Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

A global empirical system for probabilistic seasonal climate prediction

Preparing for episodes with risks of anomalous weather a month to a year ahead is an important challenge for governments, non-governmental organisations, and private companies and is dependent on the availability of reliable forecasts. The majority of operational seasonal forecasts are made using process-based dynamical models, which are complex, computationally challenging and prone to biases. Empirical forecast approaches built on statistical models to represent physical processes offer an alternative to dynamical systems and can provide either a benchmark for comparison or independent supplementary forecasts. Here, we present a simple empirical system based on multiple linear regression for producing probabilistic forecasts of seasonal surface air temperature and precipitation across the globe. The global CO2-equivalent concentration is taken as the primary predictor; subsequent predictors, including large-scale modes of variability in the climate system and local-scale information, are selected on the basis of their physical relationship with the predictand. The focus given to the climate change signal as a source of skill and the probabilistic nature of the forecasts produced constitute a novel approach to global empirical prediction. Hindcasts for the period 1961–2013 are validated against observations using deterministic (correlation of seasonal means) and probabilistic (continuous rank probability skill scores) metrics. Good skill is found in many regions, particularly for surface air temperature and most notably in much of Europe during the spring and summer seasons. For precipitation, skill is generally limited to regions with known El Niño–Southern Oscillation (ENSO) teleconnections. The system is used in a quasi-operational framework to generate empirical seasonal forecasts on a monthly basis.

Systematic and random errors between collocated satellite ice water path observations

There remains large disagreement between ice-water path (IWP) in observational data sets, largely because the sensors observe different parts of the ice particle size distribution. A detailed comparison of retrieved IWP from satellite observations in the Tropics (!30 " latitude) in 2007 was made using collocated measurements. The radio detection and ranging(radar)/light detection and ranging (lidar) (DARDAR) IWP data set, based on combined radar/lidar measurements, is used as a reference because it provides arguably the best estimate of the total column IWP. For each data set, usable IWP dynamic ranges are inferred from this comparison. IWP retrievals based on solar reflectance measurements, in the moderate resolution imaging spectroradiometer (MODIS), advanced very high resolution radiometer–based Climate Monitoring Satellite Applications Facility (CMSAF), and Pathfinder Atmospheres-Extended (PATMOS-x) datasets, were found to be correlated with DARDAR over a large IWP range (~20–7000 g m -2 ). The random errors of the collocated data sets have a close to lognormal distribution, and the combined random error of MODIS and DARDAR is less than a factor of 2, which also sets the upper limit for MODIS alone. In the same way, the upper limit for the random error of all considered data sets is determined. Data sets based on passive microwave measurements, microwave surface and precipitation products system (MSPPS), microwave integrated retrieval system (MiRS), and collocated microwave only (CMO), are largely correlated with DARDAR for IWP values larger than approximately 700 g m -2 . The combined uncertainty between these data sets and DARDAR in this range is slightly less MODIS-DARDAR, but the systematic bias is nearly an order of magnitude.

High performance polyester-based materials

Biaxially oriented films produced from semi-crystalline, semi-aromatic polyesters are utilised extensively as components within various applications, including the specialist packaging, flexible electronic and photovoltaic markets. However, the thermal performance of such polyesters, specifically poly(ethylene terephthalate) (PET) and poly(ethylene-2,6-naphthalate) (PEN), is inadequate for several applications that require greater dimensional stability at higher operating temperatures. The work described in this project is therefore primarily focussed upon the copolymerisation of rigid comonomers with PET and PEN, in order to produce novel polyester-based materials that exhibit superior thermomechanical performance, with retention of crystallinity, to achieve biaxial orientation. Rigid biphenyldiimide comonomers were readily incorporated into PEN and poly(butylene-2,6-naphthalate) (PBN) via a melt-polycondensation route. For each copoly(ester-imide) series, retention of semi-crystalline behaviour is observed throughout entire copolymer composition ratios. This phenomenon may be rationalised by cocrystallisation between isomorphic biphenyldiimide and naphthalenedicarboxylate residues, which enables statistically random copolymers to melt-crystallise despite high proportions of imide sub-units being present. In terms of thermal performance, the glass transition temperature, Tg, linearly increases with imide comonomer content for both series. This facilitated the production of several high performance PEN-based biaxially oriented films, which displayed analogous drawing, barrier and optical properties to PEN. Selected PBN copoly(ester-imide)s also possess the ability to either melt-crystallise, or form a mesophase from the isotropic state depending on the applied cooling rate. An equivalent synthetic approach based upon isomorphic comonomer crystallisation was subsequently applied to PET by copolymerisation with rigid diimide and Kevlar®-type amide comonomers, to afford several novel high performance PET-based copoly(ester-imide)s and copoly(ester-amide)s that all exhibited increased Tgs. Retention of crystallinity was achieved in these copolymers by either melt-crystallisation or thermal annealing. The initial production of a semi-crystalline, PET-based biaxially oriented film with a Tg in excess of 100 °C was successful, and this material has obvious scope for further industrial scale-up and process development.

