The Response of Normal Shocks in Diffusers

The frequency response of a normal shock in a diverging channel is calculated for application to problems of pressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic flow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation induced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the engine are discus,ed

Modeling pressure oscillations in Ramjets

Pressure oscillations in ramjet engines are approximated as one-dimensional motions and treated within linear acoustics. The exhaust nozzle is represented by the admittance function for a short choked nozzle. New results have been obtained for the quasi-steady response of a normal shock wave in the diffuser. Acoustic fields in the inlet region and in the combustion chamber are matched to provide an analytical expression of the criterion for linear stability. Combustion processes are accommodated but not treated in detail. As examples, data are discussed for two liquid-fueled engines, one having axial dump and one having side dumps

Sub-wavelength focusing meta-lens

We show that planar a plasmonic metamaterial with spatially variable meta-atom parameters can focus transmitted light into sub-wavelength hot-spots located beyond the near-field of the metamaterial. By nano-structuring a gold film we created an array of meta-lenses generating foci of 160 nm (0.2{\lambda}) in diameter when illuminated by a wavelength of 800 nm. We attribute the occurrence of sub-wavelength hotspots beyond the near field to the phenomenon of superoscillation

Optimising superoscillatory spots for far-field super-resolution imaging

Optical superoscillatory imaging, allowing unlabelled far-field super-resolution, has in recent years become reality. Instruments have been built and their super-resolution imaging capabilities demonstrated. The question is no longer whether this can be done, but how well: what resolution is practically achievable? Numerous works have optimised various particular features of superoscillatory spots, but in order to probe the limits of superoscillatory imaging we need to simultaneously optimise all the important spot features: those that define the resolution of the system. We simultaneously optimise spot size and its intensity relative to the sidebands for various fields of view, giving a set of best compromises for use in different imaging scenarios. Our technique uses the circular prolate spheroidal wave functions as a basis set on the field of view, and the optimal combination of these, representing the optimal spot, is found using a multi-objective genetic algorithm. We then introduce a less computationally demanding approach suitable for real-time use in the laboratory which, crucially, allows independent control of spot size and field of view. Imaging simulations demonstrate the resolution achievable with these spots. We show a three-order-of-magnitude improvement in the efficiency of focusing to achieve the same resolution as previously reported results, or a 26 % increase in resolution for the same efficiency of focusing

The Significance of Retinal Hemorrhage: Based on a Study of the Subsequent History of One Hundred and Eighty-Seven Cases

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Dietary flavonoid intakes and CVD incidence in the Framingham Offspring Cohort

This study examines the relationship between long-term intake of six flavonoid classes and incidence of CVD and CHD, using a comprehensive flavonoid database and repeated measures of intake, while accounting for possible confounding by components of a healthy dietary pattern. Flavonoid intakes were assessed using a FFQ among the Framingham Offspring Cohort at baseline and three times during follow-up. Cox proportional hazards regression was used to characterise prospective associations between the natural logarithms of flavonoid intakes and CVD incidence using a time-dependent approach, in which intake data were updated at each examination to represent average intakes from previous examinations. Mean baseline age was 54 years, and 45 % of the population was male. Over an average 14·9 years of follow-up among 2880 participants, there were 518 CVD events and 261 CHD events. After multivariable adjustment, only flavonol intake was significantly associated with lower risk of CVD incidence (hazard ratios (HR) per 2·5-fold flavonol increase = 0·86, Ptrend = 0·05). Additional adjustment for total fruit and vegetable intake and overall diet quality attenuated this observation (HR = 0·89, Ptrend = 0·20 and HR = 0·92, Ptrend = 0·33, respectively). There were no significant associations between flavonoids and CHD incidence after multivariable adjustment. Our findings suggest that the observed association between flavonol intake and CVD risk may be a consequence of better overall diet. However, the strength of this non-significant association was also consistent with relative risks observed in previous meta-analyses, and therefore a modest benefit of flavonol intake on CVD risk cannot be ruled out

Parameter inference in mechanistic models of cellular regulation and signalling pathways using gradient matching

A challenging problem in systems biology is parameter inference in mechanistic models of signalling pathways. In the present article, we investigate an approach based on gradient matching and nonparametric Bayesian modelling with Gaussian processes. We evaluate the method on two biological systems, related to the regulation of PIF4/5 in Arabidopsis thaliana, and the JAK/STAT signal transduction pathway

Optimizing spread dynamics on graphs by message passing

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the last decades, many efforts have been devoted to understand the typical behaviour of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception of models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem