper, we present follow-up observations of the gravitational wave event GW170817 and its electromagnetic counterpart SSS17a/DLT17ck (IAU label AT2017gfo) by 14 Australian telescopes and partner observatories as part of Australian-based and Australian-led research programs. We report early- to late-time multi-wavelength observations, including optical imaging and spectroscopy, mid-infrared imaging, radio imaging, and searches for fast radio bursts. Our optical spectra reveal that the transient source emission cooled from approximately 6 400 K to 2 100 K over a 7-d period and produced no significant optical emission lines. The spectral profiles, cooling rate, and photometric light curves are consistent with the expected outburst and subsequent processes of a binary neutron star merger. Star formation in the host galaxy probably ceased at least a Gyr ago, although there is evidence for a galaxy merger. Binary pulsars with short (100 Myr) decay times are therefore unlikely progenitors, but pulsars like PSR B1534+12 with its 2.7 Gyr coalescence time could produce such a merger. The displacement (~2.2 kpc) of the binary star system from the centre of the main galaxy is not unusual for stars in the host galaxy or stars originating in the merging galaxy, and therefore any constraints on the kick velocity imparted to the progenitor are poor.

The SkyMapper Transient survey (SMT) is exploring variability in the southern sky by performing (a) a rolling search to discover and study supernovæ, and (b) a Target of Opportunity programme that uses the robotic SkyMapper Telescope at Siding Spring Observatory. The supernova survey is obtaining a non-targeted sample of Type Ia supernovæ (SNe Ia) at low redshifts, z < 0.1, and studying other interesting transients found with the search strategy. We have a Target of Opportunity programme with an automatic response mechanism to search for optical counterparts to gravitational-wave and fast radio-burst events; it benefits from SkyMapper’s large field of view of 5.7 sq. deg. and a rapid data reduction pipeline.

We present first results of the SMT survey. The SMT pipeline can process and obtain potential candidates within 12 hours of observation. It disentangles real transients from processing artefacts using a machine-learning algorithm. To date, SMT has discovered over 60 spectroscopically confirmed supernovæ, several peculiar objects, and over 40 SNe Ia including one (SNIa 2016hhd) which was found within the first few days of explosion. We have also participated in searches for optical counterparts of gravitational waves, fast radio bursts and other transients, and have published observations of the optical counterpart of the gravitational-wave event GW170817. We also participate in coordinated observations with the Deeper Wider Faster programme, and the Kepler K2 cosmology project.

An experimental program at Worthington Glacier, Alaska, U.S.A., has yielded the first in situ measurement of the full stress tensor in glacier ice. Measurements were made with an array of stiff (low-compliance) normal-force sensors frozen into a borehole at 120 m depth. Freezing in temperate ice was accomplished by a down-hole heat exchanger which extracted heat at a rate of 15 W. Under slowly varying stress conditions, relaxation of stress anomalies by viscous creep following drilling of the hole and installation of the sensors allows for equilibration of measured stresses with far-field stresses. Equilibration of local and far-field stresses was confirmed and pressure sensors calibrated in laboratory experiments prior to the field program. Results of the stress measurements show principal axes of the stress tensor oriented in directions consistent with the geometry of the glacier and broadly consistent with measured englacial strain rate. The magnitudes of stress-tensor components are more error-prone and more sensitive to uncertainty in sensor magnitude than uncertainty in sensor orientation. Mean stress determined by pressure measurements agrees with estimated lithostatic overburden to within approximately 15%. Unexpected results include a stress perturbation lasting about 5 days that caused a rotation of the orientations of the principal stress axes of approximately 5° about an axis pointing in the down-flow direction.

Observations from basal water-pressure sensors along the length of Bench Glacier, Alaska, USA, show that diurnal fluctuations of water pressure are seasonal and restricted to summer. Most notable about these fluctuations is their disappearance in the late summer and early autumn, long before the seasonal end of diurnal meltwater input. Here we present data documenting the end of diurnal water-pressure fluctuations during the 2002 and 2003 melt seasons. The end of diurnal fluctuations occurred abruptly in multiple boreholes spaced meters to kilometers apart. There was no obvious spatial progression of termination events, and a clear correlation with meteorological forcing or discharge in the outlet stream was not apparent. After diurnal pressure fluctuations ended, basal water pressure returned to a high, generally steady, value either in an irregular pattern or by a distinct increase. This high water pressure was interrupted by episodic, acyclic events throughout the autumn before becoming stable and high in winter.

Values of the strain-rate tensor represented at a 20 m length scale are found to explain the pattern and orientation of crevasses in a 0.13 km2 reach of Worthington Glacier, Alaska, U.S.A. The flow field of the reach is constructed from surveyed displacements of 110 markers spaced 20-30 m apart. A velocity gradient method is then used to calculate values of the principal strain-rate axes at the nodes of a 20 m x 20 m orthogonal grid. Crevasses in the study reach are of two types, splaying and transverse, and are everywhere normal to the trajectories of greatest (most tensile) principal strain rate. Splaying crevasses exist where the longitudinal strain rate ( x ) is ≤ 0 and transverse crevasses are present under longitudinally extending flow (i.e. x > 0). The orientation of crevasses changes in the down-glacier direction, but the calculated rotation by the flow field does not account for this change in orientation. Observations suggest that individual crevasses represent local values of the regional flow field and are transient on the time-scale of 1-2 years; they are not persistent features that are translated and rotated by flow. Crevasse patterns are thus found to be a useful tool for mapping the strain-rate tensor in this reach of a temperate valley glacier.

