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    ABSTRACT: A resolution of the St Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.
    Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 12/2011; 369(1956):4913-31. DOI:10.1098/rsta.2011.0065
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    ABSTRACT: Aim  Comparative evidence for phylogenetic niche conservatism – the tendency for lineages to retain their ancestral niches over long time scales – has so far been mixed, depending on spatial and taxonomic scale. We quantify and compare conservatism in the climatic factors defining range boundaries in extant continental mammals and amphibians in order to identify those factors that are most evolutionarily conserved, and thus hypothesized to have played a major role in determining the geographic distributions of many species. We also test whether amphibians show stronger signals of climatic niche conservatism, as expected from their greater physiological sensitivity and lower dispersal abilities.Location  Global; continental land masses excluding Antarctica.Methods  We used nearly complete global distributional databases to estimate the climatic niche conservatism in extant continental mammals and amphibians. We characterized the climatic niche of each species by using a suite of variables and separately investigate conservatism in each variable using both taxonomic and phylogenetic approaches. Finally, we explored the spatial, taxonomic and phylogenetic patterns in recent climatic niche evolution.Results  Amphibians and mammals showed congruent patterns of conservatism in cold tolerance, with assemblages of escapee species (i.e. those escaping most from the climatic constraints of their ancestors) aggregated in the North Temperate Zone.Main conclusions  The relative strength of climatic niche conservatism varies across the variables tested, but is strongest for cold tolerance in both mammals and amphibians. Despite the apparent conservatism in this variable, there is also a strong signal of recent evolutionary shifts in cold tolerance in assemblages inhabiting the North Temperate Zone. Our results thus indicate that distribution patterns of both taxa are influenced by both niche conservatism and niche evolution.
    Journal of Biogeography 11/2011; 38(12):2237 - 2247. DOI:10.1111/j.1365-2699.2011.02570.x
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    ABSTRACT: a b s t r a c t Accurate representation of geostrophic and hydrostatic balance is an essential requirement for numerical modelling of geophysical flows. Potentially, unstructured mesh numerical methods offer significant ben-efits over conventional structured meshes, including the ability to conform to arbitrary bounding topog-raphy in a natural manner and the ability to apply dynamic mesh adaptivity. However, there is a need to develop robust schemes with accurate representation of physical balance on arbitrary unstructured meshes. We discuss the origin of physical balance errors in a finite element discretisation of the Navier–Stokes equations using the fractional timestep pressure projection method. By considering the Helmholtz decomposition of forcing terms in the momentum equation, it is shown that the components of the buoyancy and Coriolis accelerations that project onto the non-divergent velocity tendency are the small residuals between two terms of comparable magnitude. Hence there is a potential for significant injection of imbalance by a numerical method that does not compute these residuals accurately. This observation is used to motivate a balanced pressure decomposition method whereby an additional ''bal-anced pressure'' field, associated with buoyancy and Coriolis accelerations, is solved for at increased accu-racy and used to precondition the solution for the dynamical pressure. The utility of this approach is quantified in a fully non-linear system in exact geostrophic balance. The approach is further tested via quantitative comparison of unstructured mesh simulations of the thermally driven rotating annulus against laboratory data. Using a piecewise linear discretisation for velocity and pressure (a stabilised P 1 P 1 discretisation), it is demonstrated that the balanced pressure decomposition method is required for a physically realistic representation of the system.
    Ocean Modelling 04/2011; 39(3). DOI:10.1016/j.ocemod.2011.04.009
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    ABSTRACT: In organic solar cells, high open circuit voltages may be obtained by choosing materials with a high offset between the donor highest occupied molecular orbital (HOMO) and acceptor lowest unoccupied molecular orbital (LUMO). However, increasing this energy offset can also lead to photophysical processes that compete with charge separation. In this paper the formation of triplet states is addressed in blends of polyfluorene polymers with a series of PCBM multi-adducts. Specifically, it is demonstrated that the formation of such triplets occurs when the offset energy between donor ionization potential and acceptor electron affinity is ∼1.6 eV or greater. Spectroscopic measurements support a mechanism of resonance energy transfer for triplet formation, influenced by the energy levels of the materials, but also demonstrate that the competition between processes at the donor–acceptor interface is strongly influenced by morphology.
