Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

X-Ray studies of the physics of matter around super-massive black-holes in nearby Seyfert galaxies

Seyfert galaxies are the closest active galactic nuclei. As such, we can use them to test the physical properties of the entire class of objects. To investigate their general properties, I took advantage of different methods of data analysis. In particular I used three different samples of objects, that, despite frequent overlaps, have been chosen to best tackle different topics: the heterogeneous BeppoS AX sample was thought to be optimized to test the average hard X-ray (E above 10 keV) properties of nearby Seyfert galaxies; the X-CfA was thought the be optimized to compare the properties of low-luminosity sources to the ones of higher luminosity and, thus, it was also used to test the emission mechanism models; finally, the XMM–Newton sample was extracted from the X-CfA sample so as to ensure a truly unbiased and well defined sample of objects to define the average properties of Seyfert galaxies. Taking advantage of the broad-band coverage of the BeppoS AX MECS and PDS instruments (between ~2-100 keV), I infer the average X-ray spectral propertiesof nearby Seyfert galaxies and in particular the photon index (~1.8), the high-energy cut-off (~290 keV), and the relative amount of cold reflection (~1.0). Moreover the unified scheme for active galactic nuclei was positively tested. The distribution of isotropic indicators used here (photon index, relative amount of reflection, high-energy cut-off and narrow FeK energy centroid) are similar in type I and type II objects while the absorbing column and the iron line equivalent width significantly differ between the two classes of sources with type II objects displaying larger absorbing columns. Taking advantage of the XMM–Newton and X–CfA samples I also deduced from measurements that 30 to 50% of type II Seyfert galaxies are Compton thick. Confirming previous results, the narrow FeK line is consistent, in Seyfert 2 galaxies, with being produced in the same matter responsible for the observed obscuration. These results support the basic picture of the unified model. Moreover, the presence of a X-ray Baldwin effect in type I sources has been measured using for the first time the 20-100 keV luminosity (EW proportional to L(20-100)^(−0.22±0.05)). This finding suggests that the torus covering factor may be a function of source luminosity, thereby suggesting a refinement of the baseline version of the unifed model itself. Using the BeppoSAX sample, it has been also recorded a possible correlation between the photon index and the amount of cold reflection in both type I and II sources. At a first glance this confirms the thermal Comptonization as the most likely origin of the high energy emission for the active galactic nuclei. This relation, in fact, naturally emerges supposing that the accretion disk penetrates, depending to the accretion rate, the central corona at different depths (Merloni et al. 2006): the higher accreting systems hosting disks down to the last stable orbit while the lower accreting systems hosting truncated disks. On the contrary, the study of the well defined X–C f A sample of Seyfert galaxies has proved that the intrinsic X-ray luminosity of nearby Seyfert galaxies can span values between 10^(38−43) erg s^−1, i.e. covering a huge range of accretion rates. The less efficient systems have been supposed to host ADAF systems without accretion disk. However, the study of the X–CfA sample has also proved the existence of correlations between optical emission lines and X-ray luminosity in the entire range of L_(X) covered by the sample. These relations are similar to the ones obtained if high-L objects are considered. Thus the emission mechanism must be similar in luminous and weak systems. A possible scenario to reconcile these somehow opposite indications is assuming that the ADAF and the two phase mechanism co-exist with different relative importance moving from low-to-high accretion systems (as suggested by the Gamma vs. R relation). The present data require that no abrupt transition between the two regimes is present. As mentioned above, the possible presence of an accretion disk has been tested using samples of nearby Seyfert galaxies. Here, to deeply investigate the flow patterns close to super-massive black-holes, three case study objects for which enough counts statistics is available have been analysed using deep X-ray observations taken with XMM–Newton. The obtained results have shown that the accretion flow can significantly differ between the objects when it is analyzed with the appropriate detail. For instance the accretion disk is well established down to the last stable orbit in a Kerr system for IRAS 13197-1627 where strong light bending effect have been measured. The accretion disk seems to be formed spiraling in the inner ~10-30 gravitational radii in NGC 3783 where time dependent and recursive modulation have been measured both in the continuum emission and in the broad emission line component. Finally, the accretion disk seems to be only weakly detectable in rk 509, with its weak broad emission line component. Finally, blueshifted resonant absorption lines have been detected in all three objects. This seems to demonstrate that, around super-massive black-holes, there is matter which is not confined in the accretion disk and moves along the line of sight with velocities as large as v~0.01-0.4c (whre c is the speed of light). Wether this matter forms winds or blobs is still matter of debate together with the assessment of the real statistical significance of the measured absorption lines. Nonetheless, if confirmed, these phenomena are of outstanding interest because they offer new potential probes for the dynamics of the innermost regions of accretion flows, to tackle the formation of ejecta/jets and to place constraints on the rate of kinetic energy injected by AGNs into the ISM and IGM. Future high energy missions (such as the planned Simbol-X and IXO) will likely allow an exciting step forward in our understanding of the flow dynamics around black holes and the formation of the highest velocity outflows.

