Distortion of spheres and surfaces in space

It is known that the surface of a cone over the unit disc with large height has smaller distortion than the standard embedding of the 2-sphere in $\mathbb R^3$. In this note we show that distortion minimisers exist among convex embedded 2-spheres and have uniformly bounded eccentricity. Moreover, we prove that $\pi/2$ is a sharp lower bound on the distortion of embedded closed surfaces of positive genus.Comment: 9 pages, 1 figur

Load control strategies for hydrogen fuelled IC engines

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On the applicability of empirical heat transfer models for hydrogen combustion engines

Hydrogen-fuelled internal combustion engines are being investigated as an alternative for current drive trains because they have a high efficiency, near-zero noxious and zero tailpipe greenhouse gas emissions. A thermodynamic model of the engine cycle would enable a cheap and fast optimization of engine settings for operation on hydrogen, facilitating the development of these engines. The accuracy of the heat transfer submodel within the thermodynamic model is important to simulate accurately the emissions of oxides of nitrogen which are influenced by the maximum gas temperature. These emissions can occur in hydrogen internal combustion engines at high loads and they are an important constraint for power and efficiency optimization. The most common heat transfer models in engine research are those from Annand and Woschni. These models are developed for fossil fuels, which have different combustion properties. Therefore, they need to be evaluated for hydrogen. We have measured the heat flux and the wall temperature in an engine that can run on hydrogen and methane. This paper describes an evaluation of the models of Annand and Woschni, using those heat flux measurements and assesses if the models capture the effect of changing combustion and fuel properties. The models fail on all the tests, so they need to be improved to accurately model the heat transfer generated by hydrogen combustion

Investigation of the influence of engine settings on the heat flux in a hydrogen- and methane-fueled spark ignition engine

Hydrogen-fueled internal combustion engines are a possible solution to make transportation more ecological. Only emissions of oxides of nitrogen (NOx) occur at high loads, being a constraint for power and efficiency optimization. A thermodynamic model of the engine cycle enables a cheap and fast optimization of engine settings. It needs to accurately predict the heat transfer in the engine because the NOx emissions are influenced by the maximum gas temperature. However, the existing engine heat transfer models in the literature are developed for fossil fuels and they have been cited to be inaccurate for hydrogen. We have measured the heat transfer inside a spark ignited engine with a thermopile to investigate the heat transfer process of hydrogen and to find the differences with a fossil fuel. This paper describes the effects of the compression ratio, ignition timing and mixture richness on the heat transfer process, comparing hydrogen with methane. A convection coefficient is used to separate the effect of the temperature difference between the gas and the wall from the influence of the gas movement and combustion. The paper shows that the convection coefficient gives more insight in the heat transfer process in a combustion engine despite the assumptions involved in its definition. The comparison between hydrogen and methane demonstrates, in contrast to what is believed, that the heat loss of hydrogen can be lower

The Red Queen and the persistence of linkage-disequilibrium oscillations in finite and infinite populations

<p>Abstract</p> <p>Background</p> <p>The Red Queen Hypothesis (RQH) suggests that the coevolutionary dynamics of host-parasite systems can generate selection for increased host recombination. Since host-parasite interactions often have a strong genetic basis, recombination between different hosts can increase the fraction of novel and potentially resistant offspring genotypes. A prerequisite for this mechanism is that host-parasite interactions generate persistent oscillations of linkage disequilibria (LD).</p> <p>Results</p> <p>We use deterministic and stochastic models to investigate the persistence of LD oscillations and its impact on the RQH. The standard models of the Red Queen dynamics exhibit persistent LD oscillations under most circumstances. Here, we show that altering the standard model from discrete to continuous time or from simultaneous to sequential updating results in damped LD oscillations. This suggests that LD oscillations are structurally not robust. We then show that in a stochastic regime, drift can counteract this dampening and maintain the oscillations. In addition, we show that the amplitude of the oscillations and therefore the strength of the resulting selection for or against recombination are inversely proportional to the size of the (host) population.</p> <p>Conclusion</p> <p>We find that host parasite-interactions cannot generally maintain oscillations in the absence of drift. As a consequence, the RQH can strongly depend on population size and should therefore not be interpreted as a purely deterministic hypothesis.</p