    Advanced Functional Materials 08/2010; 20(16):2701 - 2708. DOI:10.1002/adfm.201000477
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    ABSTRACT: Two groups of cobalt (Co) catalysts, supported on SBA-15 and MCM-41, respectively, were prepared by incipient wetness impregnation and tested for their influence on the thermal decomposition of acetyl cellulose. γ-Al2O3 supported Co catalysts were investigated as a comparison. A thermogravimetric analyser coupled with a mass spectrometer (TG-MS) was used to examine the influence of catalyst loading, support material and the presence of additional water vapour on H2 production and selectivity. Normalization of the raw MS data enabled semi-quantitative analysis of the product gas distribution, which facilitated reliable comparison between different experimental conditions. Catalysts were characterized by physisorption, chemisorption, TGA, XRD, SEM and TEM. SBA-15 and MCM-41 supported catalysts significantly elevated the yield and selectivity of H2, under dry Ar and with the injection of additional water vapour, when compared with the γ-Al2O3 support. 15 wt.%Co/SBA-15 and 10 wt.%Co/MCM-41 were identified as the most active catalysts from the two groups with indicative yields of 202 and 303 ml H2/g cellulose, respectively. The 10 wt.%Co/MCM-41 catalyst gave with the highest H2 selectivity reaching 21.7% of the dry product gas.
    Applied Catalysis B Environmental 06/2010; 97(1-2-97):142-150. DOI:10.1016/j.apcatb.2010.03.034
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    ABSTRACT: Moist singular vectors (MSV) have been applied successfully to predicting mid-latitude storms growing in association with latent heat of condensation. Tropical cyclone sensitivity has also been assessed. There is now considerable interest in its application for singular vector computation in the tropics and tropical perturbations for the ensemble system on a wider basis than targeting tropical cyclones. Extending this approach to more general tropical weather systems, MSVs are evaluated here for understanding African easterly waves (AEWs) and associated rainfall. These are arguably, the tropical systems that exhibit dynamical organization in a manner that is most similar to extra-tropical weather systems, and yet provide the context for convection that is of great importance both in their development and their subsequent behaviour, in their impact on society and in yielding ideas on the interaction between physics and dynamics in the tropical atmosphere that may have more general relevance. The systematic errors that can plague the forecast skill in this region may be improved by process studies aimed at understanding the fundamental dynamics governing the WAM. Here we present results from a study that aims to use MSVs to build on our recently gained theoretical insights from normal mode studies of the moist AEJ-AEW system, and to learn for practical purposes, whether MSVs targeted on W. Africa could be suitable as perturbations to the ECMWF ensemble system for improving AEW prediction and associated rainfall. First results, without initial moisture perturbations, suggest MSVs may be used advantageously. Perturbations bear similar structural and energy profiles to previous idealised non-linear studies and observations. Strong sensitivities prevail in the metrics and trajectories chosen. The benefits of including initial moisture perturbations are appraised in the light of these findings with emphasis on perturbation growth mechanisms and the sensitivity of short-range forecasts for precipitation based on AEWs that developed during the AMMA SOP.
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    ABSTRACT: Landslides impacting into or occurring under water generate waves, which can have devastating environmental consequences. Depending on the characteristics of the landslide the waves can have significant amplitude and potentially propagate over large distances. Linear models of classical earthquake-generated tsunamis cannot reproduce the highly nonlinear generation mechanisms required to accurately predict the consequences of landslide-generated tsunamis. Also, laboratory-scale experimental investigation is limited to simple geometries and short time-scales before wave reflections contaminate the data. Computational fluid dynamics models based on the nonlinear Navier-Stokes equations can simulate landslide-tsunami generation at realistic scales. However, traditional chessboard-like structured meshes introduce superfluous resolution and hence the computing power required for such a simulation can be prohibitively high, especially in three dimensions. Unstructured meshes allow the grid spacing to vary rapidly from high resolution in the vicinity of small scale features to much coarser, lower resolution in other areas. Combining this variable resolution with dynamic mesh adaptivity allows such high resolution zones to follow features like the interface between the landslide and the water whilst minimising the computational costs. Unstructured meshes are also better suited to representing complex geometries and bathymetries allowing more realistic domains to be simulated. Modelling multiple materials, like water, air and a landslide, on an unstructured adaptive mesh poses significant numerical challenges. Novel methods of interface preservation must be considered and coupled to a flow model in such a way that ensures conservation of the different materials. Furthermore this conservation property must be maintained during successive stages of mesh optimisation and interpolation. In this paper we validate a new multi-material adaptive unstructured fluid dynamics model against the well-known Lituya Bay landslide-generated wave experiment and case study [1]. In addition, we explore the effect of physical parameters, such as the shape, velocity and viscosity of the landslide, on wave amplitude and run-up, to quantify their influence on the landslide-tsunami hazard. As well as reproducing the experimental results, the model is shown to have excellent conservation and bounding properties. It also requires fewer nodes than an equivalent resolution fixed mesh simulation, therefore minimising at least one aspect of the computational cost. These computational savings are directly transferable to higher dimensions and some initial three dimensional results are also presented. These reproduce the experiments of DiRisio et al. [2], where an 80cm long landslide analogue was released from the side of an 8.9m diameter conical island in a 50 × 30m tank of water. The resulting impact between the landslide and the water generated waves with an amplitude of 1cm at wave gauges around the island. The range of scales that must be considered in any attempt to numerically reproduce this experiment makes it an ideal case study for our multi-material adaptive unstructured fluid dynamics model. [1] FRITZ, H. M., MOHAMMED, F., & YOO, J. 2009. Lituya Bay Landslide Impact Generated Mega-Tsunami 50th Anniversary. Pure and Applied Geophysics, 166(1), 153-175. [2] DIRISIO, M., DEGIROLAMO, P., BELLOTTI, G., PANIZZO, A., ARISTODEMO, F.,
