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.

Design and Characterization of New Luminescent Sensors and Labels

The aim of this Ph.D. project has been the design and characterization of new and more efficient luminescent tools, in particular sensors and labels, for analytical chemistry, medical diagnostics and imaging. Actually both the increasing temporal and spatial resolutions that are demanded by those branches, coupled to a sensitivity that is required to reach the single molecule resolution, can be provided by the wide range of techniques based on luminescence spectroscopy. As far as the development of new chemical sensors is concerned, as chemists we were interested in the preparation of new, efficient, sensing materials. In this context, we kept developing new molecular chemosensors, by exploiting the supramolecular approach, for different classes of analytes. In particular we studied a family of luminescent tetrapodal-hosts based on aminopyridinium units with pyrenyl groups for the detection of anions. These systems exhibited noticeable changes in the photophysical properties, depending on the nature of the anion; in particular, addition of chloride resulted in a conformational change, giving an initial increase in excimeric emission. A good selectivity for dicarboxylic acid was also found. In the search for higher sensitivities, we moved our attention also to systems able to perform amplification effects. In this context we described the metal ion binding properties of three photoactive poly-(arylene ethynylene) co-polymers with different complexing units and we highlighted, for one of them, a ten-fold amplification of the response in case of addition of Zn2+, Cu2+ and Hg2+ ions. In addition, we were able to demonstrate the formation of complexes with Yb3+ an Er3+ and an efficient sensitization of their typical metal centered NIR emission upon excitation of the polymer structure, this feature being of particular interest for their possible applications in optical imaging and in optical amplification for telecommunication purposes. An amplification effect was also observed during this research in silica nanoparticles derivatized with a suitable zinc probe. In this case we were able to prove, for the first time, that nanoparticles can work as “off-on” chemosensors with signal amplification. Fluorescent silica nanoparticles can be thus seen as innovative multicomponent systems in which the organization of photophysically active units gives rise to fruitful collective effects. These precious effects can be exploited for biological imaging, medical diagnostic and therapeutics, as evidenced also by some results reported in this thesis. In particular, the observed amplification effect has been obtained thanks to a suitable organization of molecular probe units onto the surface of the nanoparticles. In the effort of reaching a deeper inside in the mechanisms which lead to the final amplification effects, we also attempted to find a correlation between the synthetic route and the final organization of the active molecules in the silica network, and thus with those mutual interactions between one another which result in the emerging, collective behavior, responsible for the desired signal amplification. In this context, we firstly investigated the process of formation of silica nanoparticles doped with pyrene derivative and we showed that the dyes are not uniformly dispersed inside the silica matrix; thus, core-shell structures can be formed spontaneously in a one step synthesis. Moreover, as far as the design of new labels is concerned, we reported a new synthetic approach to obtain a class of robust, biocompatible silica core-shell nanoparticles able to show a long-term stability. Taking advantage of this new approach we also showed the synthesis and photophysical properties of core-shell NIR absorbing and emitting materials that proved to be very valuable for in-vivo imaging. In general, the dye doped silica nanoparticles prepared in the framework of this project can conjugate unique properties, such as a very high brightness, due to the possibility to include many fluorophores per nanoparticle, high stability, because of the shielding effect of the silica matrix, and, to date, no toxicity, with a simple and low-cost preparation. All these features make these nanostructures suitable to reach the low detection limits that are nowadays required for effective clinical and environmental applications, fulfilling in this way the initial expectations of this research project.

In situ real-time investigation of Organic Ultra-Thin-Film transistors: growth, electrical properties and biosensing applications

