Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Implementazione di un codice di calcolo random close per un propellente solido

L’impacchettamento risulta essere importante in molti settori industriali, come il settore minerario, farmaceutico e soprattutto il settore spaziale, in quanto permette di massimizzare il grado di riempimento del propellente solido di un razzo ottenendo prestazioni migliori e notevoli vantaggi economici. Il lavoro di tesi presentato nel seguente elaborato consiste nello studio dell’impacchettamento casuale, in particolare il caso Random Close Packing, di un propellente solido; per fare ciò è stato implementato un codice in ambiente C++ presso l’hangar della Scuola di Ingegneria ed Architettura con sede a Forlì. L’obiettivo principale era quello di trovare la granulometria delle particelle di perclorato di ammonio e delle particelle di alluminio tali da minimizzare gli spazi lasciati vuoti dalle particelle stesse.

Liquid crystalline cellulose derivatives for mirrorless lasing

In this thesis cholesteric films made of liquid crystalline cellulose derivatives with improved optical properties were prepared. The choice of the solvent, hydrogen bond influencing additives, the synthetic realization of a very high degree of substitution on the cellulosic polymer and the use of mechanical stirring at the upper concentration limit of the liquid crystalline range were the basis for an improved alignment of the applied cellulose tricarbamates. In combination with a tuned substrate treatment and film preparation method, cholesteric films were obtained, with optical properties that were theoretically predicted and only known from low molecular weight liquid crystals so far. Subsequent polymerization allowed a permanent fixing of the alignment and the fabrication of free standing and insensitive films.rnThe incorporation of inorganic nanorods into the cholesteric host material was mediated with tailored block copolymers, available via controlled radical polymerization methods. In addition to the shape match between the rodlike mesogens of the host and the nanorods it was possible to increase the miscibility of both materials. Nevertheless, the size of the nanorods, in comparison to the mesogens, in these densely packed liquid crystalline phases as well as their long equilibration times were the reasons for phase separation. Nanorods are, in principle, valuable substitutes for organics, but their utilization in cellulosic CLC was not to be combined with a high quality alignment of the cholesteric structure.rnA swelling process of polymerized films in a dye solution or dissolving dyes in non-polymerized CLC was used for incorporation of the organic chromophores. With the first method the CLC could be aligned and polymerized without any disturbance due to dye molecules. The optical properties of dye and CLC were matched, with regard to mirrorless lasing devices. The dye was optically excited and laser emission supported by the cholesteric cavity was obtained. The polarization and wavelength of the emitted radiation as well as its bandwidth, the obtained interference pattern and threshold behavior of the emission proofed the feedback mechanism that was not believed to be realizable in liquid crystalline polymers. rnUtilization of a microfluidic co-flow injection device enabled us to transfer the properties of cellulosic CLC from the planar film shape to spherical micrometer sized particles. The pure material yielded particles with distorted mesogen alignment similar to films prepared by capillary flow. Dilution of the CLC with a solvent that migrated into the carrier phase during particle preparation provided the basis for particles with well ordered areas. rnAlthough cellulose derivatives were known for their liquid crystalline behavior for decades and synthesized in mass production, their application as feedback material was affected by bad optical properties. In comparison to low molar mass compounds, the low degree of order in the CLC phase was the cause. With the improved material, defined lasing emission was shown and characterized. Derivatives of cellulose are desirable materials, because, as a renewable resource, they are available in large amounts for a low price and need only simple derivatization reactions. The fabrication of CLC films with tunable lasing emission, for which this thesis can provide a starting point, is in good agreement with today's requirements of modern technology and its miniaturization.rn

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Organic lasing: correlation between molecular structure, optical and optoelectronic properties

