Trends in reported flooding in the UK: 1884-2013

A long term dataset of reported flooding based on reports from the UK Meteorological Office and the UK Centre for Ecology and Hydrology is described. This is possibly a unique dataset as the authors are unaware of any other 100+ year records of flood events and their consequences on a national scale. Flood events are classified by severity based upon qualitative descriptions. There is an increase in the number of reported flood events over time associated with an increased exposure to flooding as floodplain areas were developed. The data was de-trended for exposure, using population and dwelling house data. The adjusted record shows no trend in reported flooding over time, but there is significant decade to decade variability. This study opens a new approach considering flood occurrence over a long timescale using reported information (and thus likely effects on society) rather than just considering trends in extreme hydrological conditions.<br/

A note on the Cops & Robber game on graphs embedded in non-orientable surfaces

The Cops and Robber game is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if they can catch the robber. The minimum number of cops needed to win on a graph is called its cop number. It is known that the cop number of a graph embedded on a surface $X$ of genus $g$ is at most $3g/2 + 3$, if $X$ is orientable (Schroeder 2004), and at most $2g+1$, otherwise (Nowakowski & Schroeder 1997). We improve the bounds for non-orientable surfaces by reduction to the orientable case using covering spaces. As corollaries, using Schroeder's results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3; the cop number of graphs embeddable in the Klein Bottle is at most 4, and an upper bound is $3g/2 + 3/2$ for all other $g$.Comment: 5 pages, 1 figur

Estimating the long-term historic evolution of exposure to flooding of coastal populations

Coastal managers face the task of assessing and managing flood risk. This requires knowledge of the area of land, the number of people, properties and other infrastructure potentially affected by floods. Such analyses are usually static; i.e. they only consider a snapshot of the current situation. This misses the opportunity to learn about the role of key drivers of historical changes in flood risk, such as development and population rise in the coastal flood plain and sea-level rise.In this paper, we develop and apply a method to analyse the temporal evolution of residential population exposure to coastal flooding. It uses readily available data in a GIS environment. We examine how population and sea level change modify exposure over two centuries in two neighbouring coastal sites: Portsea and Hayling Islands on the UK south coast. The analysis shows that flood exposure changes as a result of increases in population, changes in coastal population density and sea level rise. The results indicate that to date, population change is the dominant driver of the increase in exposure to flooding in the study sites, but climate change may outweigh this in the future. A full analysis of flood risk is not possible as data on historic defences and wider vulnerability are not available. Hence, the historic evolution of flood exposure is as close as we can get to a historic evolution of flood risk.The method is applicable anywhere that suitable floodplain geometry, sea level and population datasets are available and could be widely applied, and will help inform coastal managers of the time evolution in coastal flood drivers<br/

Entanglements in polymer nanocomposites containing spherical nanoparticles

We investigate the polymer packing around nanoparticles and polymer/nanoparticle topological constraints (entanglements) in nanocomposites containing spherical nanoparticles in comparison to pure polymer melts using molecular dynamics (MD) simulations. The polymer–nanoparticle attraction leads to good dispersion of nanoparticles. We observe an increase in the number of topological constraints (decrease of total entanglement length Ne with nanoparticle loading in the polymer matrix) in nanocomposites due to nanoparticles, as evidenced by larger contour lengths of the primitive paths. An increase of the nanoparticle radius reduces the polymer–particle entanglements. These studies demonstrate that the interaction between polymers and nanoparticles does not affect the total entanglement length because in nanocomposites with small nanoparticles, the polymer–nanoparticles topological constraints dominat

Polymer conformations in polymer nanocomposites containing spherical nanoparticles

We investigate the effect of various spherical nanoparticles on chain dimensions in polymer melts for high nanoparticle loading which is larger than the percolation threshold, using molecular dynamics simulations. We show that polymer chains are unperturbed by the presence of repulsive nanoparticles. In contrast polymer chains can be perturbed by the presence of attractive nanoparticles when the polymer radius of gyration is larger than the nanoparticle radius. At high nanoparticle loading, chains can be stretched and flattened by the nanoparticles, even oligomers can expand under the presence of attractive nanoparticles of very small size

Feedback stabilization and Lyapunov functions

International audienceGiven a locally defined, nondifferentiable but Lipschitz Lyapunov function, we construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A further result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish a robustness property of the feedback relative to measurement error commensurate with the sampling rate of the control im- plementation scheme

An almost sure limit theorem for super-Brownian motion

We establish an almost sure scaling limit theorem for super-Brownian motion on $\mathbb{R}^d$ associated with the semi-linear equation $u_t = {1/2}\Delta u +\beta u-\alpha u^2$, where $\alpha$ and $\beta$ are positive constants. In this case, the spectral theoretical assumptions that required in Chen et al (2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in $\mathbb{R}^d$.Comment: 14 page

Low Timing Jitter Detector for Gigahertz Quantum Key Distribution

A superconducting single-photon detector based on a niobium nitride nanowire is demonstrated in an optical-fibre-based quantum key distribution test bed operating at a clock rate of 3.3 GHz and a transmission wavelength of 850 nm. The low jitter of the detector leads to significant reduction in the estimated quantum bit error rate and a resultant improvement in the secrecy efficiency compared to previous estimates made by use of silicon single-photon avalanche detectors.Comment: 11 pages, including 2 figure