Evolution PDEs and augmented eigenfunctions. half line.

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is no suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of augmented eigenfunctions, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.

Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

New insights into the compressibility and high-pressure stability of Ni(CN)2: a combined study of neutron diffraction, Raman spectroscopy, and inelastic neutron scattering

Nickel cyanide is a layered material showing markedly anisotropic behaviour. High-pressure neutron diffraction measurements show that at pressures up to 20.1 kbar, compressibility is much higher in the direction perpendicular to the layers, c, than in the plane of the strongly chemically bonded metal-cyanide sheets. Detailed examination of the behaviour of the tetragonal lattice parameters, a and c, as a function of pressure reveal regions in which large changes in slope occur, for example, in c(P) at 1 kbar. The experimental pressure dependence of the volume data is fitted to a bulk modulus, B0, of 1050 (20) kbar over the pressure range 0–1 kbar, and to 124 (2) kbar over the range 1–20.1 kbar. Raman spectroscopy measurements yield additional information on how the structure and bonding in the Ni(CN)2 layers change with pressure and show that a phase change occurs at about 1 kbar. The new high-pressure phase, (Phase PII), has ordered cyanide groups with sheets of D4h symmetry containing Ni(CN)4 and Ni(NC)4 groups. The Raman spectrum of phase PII closely resembles that of the related layered compound, Cu1/2Ni1/2(CN)2, which has previously been shown to contain ordered C≡N groups. The phase change, PI to PII, is also observed in inelastic neutron scattering studies which show significant changes occurring in the phonon spectra as the pressure is raised from 0.3 to 1.5 kbar. These changes reflect the large reduction in the interlayer spacing which occurs as Phase PI transforms to Phase PII and the consequent increase in difficulty for out-of-plane atomic motions. Unlike other cyanide materials e.g. Zn(CN)2 and Ag3Co(CN)6, which show an amorphization and/or a decomposition at much lower pressures (~100 kbar), Ni(CN)2 can be recovered after pressurising to 200 kbar, albeit in a more ordered form.

Climatology and variability of trace gases in extratropical double-tropopause regions from MLS, HIRDLS, and ACE-FTS measurements

Upper tropospheric and lower stratospheric measurements from the Aura Microwave Limb Sounder (MLS), the Aura High Resolution Dynamics Limb Sounder (HIRDLS), and the Atmospheric Chemistry Experiment-Fourier transform spectrometer (ACE-FTS) are used to present the first global climatological comparison of extratropical, nonpolar trace gas distributions in double-tropopause (DT) and single-tropopause (ST) regions. Stratospheric tracers, O3, HNO3, and HCl, have lower mixing ratios ∼2–8 km above the primary (lowermost) tropopause in DT than in ST regions in all seasons, with maximum Northern Hemisphere (NH) differences near 50% in winter and 30% in summer. Southern Hemisphere winter differences are somewhat smaller, but summer differences are similar in the two hemispheres. H2O in DT regions of both hemispheres shows strong negative anomalies in November through February and positive anomalies in July through October, reflecting the strong seasonal cycle in H2O near the tropical tropopause. CO and other tropospheric tracers examined have higher DT than ST values 2–7 km above the primary tropopause, with the largest differences in winter. Large DT-ST differences extend to high NH latitudes in fall and winter, with longitudinal maxima in regions associated with enhanced wave activity and subtropical jet variations. Results for O3 and HNO3 agree closely between MLS and HIRDLS, and differences from ACE-FTS are consistent with its sparse and irregular midlatitude sampling. Consistent signatures in climatological trace gas fields provide strong evidence that transport from the tropical upper troposphere into the layer between double tropopauses is an important pathway for stratosphere-troposphere exchange.

A new regime of carbon counting: the practices and politics of accounting for everyday carbon through C02e

Inspired by the commercial desires of global brands and retailers to access the lucrative green consumer market, carbon is increasingly being counted and made knowable at the mundane sites of everyday production and consumption, from the carbon footprint of a plastic kitchen fork to that of an online bank account. Despite the challenges of counting and making commensurable the global warming impact of a myriad of biophysical and societal activities, this desire to communicate a product or service's carbon footprint has sparked complicated carbon calculative practices and enrolled actors at literally every node of multi-scaled and vastly complex global supply chains. Against this landscape, this paper critically analyzes the counting practices that create the ‘e’ in ‘CO2e’. It is shown that, central to these practices are a series of tools, models and databases which, in building upon previous work (Eden, 2012 and Star and Griesemer, 1989) we conceptualize here as ‘boundary objects’. By enrolling everyday actors from farmers to consumers, these objects abstract and stabilize greenhouse gas emissions from their messy material and social contexts into units of CO2e which can then be translated along a product's supply chain, thereby establishing a new currency of ‘everyday supply chain carbon’. However, in making all greenhouse gas-related practices commensurable and in enrolling and stabilizing the transfer of information between multiple actors these objects oversee a process of simplification reliant upon, and subject to, a multiplicity of approximations, assumptions, errors, discrepancies and/or omissions. Further the outcomes of these tools are subject to the politicized and commercial agendas of the worlds they attempt to link, with each boundary actor inscribing different meanings to a product's carbon footprint in accordance with their specific subjectivities, commercial desires and epistemic framings. It is therefore shown that how a boundary object transforms greenhouse gas emissions into units of CO2e, is the outcome of distinct ideologies regarding ‘what’ a product's carbon footprint is and how it should be made legible. These politicized decisions, in turn, inform specific reduction activities and ultimately advance distinct, specific and increasingly durable transition pathways to a low carbon society.

The water vapour continuum in near-infrared windows – current understanding and prospects for its inclusion in spectroscopic databases

Spectroscopic catalogues, such as GEISA and HITRAN, do not yet include information on the water vapour continuum that pervades visible, infrared and microwave spectral regions. This is partly because, in some spectral regions, there are rather few laboratory measurements in conditions close to those in the Earth’s atmosphere; hence understanding of the characteristics of the continuum absorption is still emerging. This is particularly so in the near-infrared and visible, where there has been renewed interest and activity in recent years. In this paper we present a critical review focusing on recent laboratory measurements in two near-infrared window regions (centred on 4700 and 6300 cm−1) and include reference to the window centred on 2600 cm−1 where more measurements have been reported. The rather few available measurements, have used Fourier transform spectroscopy (FTS), cavity ring down spectroscopy, optical-feedback – cavity enhanced laser spectroscopy and, in very narrow regions, calorimetric interferometry. These systems have different advantages and disadvantages. Fourier Transform Spectroscopy can measure the continuum across both these and neighbouring windows; by contrast, the cavity laser techniques are limited to fewer wavenumbers, but have a much higher inherent sensitivity. The available results present a diverse view of the characteristics of continuum absorption, with differences in continuum strength exceeding a factor of 10 in the cores of these windows. In individual windows, the temperature dependence of the water vapour self-continuum differs significantly in the few sets of measurements that allow an analysis. The available data also indicate that the temperature dependence differs significantly between different near-infrared windows. These pioneering measurements provide an impetus for further measurements. Improvements and/or extensions in existing techniques would aid progress to a full characterisation of the continuum – as an example, we report pilot measurements of the water vapour self-continuum using a supercontinuum laser source coupled to an FTS. Such improvements, as well as additional measurements and analyses in other laboratories, would enable the inclusion of the water vapour continuum in future spectroscopic databases, and therefore allow for a more reliable forward modelling of the radiative properties of the atmosphere. It would also allow a more confident assessment of different theoretical descriptions of the underlying cause or causes of continuum absorption.