Biases in comparative analyses of extinction risk: mind the gap

1. Comparative analyses are used to address the key question of what makes a species more prone to extinction by exploring the links between vulnerability and intrinsic species’ traits and/or extrinsic factors. This approach requires comprehensive species data but information is rarely available for all species of interest. As a result comparative analyses often rely on subsets of relatively few species that are assumed to be representative samples of the overall studied group. 2. Our study challenges this assumption and quantifies the taxonomic, spatial, and data type biases associated with the quantity of data available for 5415 mammalian species using the freely available life-history database PanTHERIA. 3. Moreover, we explore how existing biases influence results of comparative analyses of extinction risk by using subsets of data that attempt to correct for detected biases. In particular, we focus on links between four species’ traits commonly linked to vulnerability (distribution range area, adult body mass, population density and gestation length) and conduct univariate and multivariate analyses to understand how biases affect model predictions. 4. Our results show important biases in data availability with c.22% of mammals completely lacking data. Missing data, which appear to be not missing at random, occur frequently in all traits (14–99% of cases missing). Data availability is explained by intrinsic traits, with larger mammals occupying bigger range areas being the best studied. Importantly, we find that existing biases affect the results of comparative analyses by overestimating the risk of extinction and changing which traits are identified as important predictors. 5. Our results raise concerns over our ability to draw general conclusions regarding what makes a species more prone to extinction. Missing data represent a prevalent problem in comparative analyses, and unfortunately, because data are not missing at random, conventional approaches to fill data gaps, are not valid or present important challenges. These results show the importance of making appropriate inferences from comparative analyses by focusing on the subset of species for which data are available. Ultimately, addressing the data bias problem requires greater investment in data collection and dissemination, as well as the development of methodological approaches to effectively correct existing biases.

A morphometric comparison of the Namib and southwest Kalahari dunefields using ASTER GDEM data

The increased availability of digital elevation models and satellite image data enable testing of morphometric relationships between sand dune variables (dune height, spacing and equivalent sand thickness), which were originally established using limited field survey data. These long-established geomorphological hypotheses can now be tested against very much larger samples than were possible when available data were limited to what could be collected by field surveys alone. This project uses ASTER Global Digital Elevation Model (GDEM) data to compare morphometric relationships between sand dune variables in the southwest Kalahari dunefield to those of the Namib Sand Sea, to test whether the relationships found in an active sand sea (Namib) also hold for the fixed dune system of the nearby southwest Kalahari. The data show significant morphometric differences between the simple linear dunes of the Namib sand sea and the southwest Kalahari; the latter do not show the expected positive relationship between dune height and spacing. The southwest Kalahari dunes show a similar range of dune spacings, but they are less tall, on average, than the Namib sand sea dunes. There is a clear spatial pattern to these morphometric data; the tallest and most closely spaced dunes are towards the southeast of the Kalahari dunefield; and this is where the highest values of equivalent sand thickness result. We consider the possible reasons for the observed differences and highlight the need for more studies comparing sand seas and dunefields from different environmental settings.