Organic electronics has grown enormously during the last decades driven by the encouraging results and the potentiality of these materials for allowing innovative applications, such as flexible-large-area displays, low-cost printable circuits, plastic solar cells and lab-on-a-chip devices. Moreover, their possible field of applications reaches from medicine, biotechnology, process control and environmental monitoring to defense and security requirements. However, a large number of questions regarding the mechanism of device operation remain unanswered. Along the most significant is the charge carrier transport in organic semiconductors, which is not yet well understood. Other example is the correlation between the morphology and the electrical response. Even if it is recognized that growth mode plays a crucial role into the performance of devices, it has not been exhaustively investigated. The main goal of this thesis was the finding of a correlation between growth modes, electrical properties and morphology in organic thin-film transistors (OTFTs). In order to study the thickness dependence of electrical performance in organic ultra-thin-film transistors, we have designed and developed a home-built experimental setup for performing real-time electrical monitoring and post-growth in situ electrical characterization techniques. We have grown pentacene TFTs under high vacuum conditions, varying systematically the deposition rate at a fixed room temperature. The drain source current IDS and the gate source current IGS were monitored in real-time; while a complete post-growth in situ electrical characterization was carried out. At the end, an ex situ morphological investigation was performed by using the atomic force microscope (AFM). In this work, we present the correlation for pentacene TFTs between growth conditions, Debye length and morphology (through the correlation length parameter). We have demonstrated that there is a layered charge carriers distribution, which is strongly dependent of the growth mode (i.e. rate deposition for a fixed temperature), leading to a variation of the conduction channel from 2 to 7 monolayers (MLs). We conciliate earlier reported results that were apparently contradictory. Our results made evident the necessity of reconsidering the concept of Debye length in a layered low-dimensional device. Additionally, we introduce by the first time a breakthrough technique. This technique makes evident the percolation of the first MLs on pentacene TFTs by monitoring the IGS in real-time, correlating morphological phenomena with the device electrical response. The present thesis is organized in the following five chapters. Chapter 1 makes an introduction to the organic electronics, illustrating the operation principle of TFTs. Chapter 2 presents the organic growth from theoretical and experimental points of view. The second part of this chapter presents the electrical characterization of OTFTs and the typical performance of pentacene devices is shown. In addition, we introduce a correcting technique for the reconstruction of measurements hampered by leakage current. In chapter 3, we describe in details the design and operation of our innovative home-built experimental setup for performing real-time and in situ electrical measurements. Some preliminary results and the breakthrough technique for correlating morphological and electrical changes are presented. Chapter 4 meets the most important results obtained in real-time and in situ conditions, which correlate growth conditions, electrical properties and morphology of pentacene TFTs. In chapter 5 we describe applicative experiments where the electrical performance of pentacene TFTs has been investigated in ambient conditions, in contact to water or aqueous solutions and, finally, in the detection of DNA concentration as label-free sensor, within the biosensing framework.

New polymeric materials for vascular surgery

The dramatic impact that vascular diseases have on human life quality and expectancy nowadays is the reason why both medical and scientific communities put great effort in discovering new and effective ways to fight vascular pathologies. Among the many different treatments, endovascular surgery is a minimally-invasive technique that makes use of X-ray fluoroscopy to obtain real-time images of the patient during interventions. In this context radiopaque biomaterials, i.e. materials able to absorb X-ray radiation, play a fundamental role as they are employed both to enhance visibility of devices during interventions and to protect medical staff and patients from X-ray radiations. Organic-inorganic hybrids are materials that combine characteristics of organic polymers with those of inorganic metal oxides. These materials can be synthesized via the sol-gel process and can be easily applied as thin coatings on different kinds of substrates. Good radiopacity of organic-inorganic hybrids has been recently reported suggesting that these materials might find applications in medical fields where X-ray absorption and visibility is required. The present PhD thesis aimed at developing and characterizing new radiopaque organic-inorganic hybrid materials that can find application in the vascular surgery field as coatings for the improvement of medical devices traceability as well as for the production of X-ray shielding objects and garments. Novel organic-inorganic hybrids based on different polyesters (poly-lactic acid and poly-ε-caprolactone) and polycarbonate (poly-trimethylene carbonate) as the polymeric phase and on titanium oxide as the inorganic phase were synthesized. Study of the phase interactions in these materials allowed to demonstrate that Class II hybrids (where covalent bonds exists between the two phases) can be obtained starting from any kind of polyester or polycarbonate, without the need of polymer pre-functionalization, thanks to the occurrence of transesterification reactions operated by inorganic molecules on ester and carbonate moieties. Polyester based hybrids were successfully coated via dip coating on different kinds of textiles. Coated textiles showed improved radiopacity with respect to the plain fabric while remaining soft to the touch. The hybrid was able to coat single fibers of the yarn rather than coating the yarn as a whole. Openings between yarns were maintained and therefore fabric breathability was preserved. Such coatings are promising for the production of light-weight garments for X-ray protection of medical staff during interventional fluoroscopy, which will help preventing pathologies that stem from chronic X-ray exposure. A means to increase the protection capacity of hybrid-coated fabrics was also investigated and implemented in this thesis. By synthesizing the hybrid in the presence of a suspension of radiopaque tantalum nanoparticles, PDMS-titania hybrid materials with tunable radiopacity were developed and were successfully applied as coatings. A solution for enhancing medical device radiopacity was also successfully investigated. High metal radiopacity was associated with good mechanical and protective properties of organic-inorganic hybrids in the form of a double-layer coating. Tantalum was employed as the constituent of the first layer deposited on sample substrates by means of a sputtering technique. The second layer was composed of a hybrid whose constituents are well-known biocompatible organic and inorganic components, such as the two polymers PCL and PDMS, and titanium oxide, respectively. The metallic layer conferred to the substrate good X-ray visibility. A correlation between radiopacity and coating thickness derived during this study allows to tailor radiopacity simply by controlling the metal layer sputtering deposition time. The applied metal deposition technique also permits easy shaping of the radiopaque layer, allowing production of radiopaque markers for medical devices that can be unambiguously identified by surgeons during implantation and in subsequent radiological investigations. Synthesized PCL-titania and PDMS-titania hybrids strongly adhered to substrates and show good biocompatibility as highlighted by cytotoxicity tests. The PDMS-titania hybrid coating was also characterized by high flexibility that allows it to stand large substrate deformations without detaching nor cracking, thus being suitable for application on flexible medical devices.