Biomass Gasification - Process analysis and dimensioning aspects for downdraft units and gas cleaning lines

In such territories where food production is mostly scattered in several small / medium size or even domestic farms, a lot of heterogeneous residues are produced yearly, since farmers usually carry out different activities in their properties. The amount and composition of farm residues, therefore, widely change during year, according to the single production process periodically achieved. Coupling high efficiency micro-cogeneration energy units with easy handling biomass conversion equipments, suitable to treat different materials, would provide many important advantages to the farmers and to the community as well, so that the increase in feedstock flexibility of gasification units is nowadays seen as a further paramount step towards their wide spreading in rural areas and as a real necessity for their utilization at small scale. Two main research topics were thought to be of main concern at this purpose, and they were therefore discussed in this work: the investigation of fuels properties impact on gasification process development and the technical feasibility of small scale gasification units integration with cogeneration systems. According to these two main aspects, the present work was thus divided in two main parts. The first one is focused on the biomass gasification process, that was investigated in its theoretical aspects and then analytically modelled in order to simulate thermo-chemical conversion of different biomass fuels, such as wood (park waste wood and softwood), wheat straw, sewage sludge and refuse derived fuels. The main idea is to correlate the results of reactor design procedures with the physical properties of biomasses and the corresponding working conditions of gasifiers (temperature profile, above all), in order to point out the main differences which prevent the use of the same conversion unit for different materials. At this scope, a gasification kinetic free model was initially developed in Excel sheets, considering different values of air to biomass ratio and the downdraft gasification technology as particular examined application. The differences in syngas production and working conditions (process temperatures, above all) among the considered fuels were tried to be connected to some biomass properties, such elementary composition, ash and water contents. The novelty of this analytical approach was the use of kinetic constants ratio in order to determine oxygen distribution among the different oxidation reactions (regarding volatile matter only) while equilibrium of water gas shift reaction was considered in gasification zone, by which the energy and mass balances involved in the process algorithm were linked together, as well. Moreover, the main advantage of this analytical tool is the easiness by which the input data corresponding to the particular biomass materials can be inserted into the model, so that a rapid evaluation on their own thermo-chemical conversion properties is possible to be obtained, mainly based on their chemical composition A good conformity of the model results with the other literature and experimental data was detected for almost all the considered materials (except for refuse derived fuels, because of their unfitting chemical composition with the model assumptions). Successively, a dimensioning procedure for open core downdraft gasifiers was set up, by the analysis on the fundamental thermo-physical and thermo-chemical mechanisms which are supposed to regulate the main solid conversion steps involved in the gasification process. Gasification units were schematically subdivided in four reaction zones, respectively corresponding to biomass heating, solids drying, pyrolysis and char gasification processes, and the time required for the full development of each of these steps was correlated to the kinetics rates (for pyrolysis and char gasification processes only) and to the heat and mass transfer phenomena from gas to solid phase. On the basis of this analysis and according to the kinetic free model results and biomass physical properties (particles size, above all) it was achieved that for all the considered materials char gasification step is kinetically limited and therefore temperature is the main working parameter controlling this step. Solids drying is mainly regulated by heat transfer from bulk gas to the inner layers of particles and the corresponding time especially depends on particle size. Biomass heating is almost totally achieved by the radiative heat transfer from the hot walls of reactor to the bed of material. For pyrolysis, instead, working temperature, particles size and the same nature of biomass (through its own pyrolysis heat) have all comparable weights on the process development, so that the corresponding time can be differently depending on one of these factors according to the particular fuel is gasified and the particular conditions are established inside the gasifier. The same analysis also led to the estimation of reaction zone volumes for each biomass fuel, so as a comparison among the dimensions of the differently fed gasification units was finally accomplished. Each biomass material showed a different volumes distribution, so that any dimensioned gasification unit does not seem to be suitable for more than one biomass species. Nevertheless, since reactors diameters were found out quite similar for all the examined materials, it could be envisaged to design a single units for all of them by adopting the largest diameter and by combining together the maximum heights of each reaction zone, as they were calculated for the different biomasses. A total height of gasifier as around 2400mm