In this thesis mainly two alternating indenofluorene-phenanthrene copolymers were investigated with a variety of spectroscopic and optoelectronic experiments. The different experimental techniques allowed to retrieve deeper insights into their unique optical as well as optoelectronic properties. The motivation of the research presented in this work was to correlate their photophysical properties with respect to their application in electrically pumped lasing. This thesis begins with the description of optical properties studied by classical absorption and emission spectroscopy and successively describes an overall picture regarding their excited state dynamics occurring after photoexcitation studied by time-resolved spectroscopy. The different spectroscopic methods do not only allow to elucidate the different optical transitions occurring in this class of materials, but also contribute to a better understanding of exciton dynamics and exciton interaction with respect to the molecular structure as well as aggregation and photooxidation of the polymers. Furthermore, the stimulated emission properties were analyzed by amplified spontaneous emission (ASE) experiments. Especially one of the investigated materials, called BLUE-1, showed outstanding optical properties including a high optical gain, a low threshold for ASE and low optical losses. Apart from the optical experiments, the charge carrier mobility was measured with the time-of-flight technique and a comparably high hole mobility on the order of 1 x 10-² cm²/(Vs) was determined for BLUE-1 which makes this material promising for organic lasing. The impact of the high charge carrier mobility in this material class was further analyzed in different optoelectronic devices such as organic LEDs (OLEDs) and organic solar cells.

Crystallization and morphology of the PLLA phase within random poly (L-lactide-ran-ɛ-caprolactone)

This work has mainly focused on the poly (L-lactide) (PLLA) which is a material for multiple applications with performances comparable to those of petrochemical polymers (PP, PS, PET, etc. ...), readily recyclable and also compostable. However, PLLA has certain shortcomings that limit its applications. It is a brittle, hard polymer with a very low elongation at break, hydrophobic, exhibits low crystallization kinetics and takes a long time to degrade. The properties of PLLA may be modified by copolymerization (random, block, and graft) of L-lactide monomers with other co-monomers. In this thesis it has been studied the crystallization and morphology of random copolymers poly (L-lactide-ran-ε-caprolactone) with different compositions of the two monomers since the physical, mechanical, optical and chemical properties of a material depend on this behavior. Thermal analyses were performed by differential scanning calorimetry (DSC) and thermogravimetry (TGA) to observe behaviors due to the different compositions of the copolymers. The crystallization kinetics and morphology of poly (L-lactide-ran-ε-caprolactone) was investigated by polarized light optical microscopy (PLOM) and differential scanning calorimetry (DSC). Their thermal behavior was observed with crystallization from melt. It was observed that with increasing amounts of PCL in the copolymer, there is a decrease of the thermal degradation. Studies on the crystallization kinetics have shown that small quantities of PCL in the copolymer increase the overall crystallization kinetics and the crystal growth rate which decreases with higher quantities of PCL.

Studio e implementazione di un modello random-close per propellenti solidi

L'obiettivo di questo lavoro di tesi è quello di implementare un codice di calcolo, attraverso l'algoritmo di Lubachevsky-Stillinger, in modo da poter prevedere la frazione volumetrica occupata dalle particelle solide che costituiscono il grain negli endoreattori a propellente solido. Particolare attenzione verrà rivolta al problema dell'impacchettamento sferico random (Random-Close Packing) che tale algoritmo cerca di modellare, e le ipotesi per cui tale modellazione può essere applicata al tipo di problema proposto. Inoltre saranno descritte le procedure effettuate per l'ottenimento dei risultati numerici delle simulazioni e la loro motivazione, oltre ai limiti del modello utilizzato e alle migliorie apportate per un'esecuzione più efficiente e veloce.

Progetto vhdl di un nucleo di calcolo per misure di impedenza basate su segnali pseudo-random

In questo elaborato si affronta il progetto di un nucleo di calcolo per misure d'impedenza sulla pelle tramite l'utilizzo di segnali pseudo-random. La misura viene effettuata applicando il segnale casuale all'impedenza per ottenere la risposta impulsiva tramite un'operazione di convoluzione. Il nucleo di calcolo è stato implementato in VHDL.