Background minimization issues for next generation hard X-ray focusing telescopes

The hard X-ray band (10 - 100 keV) has been only observed so far by collimated and coded aperture mask instruments, with a sensitivity and an angular resolution lower than two orders of magnitude as respects the current X-ray focusing telescopes operating below 10 - 15 keV. The technological advance in X-ray mirrors and detection systems is now able to extend the X-ray focusing technique to the hard X-ray domain, filling the gap in terms of observational performances and providing a totally new deep view on some of the most energetic phenomena of the Universe. In order to reach a sensitivity of 1 muCrab in the 10 - 40 keV energy range, a great care in the background minimization is required, a common issue for all the hard X-ray focusing telescopes. In the present PhD thesis, a comprehensive analysis of the space radiation environment, the payload design and the resulting prompt X-ray background level is presented, with the aim of driving the feasibility study of the shielding system and assessing the scientific requirements of the future hard X-ray missions. A Geant4 based multi-mission background simulator, BoGEMMS, is developed to be applied to any high energy mission for which the shielding and instruments performances are required. It allows to interactively create a virtual model of the telescope and expose it to the space radiation environment, tracking the particles along their path and filtering the simulated background counts as a real observation in space. Its flexibility is exploited to evaluate the background spectra of the Simbol-X and NHXM mission, as well as the soft proton scattering by the X-ray optics and the selection of the best shielding configuration. Altough the Simbol-X and NHXM missions are the case studies of the background analysis, the obtained results can be generalized to any future hard X-ray telescope. For this reason, a simplified, ideal payload model is also used to select the major sources of background in LEO. All the results are original contributions to the assessment studies of the cited missions, as part of the background groups activities.

Measurement of the muon-induced neutron flux at LNGS with the LVD experiment

In this thesis we describe in detail the Monte Carlo simulation (LVDG4) built to interpret the experimental data collected by LVD and to measure the muon-induced neutron yield in iron and liquid scintillator. A full Monte Carlo simulation, based on the Geant4 (v 9.3) toolkit, has been developed and validation tests have been performed. We used the LVDG4 to determine the active vetoing and the shielding power of LVD. The idea was to evaluate the feasibility to host a dark matter detector in the most internal part, called Core Facility (LVD-CF). The first conclusion is that LVD is a good moderator, but the iron supporting structure produce a great number of neutrons near the core. The second conclusions is that if LVD is used as an active veto for muons, the neutron flux in the LVD-CF is reduced by a factor 50, of the same order of magnitude of the neutron flux in the deepest laboratory of the world, Sudbury. Finally, the muon-induced neutron yield has been measured. In liquid scintillator we found $(3.2 \pm 0.2) \times 10^{-4}$ n/g/cm$^2$, in agreement with previous measurements performed at different depths and with the general trend predicted by theoretical calculations and Monte Carlo simulations. Moreover we present the first measurement, in our knowledge, of the neutron yield in iron: $(1.9 \pm 0.1) \times 10^{-3}$ n/g/cm$^2$. That measurement provides an important check for the MC of neutron production in heavy materials that are often used as shield in low background experiments.

