A fresh perspective on canonical extensions for bounded lattices

This paper presents a novel treatment of the canonical extension of a bounded lattice, in the spirit of thetheory of natural dualities. At the level of objects, this can be achieved by exploiting the topological representation due to M. Ploscica, and the canonical extension can be obtained in the same manner as can be done in the distributive case by exploiting Priestley duality. To encompass both objects and morphismsthe Ploscica representation is replaced by a duality due to Allwein and Hartonas, recast in the style of Ploscica's paper. This leads to a construction of canonical extension valid for all bounded lattices,which is shown to be functorial, with the property that the canonical extension functor decomposes asthe composite of two functors, each of which acts on morphisms by composition, in the manner of hom-functors

The apparent anticorrelation between the mass opacity of interstellar dust and the surface density of interstellar gas

Recent analyses of Herschel observations suggest that in nearby disc galaxies the dust mass opacity at 500μm⁠, κ500, decreases with increasing gas surface density, ΣISM. This apparent anticorrelation between κ500 and ΣISM is opposite to the behaviour expected from theoretical dust evolution models; in such models, dust in denser, cooler regions (i.e. regions of increased ΣISM) tends to grow and therefore to have increased κ500. We show, using a toy model, that the presence of a range of dust temperatures along the line of sight can lead to spuriously low estimated values of κ500. If in regions of higher ΣISM the range of dust temperatures extends to lower values (as seems likely), the magnitude of this effect may be sufficient to explain the apparent anticorrelation between κ500 and ΣISM. Therefore there may not be any need for spatial variation in the intrinsic dust properties that run counter to theoretical expectations

Molecular line signatures of cloud-cloud collisions

Collisions between interstellar gas clouds are potentially an important mechanism for triggering star formation. This is because they are able to rapidly generate large masses of dense gas. Observationally, cloud collisions are often identified in position-velocity (PV) space through bridging features between intensity peaks, usually of CO emission. Using a combination of hydrodynamical simulations, time-dependent chemistry, and radiative transfer, we produce synthetic molecular line observations of overlapping clouds that are genuinely colliding, and overlapping clouds that are just chance superpositions. Molecules tracing denser material than CO, such as NH$_3$ and HCN, reach peak intensity ratios of $0.5$ and $0.2$ with respect to CO in the `bridging feature' region of PV space for genuinely colliding clouds. For overlapping clouds that are just chance superpositions, the peak NH$_3$ and HCN intensities are co-located with the CO intensity peaks. This represents a way of confirming cloud collisions observationally, and distinguishing them from chance alignments of unrelated material.Comment: 7 pages, 4 figures, MNRAS accepte

The impact of individualised funding on the wellbeing of mothers raising an autistic child in Aotearoa New Zealand

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Fluctuations of 1/f1/f noise and the low frequency cutoff paradox

Recent experiments on blinking quantum dots and weak turbulence in liquid crystals reveal the fundamental connection between $1/f$ noise and power law intermittency. The non-stationarity of the process implies that the power spectrum is random -- a manifestation of weak ergodicity breaking. Here we obtain the universal distribution of the power spectrum, which can be used to identify intermittency as the source of the noise. We solve an outstanding paradox on the non integrability of $1/f$ noise and the violation of Parseval's theorem. We explain why there is no physical low frequency cutoff and therefore cannot be found in experiments.Comment: 5 pages, 2 figures, supplementary material (4 pages

Optimal molecular alignment and orientation through rotational ladder climbing

We study the control by electromagnetic fields of molecular alignment and orientation, in a linear, rigid rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the spectrum and acts by resonantly exciting the rotation of the molecule progressively from the ground state, i.e., by rotational ladder climbing. This mechanism is present not only when maximizing orientation or alignment, but also when using prescribed target states that simultaneously optimize the efficiency of orientation/alignment and its duration. The extension of the optimization method to consider a finite rotational temperature is also presented.Comment: 14 pages, 12 figure

Line emission from filaments in molecular clouds

Filamentary structures are often identified in column density maps of molecular clouds, and appear to be important for both low- and high-mass star formation. Theoretically, these structures are expected to form in regions where the supersonic cloud-scale turbulent velocity field converges. While this model of filament formation successfully reproduces several of their properties derived from column densities, it is unclear whether it can also reproduce their kinematic features. We use a combination of hydrodynamical, chemical and radiative transfer modelling to predict the emission properties of these dynamically-forming filaments in the $^{13}$CO, HCN and N$_2$H$^+$ $J=1-0$ rotational lines. The results are largely in agreement with observations; in particular, line widths are typically subsonic to transonic, even for filaments which have formed from highly supersonic inflows. If the observed filaments are formed dynamically, as our results suggest, no equilibrium analysis is possible, and simulations which presuppose the existence of a filament are likely to produce unrealistic results.Comment: 9 pages, 9 figures. MNRAS accepte

The state of the upper mantle beneath Southern Africa

We present a new upper mantle seismic model for southern Africa based on the fitting of a large (3622 waveforms) multi-mode surface wave data set with propagation paths significantly shorter (≤ 6000 km) than those in globally-derived surface wave models. The seismic lithosphere beneath the cratonic region of southern Africa in this model is about 175 ± 25 km thick, consistent with other recent surface wave models, but significantly thinner than indicated by teleseismic body-wave tomography. We determine the in situ geotherm from kimberlite nodules from beneath the same region and find the thermal lithosphere model that best fits the nodule data has a mechanical boundary layer thickness of 186 km and a thermal lithosphere thickness of 204 km, in very good agreement with the seismic measurement. The shear wave velocity determined from analyzes of the kimberlite nodule compositions agree with the seismic shear wave velocity to a depth of not, vert, similar150 km. However, the shear wave velocity decrease at the base of the lid seen in the seismic model does not correspond to a change in mineralogy. Recent experimental studies of the shear wave velocity in olivine as a function of temperature and period of oscillation demonstrate that this wave speed decrease can result from grain boundary relaxation at high temperatures at the period of seismic waves. This decrease in velocity occurs where the mantle temperature is close to the melting temperature (within not, vert, similar100 °C)