Fluctuation properties in random walks on networks and simple integrate and fire models

In questa tesi si è studiato l’insorgere di eventi critici in un semplice modello neurale del tipo Integrate and Fire, basato su processi dinamici stocastici markoviani definiti su una rete. Il segnale neurale elettrico è stato modellato da un flusso di particelle. Si è concentrata l’attenzione sulla fase transiente del sistema, cercando di identificare fenomeni simili alla sincronizzazione neurale, la quale può essere considerata un evento critico. Sono state studiate reti particolarmente semplici, trovando che il modello proposto ha la capacità di produrre effetti "a cascata" nell’attività neurale, dovuti a Self Organized Criticality (auto organizzazione del sistema in stati instabili); questi effetti non vengono invece osservati in Random Walks sulle stesse reti. Si è visto che un piccolo stimolo random è capace di generare nell’attività della rete delle fluttuazioni notevoli, in particolar modo se il sistema si trova in una fase al limite dell’equilibrio. I picchi di attività così rilevati sono stati interpretati come valanghe di segnale neurale, fenomeno riconducibile alla sincronizzazione.

Mission synthesis of sine-on-random excitations for accelerated vibration qualification testing

In most real-life environments, mechanical or electronic components are subjected to vibrations. Some of these components may have to pass qualification tests to verify that they can withstand the fatigue damage they will encounter during their operational life. In order to conduct a reliable test, the environmental excitations can be taken as a reference to synthesize the test profile: this procedure is referred to as “test tailoring”. Due to cost and feasibility reasons, accelerated qualification tests are usually performed. In this case, the duration of the original excitation which acts on the component for its entire life-cycle, typically hundreds or thousands of hours, is reduced. In particular, the “Mission Synthesis” procedure lets to quantify the induced damage of the environmental vibration through two functions: the Fatigue Damage Spectrum (FDS) quantifies the fatigue damage, while the Maximum Response Spectrum (MRS) quantifies the maximum stress. Then, a new random Power Spectral Density (PSD) can be synthesized, with same amount of induced damage, but a specified duration in order to conduct accelerated tests. In this work, the Mission Synthesis procedure is applied in the case of so-called Sine-on-Random vibrations, i.e. excitations composed of random vibrations superimposed on deterministic contributions, in the form of sine tones typically due to some rotating parts of the system (e.g. helicopters, engine-mounted components, …). In fact, a proper test tailoring should not only preserve the accumulated fatigue damage, but also the “nature” of the excitation (in this case the sinusoidal components superimposed on the random process) in order to obtain reliable results. The classic time-domain approach is taken as a reference for the comparison of different methods for the FDS calculation in presence of Sine-on-Random vibrations. Then, a methodology to compute a Sine-on-Random specification based on a mission FDS is presented.

On the recurrence of random walks in Lévy random environments

This thesis investigates one-dimensional random walks in random environment whose transition probabilities might have an infinite variance. The ergodicity of the dynamical system ''from the point of view of the particle'' is proved under the assumptions of transitivity and existence of an absolutely continuous steady state on the space of the environments. We show that, if the average of the local drift over the environments is summable and null, then the RWRE is recurrent. We provide an example satisfying all the hypotheses.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Atlas-Based Segmentation of Brain Tumor Images Using a Markov Random Field-Based Tumor Growth Model and Non-Rigid Registration

We propose a new and clinically oriented approach to perform atlas-based segmentation of brain tumor images. A mesh-free method is used to model tumor-induced soft tissue deformations in a healthy brain atlas image with subsequent registration of the modified atlas to a pathologic patient image. The atlas is seeded with a tumor position prior and tumor growth simulating the tumor mass effect is performed with the aim of improving the registration accuracy in case of patients with space-occupying lesions. We perform tests on 2D axial slices of five different patient data sets and show that the approach gives good results for the segmentation of white matter, grey matter, cerebrospinal fluid and the tumor.