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The occurrence of local high-pollution episodes in densely populated urban areas, which have huge fleets of vehicles, is currently one of the most worrying problems associated with air pollution worldwide. Such episodes are produced under specific meteorological conditions, which favour the sudden increase of levels of air pollutants. This study has investigated the influence of the mixing layer height (MLH) on the concentration levels of atmospheric pollutants and daily mortality in Madrid, Spain, during the period 2011–2014. It may help to understand the causes and impact of local high-pollution episodes. MLH at midday over Madrid was daily estimated from meteorological radio soundings. Then, days with different MLH over this urban area were characterized by meteorological parameters registered at different levels of an instrumented tower and by composite sea level pressure maps, representing the associated synoptic meteorological scenarios. Next, statistically significant associations between MLH and levels of PM10, PM2.5, NO, NO2, CO and ultra-fine particles number concentrations registered at representative monitoring stations were evaluated. Finally, associations between all-natural cause daily mortality in Madrid, MLH, and air pollutants were estimated using conditional Poisson regression models. The reduction of MLH to values below 482 m above-ground level under strong atmospheric stagnation conditions was accompanied by a statistically significant increase in levels of NO, NO2, CO, PM2.5 and ultra-fine particle number concentrations at urban-traffic and suburban monitoring sites. The decrease of the MLH was also associated to a linear increase of the daily number of exceedances of the UE NO2 hourly limit value (200 μg/m3) and levels of air pollutants at hotspot urban-traffic monitoring stations. Also, a statistically significant association of the MLH with all-natural cause daily mortality was obtained. When the MLH increased by 830 m, the risk of mortality decreased by 2.5% the same day and by 3.3% the next day, when African dust episodic days were excluded. They were also higher in absolute terms than the increases in risk of mortality that were determined for the exposition to any other air pollutant. Our results suggest that when the prediction models foresee values of MLH below 482 m above-ground level in Madrid, the evolution of high-contamination episodes will be very favourable. Therefore, short-term policy measures will have to be implemented to reduce NO, NO2, CO, PM2.5 and ultra-fine particle emissions from anthropogenic sources in this southern European urban location. [ABSTRACT FROM AUTHOR]

This study has assessed the influence of the origin of air mass on levels of particulate matter (PM10) and chemical composition (SO42− and NO3−) in the air basin of Madrid. A data set of back-trajectories of air mass arriving to this area of study from 15 June 15 2009 to 8 July 2011 has been analyzed. Firstly, the cluster analysis statistical method has been used to group the back-trajectories into 5 sets according to the angle, direction, and speed of the air mass. Afterwards, the synoptic meteorological scenarios associated with each cluster were obtained and interpreted. Subsequently, an analysis was made on the influence of these clusters on the surface levels of particulate pollutants recorded in a regional background station ("El Atazar"), as well as in two urban background stations ("Casa de Campo" and "CIEMAT"). Finally, potential source areas of PM10, SO42−, and NO3− that contributed to the increase in their background levels in the Madrid air basin were detected by analyzing residence times of trajectories. Transport of mineral desert dust is probably the main cause of the increase of regional and urban background levels of PM10 in the Madrid air basin. In the case of SO42−, relatively high levels were registered, associated with air mass coming from Southern Europe and the Mediterranean Sea. In these regions, strong emissions of SO42− are produced due to industrial combustion and maritime traffic. Otherwise, relatively high levels of NO3− were registered during meteorological situations defined by a low baric gradient in the Iberian Peninsula. This meteorological pattern favors the accumulation of emissions from local and regional sources. Besides, the main urban centers of northeastern Europe and industrial areas located in the north African coast were also identified as potential source areas of NO3−. The statistical analysis of the back-trajectories by different methods and the comparison of the results obtained with observational data confirmed that numerous industrial areas in Europe and North Africa, as well as natural ones, such as deserts, had an influence on the regional and urban background levels of mass and chemical composition of particulate matter in the Madrid air basin, under the development of specific synoptic meteorological situations. [ABSTRACT FROM AUTHOR]

We study the integrable system of first order differential equations $$\omega _i(v)'=\alpha _i\,\prod _{j\ne i}\omega _j(v)$$ , $$(1\le i, j\le N)$$ as an initial value problem, with real coefficients $$\alpha _i$$ and initial conditions $$\omega _i(0)$$ . The geometrical structure of the system allows to express it as a Poisson system. The analysis is based on its quadratic first integrals. For each dimension N, the system defines a family of functions, generically hyperelliptic functions. When $$N=3$$ , this system generalizes the classic Euler system for the reduced flow of the free rigid body problem; thus, we call it N-extended Euler system ( N-EES). In this paper, the cases $$N=4$$ and $$N=5$$ are studied, generalizing Jacobi elliptic functions which are defined as a 3-EES. The $$N=4$$ case was proposed in Hille (Lectures on Ordinary Differential Equations. Addison-Wesley, Reading, ), and the solution is presented in Abdel-Salam (Z Naturforsch A 64a:639-645, ; it is still expressed as elliptic functions. The hyperelliptic functions arise for the $$N=5$$ case, which also contain special solutions in elliptic form. Taking into account the nested structure of the N-EES, we propose reparametrizations of the type $${\mathrm{d}}v^*=g(\omega _i)\,{\mathrm{d}}v$$ that separate geometry from dynamic. Some of those parametrizations turn out to be generalization of the Jacobi amplitude. [ABSTRACT FROM AUTHOR]

K. Meyer has advocated for the study of elliptic functions and integrals from a dynamical systems point of view. Here, we follow his advice and we propose the bidimensional Hamiltonian Duffing oscillator as a model; it allows us to deal with the elliptic integral of third kind directly. Focusing on bounded trajectories we do a detailed analysis of the solutions in the three regions defined by the parameters. In our opinion, for the study of elliptic functions, the model presented here represents an alternative to the pendulum or the free rigid body systems. [ABSTRACT FROM AUTHOR]