Ricerca di criteri analitico-progettuali per la riqualificazione paesaggistica di strutture e infrastrutture in aziende agricole multifunzionali.

Obiettivo generale dello studio è rivolto alla definizione di linee d’indirizzo volte alla riqualificazione paesaggistica, per l’integrazione ed il recupero delle corti e degli edifici moderni dei centri aziendali agricoli a carattere multifunzionale in territorio rurale, attraverso soluzioni appropriate sia sul piano tecnologico-formale che su quello economico-funzionale. Con riferimento ad un’area studio sovracomunale della provincia di Bologna (Regione Emilia-Romagna), si è determinato, quale obiettivo specifico, l’individuazione delle possibili soluzioni di riqualificazione, da realizzarsi in economia, cioè primariamente attraverso i mezzi e le competenze normalmente disponibili in un’azienda agricola di questo tipo. A seguito del riconoscimento dei caratteri specifici e dei tipi edilizi degli edifici rurali tradizionali nella pianura emiliano romagnola, dell’identificazione delle metodologie d’indagine dei caratteri degli edifici rurali in letteratura, nonché dell’analisi della normativa di riferimento in materia di aziende multifunzionali, sono state definite le aziende studio, appartenenti ad aree geografiche differenti. La metodologia d’indagine individuata è stata condotta per la determinazione delle tipologie costruttive, dei materiali utilizzati e dei requisiti delle aziende, in relazione alle diverse specificità, alla definizione funzionale degli spazi costruiti, degli spazi aperti e delle differenti relazioni fra essi e l’identificazione ed analisi dei percorsi delle diverse tipologie di fruitori. L’identificazione delle criticità dei caratteri architettonici riscontrate, sia negli edifici agricoli sia nella corte, ha condotto al riconoscimento degli ambiti di intervento per la progettazione delle soluzioni di riqualificazione funzionale e paesaggistica, attraverso lo studio delle possibili soluzioni per la schermatura o rivalorizzazione sia degli edifici moderni di servizio all’agricoltura (analizzando le potenzialità progettuali offerte dalle pareti verdi, dai brise soleil, dalle facciate ventilate o da intonaci e tinteggiature), sia per la riqualificazione dei percorsi e degli aspetti paesaggistici (intervenendo sulla proposta di materiali da pavimentazione, e delle essenze da utilizzare), da realizzarsi in economia, ma comparati con alternative proposte di tipo commerciale.

High-Speed Laser Processing of Thin Single and Multi-Layer Films

Theoretical models are developed for the continuous-wave and pulsed laser incision and cut of thin single and multi-layer films. A one-dimensional steady-state model establishes the theoretical foundations of the problem by combining a power-balance integral with heat flow in the direction of laser motion. In this approach, classical modelling methods for laser processing are extended by introducing multi-layer optical absorption and thermal properties. The calculation domain is consequently divided in correspondence with the progressive removal of individual layers. A second, time-domain numerical model for the short-pulse laser ablation of metals accounts for changes in optical and thermal properties during a single laser pulse. With sufficient fluence, the target surface is heated towards its critical temperature and homogeneous boiling or "phase explosion" takes place. Improvements are seen over previous works with the more accurate calculation of optical absorption and shielding of the incident beam by the ablation products. A third, general time-domain numerical laser processing model combines ablation depth and energy absorption data from the short-pulse model with two-dimensional heat flow in an arbitrary multi-layer structure. Layer removal is the result of both progressive short-pulse ablation and classical vaporisation due to long-term heating of the sample. At low velocity, pulsed laser exposure of multi-layer films comprising aluminium-plastic and aluminium-paper are found to be characterised by short-pulse ablation of the metallic layer and vaporisation or degradation of the others due to thermal conduction from the former. At high velocity, all layers of the two films are ultimately removed by vaporisation or degradation as the average beam power is increased to achieve a complete cut. The transition velocity between the two characteristic removal types is shown to be a function of the pulse repetition rate. An experimental investigation validates the simulation results and provides new laser processing data for some typical packaging materials.