would be obtained in this case. Besides, by arranging air injecting nozzles at different levels along the reactor, gasification zone could be properly set up according to the particular material is in turn gasified. Finally, since gasification and pyrolysis times were found to considerably change according to even short temperature variations, it could be also envisaged to regulate air feeding rate for each gasified material (which process temperatures depend on), so as the available reactor volumes would be suitable for the complete development of solid conversion in each case, without even changing fluid dynamics behaviour of the unit as well as air/biomass ratio in noticeable measure. The second part of this work dealt with the gas cleaning systems to be adopted downstream the gasifiers in order to run high efficiency CHP units (i.e. internal engines and micro-turbines). Especially in the case multi–fuel gasifiers are assumed to be used, weightier gas cleaning lines need to be envisaged in order to reach the standard gas quality degree required to fuel cogeneration units. Indeed, as the more heterogeneous feed to the gasification unit, several contaminant species can simultaneously be present in the exit gas stream and, as a consequence, suitable gas cleaning systems have to be designed. In this work, an overall study on gas cleaning lines assessment is carried out. Differently from the other research efforts carried out in the same field, the main scope is to define general arrangements for gas cleaning lines suitable to remove several contaminants from the gas stream, independently on the feedstock material and the energy plant size The gas contaminant species taken into account in this analysis were: particulate, tars, sulphur (in H2S form), alkali metals, nitrogen (in NH3 form) and acid gases (in HCl form). For each of these species, alternative cleaning devices were designed according to three different plant sizes, respectively corresponding with 8Nm3/h, 125Nm3/h and 350Nm3/h gas flows. Their performances were examined on the basis of their optimal working conditions (efficiency, temperature and pressure drops, above all) and their own consumption of energy and materials. Successively, the designed units were combined together in different overall gas cleaning line arrangements, paths, by following some technical constraints which were mainly determined from the same performance analysis on the cleaning units and from the presumable synergic effects by contaminants on the right working of some of them (filters clogging, catalysts deactivation, etc.). One of the main issues to be stated in paths design accomplishment was the tars removal from the gas stream, preventing filters plugging and/or line pipes clogging At this scope, a catalytic tars cracking unit was envisaged as the only solution to be adopted, and, therefore, a catalytic material which is able to work at relatively low temperatures was chosen. Nevertheless, a rapid drop in tars cracking efficiency was also estimated for this same material, so that an high frequency of catalysts regeneration and a consequent relevant air consumption for this operation were calculated in all of the cases. Other difficulties had to be overcome in the abatement of alkali metals, which condense at temperatures lower than tars, but they also need to be removed in the first sections of gas cleaning line in order to avoid corrosion of materials. In this case a dry scrubber technology was envisaged, by using the same fine particles filter units and by choosing for them corrosion resistant materials, like ceramic ones. Besides these two solutions which seem to be unavoidable in gas cleaning line design, high temperature gas cleaning lines were not possible to be achieved for the two larger plant sizes, as well. Indeed, as the use of temperature control devices was precluded in the adopted design procedure, ammonia partial oxidation units (as the only considered methods for the abatement of ammonia at high temperature) were not suitable for the large scale units, because of the high increase of reactors temperature by the exothermic reactions involved in the process. In spite of these limitations, yet, overall arrangements for each considered plant size were finally designed, so that the possibility to clean the gas up to the required standard degree was technically demonstrated, even in the case several contaminants are simultaneously present in the gas stream. Moreover, all the possible paths defined for the different plant sizes were compared each others on the basis of some defined operational parameters, among which total pressure drops, total energy losses, number of units and secondary materials consumption. On the basis of this analysis, dry gas cleaning methods proved preferable to the ones including water scrubber technology in al of the cases, especially because of the high water consumption provided by water scrubber units in ammonia adsorption process. This result is yet connected to the possibility to use activated carbon units for ammonia removal and Nahcolite adsorber for chloride acid. The very high efficiency of this latter material is also remarkable. Finally, as an estimation of the overall energy loss pertaining the gas cleaning process, the total enthalpy losses estimated for the three plant sizes were compared with the respective gas streams energy contents, these latter obtained on the basis of low heating value of gas only. This overall study on gas cleaning systems is thus proposed as an analytical tool by which different gas cleaning line configurations can be evaluated, according to the particular practical application they are adopted for and the size of cogeneration unit they are connected to.

