Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Variability analysis of discrete event series and wavefront patterns in surface electrocardiogram: contributions to psychophysiological and clinical research

The surface electrocardiogram (ECG) is an established diagnostic tool for the detection of abnormalities in the electrical activity of the heart. The interest of the ECG, however, extends beyond the diagnostic purpose. In recent years, studies in cognitive psychophysiology have related heart rate variability (HRV) to memory performance and mental workload. The aim of this thesis was to analyze the variability of surface ECG derived rhythms, at two different time scales: the discrete-event time scale, typical of beat-related features (Objective I), and the “continuous” time scale of separated sources in the ECG (Objective II), in selected scenarios relevant to psychophysiological and clinical research, respectively. Objective I) Joint time-frequency and non-linear analysis of HRV was carried out, with the goal of assessing psychophysiological workload (PPW) in response to working memory engaging tasks. Results from fourteen healthy young subjects suggest the potential use of the proposed indices in discriminating PPW levels in response to varying memory-search task difficulty. Objective II) A novel source-cancellation method based on morphology clustering was proposed for the estimation of the atrial wavefront in atrial fibrillation (AF) from body surface potential maps. Strong direct correlation between spectral concentration (SC) of atrial wavefront and temporal variability of the spectral distribution was shown in persistent AF patients, suggesting that with higher SC, shorter observation time is required to collect spectral distribution, from which the fibrillatory rate is estimated. This could be time and cost effective in clinical decision-making. The results held for reduced leads sets, suggesting that a simplified setup could also be considered, further reducing the costs. In designing the methods of this thesis, an online signal processing approach was kept, with the goal of contributing to real-world applicability. An algorithm for automatic assessment of ambulatory ECG quality, and an automatic ECG delineation algorithm were designed and validated.

Comportamento dinamico fuori del piano di pareti murarie: influenza della deformabilità degli impalcati

The aim of this study was to investigate the influence of the diaphragm flexibility on the behavior of out-of-plane walls in masonry buildings. Simplified models have been developed to perform kinematic and dynamic analyses in order to compare the response of walls with different restraint conditions. Kinematic non linear analyses of assemblages of rigid blocks have been performed to obtain the acceleration-displacement curves for walls with different restraint conditions at the top. A simplified 2DOF model has been developed to analyse the dynamic response of the wall with an elastic spring at the top, following the Housner rigid behaviour hypothesis. The dissipation of energy is concentrated at every impact at the base of the wall and is modelled through the introduction of the coefficient of restitution. The sets of equations of the possible configurations of the wall, depending on the different positions of the centre of rotation at the base and at the intermediate hinge have been obtained. An algorithm for the numerical integration of the sets of the equations of motion in the time domain has been developed. Dynamic analyses of a set of walls with Gaussian impulses and recorded accelerograms inputs have been performed in order to compare the response of the simply supported wall with the one of the wall with elastic spring at the top. The influence of diaphragm stiffness Kd has been investigated determining the variation of maximum displacement demand with the value of Kd. A more regular trend has been obtained for the Gaussian input than for the recorded accelerograms.

Valutazione della risposta sismica di edifici mediante modelli anelastici equivalenti

Nella presente tesi è proposta una metodologia per lo studio e la valutazione del comportamento sismico di edifici a telaio. Il metodo prevede la realizzazione di analisi non-lineari su modelli equivalenti MDOF tipo stick, in accordo alla classificazione data nel report FEMA 440. Gli step per l’applicazione del metodo sono descritti nella tesi. Per la validazione della metodologia si sono utilizzati confronti con analisi time-history condotte su modelli tridimensionali dettagliati delle strutture studiate (detailed model). I parametri ingegneristici considerati nel confronto, nell’ottica di utilizzare il metodo proposto in un approccio del tipo Displacement-Based Design sono lo spostamento globale in sommità, gli spostamenti di interpiano, le forze di piano e la forza totale alla base. I risultati delle analisi condotte sui modelli stick equivalenti, mostrano una buona corrispondenza, ottima in certi casi, con quelli delle analisi condotte sui modelli tridimensionali dettagliati. Le time-history realizzate sugli stick model permettono però, un consistente risparmio in termini di onere computazionale e di tempo per il post-processing dei risultati ottenuti.

Transport Properties and Novel Sensing Applications of Organic Semiconducting Crystals

The present thesis is focused on the study of Organic Semiconducting Single Crystals (OSSCs) and crystalline thin films. In particular solution-grown OSSC, e.g. 4-hdroxycyanobenzene (4HCB) have been characterized in view of their applications as novel sensors of X-rays, gamma-rays, alpha particles radiations and chemical sensors. In the field of ionizing radiation detection, organic semiconductors have been proposed so far mainly as indirect detectors, i.e. as scintillators or as photodiodes. I first study the performance of 4HCB single crystals as direct X-ray detector i.e. the direct photon conversion into an electrical signal, assessing that they can operate at room temperature and in atmosphere, showing a stable and linear response with increasing dose rate. A dedicated study of the collecting electrodes geometry, crystal thickness and interaction volume allowed us to maximize the charge collection efficiency and sensitivity, thus assessing how OSSCs perform at low operating voltages and offer a great potential in the development of novel ionizing radiation sensors. To better understand the processes generating the observed X-ray signal, a comparative study is presented on OSSCs based on several small-molecules: 1,5-dinitronaphthalene (DNN), 1,8-naphthaleneimide (NTI), Rubrene and TIPS-pentacene. In addition, the proof of principle of gamma-rays and alpha particles has been assessed for 4HCB single crystals. I have also carried out an investigation of the electrical response of OSSCs exposed to vapour of volatile molecules, polar and non-polar. The last chapter deals with rubrene, the highest performing molecular crystals for electronic applications. We present an investigation on high quality, millimeter-sized, crystalline thin films (10 – 100 nm thick) realized by exploiting organic molecular beam epitaxy on water-soluble substrates. Space-Charge-Limited Current (SCLC) and photocurrent spectroscopy measurements have been carried out. A thin film transistor was fabricated onto a Cytop® dielectric layer. The FET mobility exceeding 2 cm2/Vs, definitely assess the quality of RUB films.