Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Presenting SAPUSS: solving aerosol problem by using synergistic strategies in Barcelona, Spain

This paper presents the summary of the key objectives, instrumentation and logistic details, goals, and initial scientific findings of the European Marie Curie Action SAPUSS project carried out in the western Mediterranean Basin (WMB) during September-October in autumn 2010. The key SAPUSS objective is to deduce aerosol source characteristics and to understand the atmospheric processes responsible for their generations and transformations - both horizontally and vertically in the Mediterranean urban environment. In order to achieve so, the unique approach of SAPUSS is the concurrent measurements of aerosols with multiple techniques occurring simultaneously in six monitoring sites around the city of Barcelona (NE Spain): a main road traffic site, two urban background sites, a regional background site and two urban tower sites (150 m and 545 m above sea level, 150 m and 80 m above ground, respectively). SAPUSS allows us to advance our knowledge sensibly of the atmospheric chemistry and physics of the urban Mediterranean environment. This is well achieved only because of both the three dimensional spatial scale and the high sampling time resolution used. During SAPUSS different meteorological regimes were encountered, including warm Saharan, cold Atlantic, wet European and stagnant regional ones. The different meteorology of such regimes is herein described. Additionally, we report the trends of the parameters regulated by air quality purposes (both gaseous and aerosol mass concentrations); and we also compare the six monitoring sites. High levels of traffic-related gaseous pollutants were measured at the urban ground level monitoring sites, whereas layers of tropospheric ozone were recorded at tower levels. Particularly, tower level night-time average ozone concentrations (80 +/- 25 mu g m(-3)) were up to double compared to ground level ones. The examination of the vertical profiles clearly shows the predominant influence of NOx on ozone concentrations, and a source of ozone aloft. Analysis of the particulate matter (PM) mass concentrations shows an enhancement of coarse particles (PM2.5-10) at the urban ground level (+64 %, average 11.7 mu g m(-3)) but of fine ones (PM1) at urban tower level (+28 %, average 14.4 mu g m(-3)). These results show complex dynamics of the size-resolved PM mass at both horizontal and vertical levels of the study area. Preliminary modelling findings reveal an underestimation of the fine accumulation aerosols. In summary, this paper lays the foundation of SAPUSS, an integrated study of relevance to many other similar urban Mediterranean coastal environment sites.