Analisi della dinamica e composizione chimica del particolato atmosferico mediante un modello alla mesoscala

The vertical profile of aerosol in the planetary boundary layer of the Milan urban area is studied in terms of its development and chemical composition in a high-resolution modelling framework. The period of study spans a week in summer of 2007 (12-18 July), when continuous LIDAR measurements and a limited set of balloon profiles were collected in the frame of the ASI/QUITSAT project. LIDAR observations show a diurnal development of an aerosol plume that lifts early morning surface emissions to the top of the boundary layer, reaching maximum concentration around midday. Mountain breeze from Alps clean the bottom of the aerosol layer, typically leaving a residual layer at around 1500-2000 m which may survive for several days. During the last two days under analysis, a dust layer transported from Sahara reaches the upper layers of Milan area and affects the aerosol vertical distribution in the boundary layer. Simulation from the MM5/CHIMERE modelling system, carried out at 1 km horizontal resolution, qualitatively reproduced the general features of the Milan aerosol layer observed with LIDAR, including the rise and fall of the aersol plume, the residual layer in altitude and the Saharan dust event. The simulation highlighted the importance of nitrates and secondary organics in its composition. Several sensitivity tests showed that main driving factors leading to the dominance of nitrates in the plume are temperature and gas absorption process. A modelling study turn to the analysis of the vertical aerosol profiles distribution and knowledge of the characterization of the PM at a site near the city of Milan is performed using a model system composed by a meteorological model MM5 (V3-6), the mesoscale model from PSU/NCAR and a Chemical Transport Model (CTM) CHIMERE to simulate the vertical aerosol profile. LiDAR continuous observations and balloon profiles collected during two intensive campaigns in summer 2007 and in winter 2008 in the frame of the ASI/QUITSAT project have been used to perform comparisons in order to evaluate the ability of the aerosol chemistry transport model CHIMERE to simulate the aerosols dynamics and compositions in this area. The comparisons of model aerosols with measurements are carried out over a full time period between 12 July 2007 and 18 July 2007. The comparisons demonstrate the ability of the model to reproduce correctly the aerosol vertical distributions and their temporal variability. As detected by the LiDAR, the model during the period considered, predicts a diurnal development of a plume during the morning and a clearing during the afternoon, typically the plume reaches the top of the boundary layer around mid day, in this time CHIMERE produces highest concentrations in the upper levels as detected by LiDAR. The model, moreover can reproduce LiDAR observes enhancement aerosols concentrations above the boundary layer, attributing the phenomena to dust out intrusion. Another important information from the model analysis regard the composition , it predicts that a large part of the plume is composed by nitrate, in particular during 13 and 16 July 2007 , pointing to the model tendency to overestimates the nitrous component in the particular matter vertical structure . Sensitivity study carried out in this work show that there are a combination of different factor which determine the major nitrous composition of the “plume” observed and in particular humidity temperature and the absorption phenomena are the mainly candidate to explain the principal difference in composition simulated in the period object of this study , in particular , the CHIMERE model seems to be mostly sensitive to the absorption process.