A suite of surface and basal measurements during and after borehole drilling is used to perform in situ investigation of the local basal drainage system and pressure forcing in western Greenland. Drill and borehole water temperature were monitored during borehole drilling, which was performed with dyed hot water. After drilling, borehole water pressure and basal dye concentration were measured concurrently with positions in a GPS strain diamond at the surface. Water pressure exhibited diurnal changes in antiphase with velocity. Dye monitoring in the borehole revealed stagnant basal water for nearly 2 weeks. The interpretation of initial connection to an isolated basal cavity is corroborated by the thermal signature of borehole water during hot water drilling. Measurement-based estimates of cavity size are on the order of cubic meters, and analysis indicates that small changes in its volume could induce the observed pressure variations. It is found that longitudinal coupling effects are unable to force necessary volume changes at the site. Sliding-driven basal cavity opening and elastic uplift from load transfer are plausible mechanisms controlling pressure variations. Elastic uplift requires forcing from a hydraulically connected reach, which observations suggest must be relatively small and in close proximity to the isolated cavity.

Public health recommendations do not distinguish between vitamin D2 and vitamin D3, yet disagreement exists on whether these two forms should be considered equivalent. The objective of the present study was to evaluate the effect of a daily physiological dose of vitamin D2 or vitamin D3 on 25-hydroxyvitamin D (25(OH)D) status over the winter months in healthy adults living in Dunedin, New Zealand (latitude 46°S). Participants aged 18–50 years were randomly assigned to 25 μg (1000 IU) vitamin D3 (n 32), 25 μg (1000 IU) vitamin D2 (n 31) or placebo (n 32) daily for 25 weeks beginning at the end of summer. A per-protocol approach, which included ≥ 90 % supplement compliance, was used for all analyses. Serum 25-hydroxyvitamin D3 (25(OH)D3), 25-hydroxyvitamin D2 (25(OH)D2) and parathyroid hormone (PTH) were measured at baseline and at 4, 8, 13 and 25 weeks. Geometric mean total serum 25(OH)D concentrations (sum of 25(OH)D2 and 25(OH)D3) at baseline was 80 nmol/l. After 25 weeks, participants randomised to D2 and placebo had a significant reduction in serum 25(OH)D3 concentrations over the winter months compared with vitamin D3-supplemented participants (both P< 0·001). Supplementation with vitamin D2 increased serum 25(OH)D2 but produced a 9 (95 % CI 1, 17) nmol/l greater decline in the 25(OH)D3 metabolite compared with placebo (P< 0·036). Overall, total serum 25(OH)D concentrations were 21 (95 % CI 14, 30) nmol/l lower in participants receiving vitamin D2 compared with those receiving D3 (P< 0·001), among whom total serum 25(OH)D concentrations remained unchanged. No intervention-related changes in PTH were observed. Daily supplementation of vitamin D3 was more effective than D2; however, the functional consequence of the differing metabolic response warrants further investigation.

A modified Shigella—Salmonella medium in semi-solid agar was shown to inhibit the spread of most faecal organisms through a Craigie tube, while selectively allowing the passage of Salmonella.

A medium for routine use is described.

Over a period of 3 years, in this laboratory, 90% of specimens from which salmonellas were isolated gave positive results with this medium. Over 40% of these specimens would have been reported as negative if the method had not been in use. However, 10% would have been missed if this method alone had been used. It should therefore be used in conjunction with other culture methods, of which direct plating on SS agar was the most successful in this series.

Newcastle disease virus has been shown to survive when airborne in small particles, both in the laboratory and in the open air. Field outbreaks have been studied and viable virus has been recovered from the open air short distances downwind of infected premises. Vaccination of birds leads to a great reduction in the amount of virus liberated into the air.

A theorem is derived for the hydrodynanuc image of an axially symmetric slow viscous (Stokes) flow in a sphere which is impermeable and free of shear stress. A second theorem establishes a sense in which such a flow past an arbitrary rigid surface or shear-free sphere becomes, on inversion in an arbitrary sphere with its centre on the axis of symmetry, a flow past the rigid or shear-free inverse of that surface or sphere.

The theorems are used to simplify the proofs of a number of known results for images of point singularities in plane and spherical rigid and free boundaries, and for a pair of bubbles rising steadily in line in a viscous fluid. They also give for the first time accurate numerical solutions for the velocities of each of a larger number of spherical bubbles rising quasi-steadily in line. These enable one to assess the accuracy of simple approximations to those velocities.

A simple method of reducing a parabolic partial differential equation to canonical form if it has only one term involving second derivatives is the following: find the general solution of the first-order equation obtained by ignoring that term and then seek a solution of the original equation which is a function of one more independent variable. Special cases of the method have been given before, but are not well known. Applications occur in fluid mechanics and the theory of finance, where the Black-Scholes equation yields to the method, and where the variable corresponding to time appears to run backwards, but there is an information-theoretic reason why it should.

When a gas bubble rises in a surfactant solution, the velocity field and the distribution of surfactant affect each other. This paper gives the theory for small Reynolds and internal Péclet numbers if the surfactant is gaseous or volatile, if its mass flux across the bubble and around its surface dominates its mass flux through the bulk liquid, and if slowness of both adsorption and convective diffusion must be allowed for.

The theory is tested on the experiments of Kelsall et al. (J. Chem. Soc. Faraday Trans., vol. 92, 1996, p. 3879). Their bubbles rose as expected in a pure liquid until the apparatus was opened to the atmosphere. That significantly slowed the bubbles down. The effect is so sensitive to small concentrations of slowly adsorbing or reacting surfactants that atmospheric carbon dioxide could have caused it, even though it alters the equilibrium surface tension by less than four parts per million in pure air.

There are still unexplained discrepancies between experiment and theory. Additional experiments are suggested that would help to explain them.