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    ABSTRACT: This article presents a literature review regarding the mechanisms of fuel cell degradation, accompanied by the reported range of observed degradation rates in experimental, demonstration and early commercial systems. It then synthesises and exploits this information to investigate the influence of degradation on the economic and environmental credentials of fuel cell micro-combined heat and power (micro-CHP) for the UK residential sector. The investigation applies a techno-economic model developed in the companion article designed to demarcate the key characteristics of commercially successful systems. Two distinct modes of degradation are examined; one proportional to power density in the stack, and the other proportional to thermal-cycling rate of the stack. It is found that limiting the power-density related degradation rate is very important from economic and environmental viewpoints, but thermal-cycling related degradation is less important when thermal energy storage is available because cycling can be avoided. Furthermore it is noted that techno-economic studies that ignore degradation can overestimate the marginal value of a micro-CHP system with respect to the conventional alternative by up to 45% and the CO2 emissions reduction potential by up to 57%, for performance degradation rates of 2% per MWeh output. This conclusion is noteworthy because most techno-economic analyses of fuel cells ignore degradation, potentially providing misleading results. Finally it is concluded that existing commercial degradation targets, such as the SECA targets, are appropriate for achieving marketable systems.
    International Journal of Hydrogen Energy 12/2009; 34(23-34):9558-9569. DOI:10.1016/j.ijhydene.2009.09.095
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    ABSTRACT: This article presents the concept and mathematical treatment for a techno-economic modelling framework designed to enable exploration of fuel cell micro combined heat and power (micro-CHP) system design and control. The aim is to provide a tool that can help to focus research and development attention on the system characteristics critical for commercial success of these technologies, present cost targets for developers, and to ensure policy makers provide appropriate instruments to support commercialisation. The model is distinctive in that it applies mixed integer unit commitment formulation to link design and control decisions for micro-CHP, and explicitly characterises stack degradation in a techno-economic framework. It is structured to provide depiction of the fuel cell stack and balance-of-plant, supplementary thermal-only system (e.g. tail gas burner), thermal energy storage, and electrical power storage. Technically, the fuel cell stack is characterised by steady-state thermal and electrical efficiencies for full and part-load operation, its nameplate capacity, minimum operating set-point, and stack degradation via performance loss rate proportional to power density and thermal cycling rate. The dynamics of operation are emulated via ramp limits, minimum up-time and minimum down-time constraints, and start-up and shutdown costs and energy consumptions. The primary performance evaluation metric adopted is the maximum additional capital cost a rational investor would pay for the fuel cell micro-CHP system over and above what they would pay for a competing conventional heating system. The companion article (Part 2) applies the developed model to consider the impact of stack degradation on economic and environmental performance.
    International Journal of Hydrogen Energy 12/2009; 34(23-34):9545-9557. DOI:10.1016/j.ijhydene.2009.09.094
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    ABSTRACT: 1. Ecosystem services are the benefits humans obtain from ecosystems. The importance of research into ecosystem services has been widely recognized, and rapid progress is being made. However, the prevailing approach to quantifying ecosystem services is still based on static analyses and single ser-vices, ignoring system dynamics, uncertainty and feedbacks. This is not only partly due to a lack of mechanistic understanding of processes and a dearth of empirical data, but also due to a failure to engage fully with the interdisciplinarity of the problem. 2. We argue that there is a tendency to ignore the feedbacks between and within both social and ecological systems, and a lack of explicit consideration of uncertainty. Metrics need to be developed that can predict thresholds, which requires strong linkages to underlying processes, while the devel-opment of policy for management of ecosystem services needs to be based on a broader understand-ing of value and drivers of human well-being. 3. We highlight the complexities, gaps in current knowledge and research, and the potentially promising avenues for future investigation in four priority research areas: agendas, processes, met-rics and uncertainty. 4. Synthesis and applications. The research interest in the field of ecosystem services is rapidly expanding, and can contribute significantly to the sustainable management of natural resources. However, a narrow disciplinary approach, or an approach which does not consider feedbacks within and between ecological and social systems, has the potential to produce dangerously mislead-ing policy recommendations. In contrast, if we explicitly acknowledge and address uncertainties and complexities in the provision of ecosystem services, progress may appear slower but our models will be substantially more robust and informative about the effects of environmental change.
    Journal of Applied Ecology 10/2009; 46(6). DOI:10.1111/j.1365-2664.2009.01716.x
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