On the strong uniqueness of some finite dimensional Dirichlet operators

We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.

Observations of urban boundary layer structure during a strong urban heat island event

It has long been known that the urban surface energy balance is different to that of a rural surface, and that heating of the urban surface after sunset gives rise to the Urban Heat Island (UHI). Less well known is how flow and turbulence structure above the urban surface are changed during different phases of the urban boundary layer (UBL). This paper presents new observations above both an urban and rural surface and investigates how much UBL structure deviates from classical behaviour. A 5-day, low wind, cloudless, high pressure period over London, UK, was chosen for analysis, during which there was a strong UHI. Boundary layer evolution for both sites was determined by the diurnal cycle in sensible heat flux, with an extended decay period of approximately 4 h for the convective UBL. This is referred to as the “Urban Convective Island” as the surrounding rural area was already stable at this time. Mixing height magnitude depended on the combination of regional temperature profiles and surface temperature. Given the daytime UHI intensity of 1.5∘C, combined with multiple inversions in the temperature profile, urban and rural mixing heights underwent opposite trends over the period, resulting in a factor of three height difference by the fifth day. Nocturnal jets undergoing inertial oscillations were observed aloft in the urban wind profile as soon as the rural boundary layer became stable: clear jet maxima over the urban surface only emerged once the UBL had become stable. This was due to mixing during the Urban Convective Island reducing shear. Analysis of turbulent moments (variance, skewness and kurtosis) showed “upside-down” boundary layer characteristics on some mornings during initial rapid growth of the convective UBL. During the “Urban Convective Island” phase, turbulence structure still resembled a classical convective boundary layer but with some influence from shear aloft, depending on jet strength. These results demonstrate that appropriate choice of Doppler lidar scan patterns can give detailed profiles of UBL flow. Insights drawn from the observations have implications for accuracy of boundary conditions when simulating urban flow and dispersion, as the UBL is clearly the result of processes driven not only by local surface conditions but also regional atmospheric structure.

Late Quaternary environmental change in the interior South American tropics: new insight from leaf wax stable isotopes

Stable isotope analysis of leaf waxes in a sediment core from Laguna La Gaiba, a shallow lake located at the Bolivian margin of the Pantanal wetlands, provides new perspective on vegetation and climate change in the lowland interior tropics of South America over the past 40,000 years. The carbon isotopic compositions (δ13C) of long-chain n-alkanes reveal large shifts between C3-and C4-dominated vegetation communities since the last glacial period, consistent with landscape reconstructions generated with pollen data from the same sediment core. Leaf wax δ13C values during the last glacial period reflect an open landscape composed of C4grasses and C3herbs from 41–20ka. A peak in C4abundance during the Last Glacial Maximum (LGM, ∼21ka) suggests drier or more seasonal conditions relative to the earlier glacial period, while the development of a C3-dominated forest community after 20 ka points to increased humidity during the last deglaciation. Within the Holocene, large changes in the abundance of C4 vegetation indicate a transition from drier or more seasonal conditions during the early/mid-Holocene to wetter conditions in the late Holocene coincident with increasing austral summer insolation. Strong negative correlations between leaf wax δ13C and δD values over the entire record indicate that the majority of variability in leaf wax δD at this site can be explained by variability in the magnitude of biosynthetic fractionation by different vegetation types rather than changes in meteoric water δD signatures. However, positive δD deviations from the observed δ13C–δD trends are consistent with more enriched source water and drier or more seasonal conditions during the early/mid-Holocene and LGM. Overall, our record adds to evidence of varying influence of glacial boundary conditions and orbital forcing on South American Summer Monsoon precipitation in different regions of the South American tropics. Moreover, the relationships between leaf wax stable isotopes and pollen data observed at this site underscore the complementary nature of pollen and leaf wax δ13C data for reconstructing past vegetation changes and the potentially large effects of such changes on leaf wax δD signatures.

“Pussy cat, pussy cat where have you been..?” Evaluating the use of stable isotopes, radiogenic isotopes and trace elements for investigating the ecology of Panthera leo

1. Understanding the behaviour and ecology of large carnivores is becoming increasingly important as the list of endangered species grows, with felids such as Panthera leo in some locations heading dangerously close to extinction in the wild. In order to have more reliable and effective tools to understand animal behaviour, movement and diet, we need to develop novel, integrated approaches and effective techniques to capture a detailed profile of animal foraging and movement patterns. 2. Ecological studies have shown considerable interest in using stable isotope methods, both to investigate the nature of animal feeding habits, and to map their geographical location. However, recent work has suggested that stable isotope analyses of felid fur and bone is very complex and does not correlate directly with the isotopic composition of precipitation (and hence geographical location). 3. We present new data that suggest these previous findings may be atypical, and demonstrate that isotope analyses of Felidae are suitable for both evaluating dietary inputs and establishing geo-location as they have strong environmental referents to both food and water. These data provide new evidence of an important methodology that can be applied to the family Felidae for future research in ecology, conservation, wildlife forensics and archaeological science.