Operating System Contribution to Composable Timing Behaviour in High-Integrity Real-Time Systems

The development of High-Integrity Real-Time Systems has a high footprint in terms of human, material and schedule costs. Factoring functional, reusable logic in the application favors incremental development and contains costs. Yet, achieving incrementality in the timing behavior is a much harder problem. Complex features at all levels of the execution stack, aimed to boost average-case performance, exhibit timing behavior highly dependent on execution history, which wrecks time composability and incrementaility with it. Our goal here is to restitute time composability to the execution stack, working bottom up across it. We first characterize time composability without making assumptions on the system architecture or the software deployment to it. Later, we focus on the role played by the real-time operating system in our pursuit. Initially we consider single-core processors and, becoming less permissive on the admissible hardware features, we devise solutions that restore a convincing degree of time composability. To show what can be done for real, we developed TiCOS, an ARINC-compliant kernel, and re-designed ORK+, a kernel for Ada Ravenscar runtimes. In that work, we added support for limited-preemption to ORK+, an absolute premiere in the landscape of real-word kernels. Our implementation allows resource sharing to co-exist with limited-preemptive scheduling, which extends state of the art. We then turn our attention to multicore architectures, first considering partitioned systems, for which we achieve results close to those obtained for single-core processors. Subsequently, we shy away from the over-provision of those systems and consider less restrictive uses of homogeneous multiprocessors, where the scheduling algorithm is key to high schedulable utilization. To that end we single out RUN, a promising baseline, and extend it to SPRINT, which supports sporadic task sets, hence matches real-world industrial needs better. To corroborate our results we present findings from real-world case studies from avionic industry.

Normare la vita. Biocontrollo e nuove tecnologie

Questa ricerca, suddivisa in due parti, si concentra sulle problematiche connesse alla normazione della vita e dei corpi delle donne al tempo delle biotecnologie. La Parte I è una genealogia filosofico-politica che ripercorre le tappe analitico-concettuali del dibattito intorno a biopolitica e tecnoscienza, a partire dai contributi teorici di poststrutturalismo e femminismo neomaterialista, e risponde alle domande: Cosa sono diventati i corpi nell’attuale società bio-info-modificata? Qual'è il ruolo delle scienze nelle metamorfosi che interessano soggettività e rapporti di potere? La Parte II è una cartografia dei modi in cui le biotecnologie, riguardanti i corpi delle donne, si sono sviluppate e diffuse. Essa indaga in modo transdisciplinare come in Italia, e più in generale in Europa, sono state normate le tecniche di interruzione volontaria di gravidanza e fecondazione in vitro. Ampio spazio è dedicato ai modi in cui gli attori della bioetica, istituzionale e non, i medici, laici e cattolici, e le case farmaceutiche hanno affrontato questi temi e quello della contraccezione ormonale maschile. Medicina riproduttiva e rigenerativa sono tematizzate sempre in relazione al quadro normativo, per mostrare in che modo esso influenzi l’accesso ai diritti alla salute e all’autodeterminazione delle donne. Il quadro normativo è analizzato, a sua volta, alla luce dei fatti storici più rilevanti e delle culture più diffuse. L’obiettivo della ricerca è duplice: da un lato essa ha il fine di mostrare il modo in cui i corpi delle donne, e la relativa potenza generatrice, siano diventati uno snodo fondamentale nell’articolazione del biocontrollo e nell'apertura dei nuovi mercati legati a medicina riproduttiva e rigenerativa; dall’altro si propone di argomentare come un biodiritto flessibile, a contenuto storico variabile, condiviso e partecipato, sia un’ipotesi praticabile e virtuosa, utile all'eliminazione del gender gap ancora esistente in materia di diritti riproduttivi e sessuali.