Η παρούσα εργασία αναφέρεται στη μελέτη της ηλεκτρικής εκκένωσης τύπου κορώνας και ιδιαίτερα στα ηλεκτρικά και υδροδυναμικά (ηλεκτρικός άνεμος) φαινόμενα που τη συνοδεύουν. Μια εκκένωση κορώνας είναι το φαινόμενο που δημιουργείται σε ένα αέριο διάκενο μεταξύ δύο ηλεκτροδίων διαφορετικής ακτίνας καμπυλότητας, όταν αυτά βρίσκονται υπό την επίδραση διαφοράς δυναμικού μερικών kV. Η εκκένωση κορώνας συνοδεύεται από την εμφάνιση ηλεκτρικών, οπτικών, ακουστικών, χημικών, αεροδυναμικών (ηλεκτρικός άνεμος) και ραδιοηλεκτρικών φαινομένων. Ο ηλεκτρικός άνεμος είναι ένα φαινόμενο το οποίο δημιουργείται από τη μετάδοση της ορμής των ιόντων στα ουδέτερα μόρια του αερίου οπότε παρατηρείται μία κίνηση του αερίου από το ηλεκτρόδιο με μικρή ακτίνα καμπυλότητας, προς το άλλο ηλεκτρόδιο. Το κύριο αντικείμενο της εργασίας αυτής είναι η μελέτη του φαινομένου της θετικής κορώνας, μεταξύ μιας μη συμμετρικής διάταξης ηλεκτροδίων, στον ατμοσφαιρικό αέρα. Στην άνοδο τοποθετήθηκαν μια και δύο ακίδες της ίδιας ακτίνας καμπυλότητας ενώ χρησιμοποιήθηκαν τρεις διαφορετικές κάθοδοι. Οι πειραματικές μετρήσεις είχαν ως στόχο τον προσδιορισμό της χαρακτηριστικής του μέσου ρεύματος της εκκένωσης συναρτήσει της τάσης διακένου, των παλμών του ρεύματος για διάφορες τιμές της τάσης , τον προσδιορισμό της κατανομής και της χαρακτηριστικής της ταχύτητας του ηλεκτρικού ανέμου καθώς και της χαρακτηριστικής της θερμοκρασίας του ηλεκτρικού ανέμου. Πρέπει να αναφέρουμε ότι οι μετρήσεις πραγματοποιήθηκαν για συνεχή και παλμική τάση λειτουργίας. / In this thesis, the effect of the positive corona discharge was studied. Especially, electric and hydrodynamic phenomena (corona wind) were studied. By the term “corona discharge”, one generally refers to the ensemble of phenomena which occur in a gaseous medium in the vicinity of conductors of small radius of curvature, subjected to intense, but not disruptive, electric fields. The main part of this thesis is experimental procedures that were held between a non-symmetrical set-up of electrodes in atmospheric air in order to, initially define the V-I characteristics and study the current impulses for different voltage values. Furthermore, we studied the velocity distribution and velocity characteristics of corona wind. In the last part of this work the temperature characteristics are present. It is important to mention that the experimental measurements were carried out on continuous and pulsed voltage.

Le système de FitzHugh-Nagumo stochastique est un modèle qualitatif pour la propagation de l’influx nerveux dans un neurone. Ce système lent-rapide s’écrit εdxt = (xt - xt3 + yt) dt + √εσ1 dWt(1), dyt = (a - bxt - cyt) dt + σ2 dwt(2) où a, b et c sont des réels, ε est un petit réel positif, σ1 et σ2 sont deux réels positifs représentant l’intensité du bruit, Wt(1) et Wt(2) sont deux mouvements browniens standards indépendants. Dans cette thèse, nous étudions d’abord le système déterministe associé (σ1 = σ2 = 0) et montrons qu’il est excitable. Nous regardons ensuite le cas particulier où b = 0. Dans ce cas, le comportement au voisinage du point d’équilibre est le même que celui d’un autre modèle, celui de Morris-Lecar. Nous étudions alors la loi du temps de sortie de ce voisinage. Dans le cas général, après avoir mis en évidence trois principaux régimes, nous montrons des résultats généraux sur la distribution du nombre de petites oscillations N entre deux spikes consécutifs en introduisant une chaîne de Markov. Puis nous étudions le cas particulier du régime de bruit faible. / The stochastic FitzHugh-Nagumo equations is a qualitative model for the dynamics of neuronalaction potential. This slow-fast system is written εdxt = (xt - xt3 + yt) dt + √εσ1 dWt(1), dyt = (a - bxt - cyt) dt + σ2 dwt(2) where a, b and c are real numbers, ε is a small positive real number, σ1 et σ2 are two positivereal number representing the intensity of noise, Wt(1) et Wt(2) are two standard Brownian motion independent.In this thesis, we first study the associated deterministic system (σ1 = σ2 = 0) and we show this system is excitable. Then we are interested in the particular case b = 0. In this case, the behaviorin the neighborhood of the equilibrium is the same as the Morris-Lecar model. We study the law ofthe exit time of this neighborhood. In the general case, we show there are three main regimes. Westudy the distribution of the number of small oscillations N between two consecutive spikes using a substochastic Markov chain. Then we obtain results in the case of the weak-noise regime.

The theory of impulsive dynamical systems is an important tool to describe the evolution of systems where the continuous development of a process is interrupted by abrupt changes of state. This phenomenon is called impulse. In many natural phenomena, the real deterministic models are often described by systems which involve impulses. The aim of this work is to investigate topological properties of impulsive semidynamical systems. We establish necessary and sufficient conditions to obtain uniform and orbital stability via Lyapunov functions. We solve a problem of Jake Hale for impulsive systems where we obtain the existence of a maximal compact invariant set. Also, we obtain results about almost periodic motions and asymptotically almost periodic motions in the context of impulsive systems. Some asymptotic properties for impulsive systems and for their associated discrete systems are investigated. The new results presented in this text are in the papers [11], [15] and [16]. / A teoria de sistemas dinâmicos com impulsos é apropriada para descrever processos de evolução que sofrem variações de estado de curta duração e que podem ser consideradas instantâneas. Este fenômeno é chamado impulso. Para muitos fenômenos naturais, os modelos determinísticos mais realistas são frequentemente descritos por sistemas que envolvem impulsos. O objetivo deste trabalho é estudar propriedades topológicas para sistemas semidinâmicos impulsivos. Estabelecemos condições necessárias e suficientes para obtermos estabilidade uniforme e estabilidade orbital utilizando funções do tipo Lyapunov. Resolvemos um problema de Jack Hale para os sistemas impulsivos, onde obtemos a existência de um conjunto invariante compacto maximal. Além disso, obtemos resultados de movimentos quase periódicos e movimentos assintoticamente quase periódicos para sistemas impulsivos. Algumas propriedades assintóticas são estabelecidas para um sistema impulsivo e para seu sistema discreto associado. Os resultados novos apresentados neste trabalho estão presentes nos artigos [11], [15] e [16].

In the stochastic modeling of neurons, the first passage time problem arises as a natural object of study when considering the inter spike interval distribution. In this report, we study some aspects of this problem as it arises in the context of neuroscience. In the first chapter we describe the basic neurophysiology required to model the neuron. In the second, we study the Poisson model, Stein’s model, and some diffusion models, calculating or indicating methods to compute the density of the first passage time random variable or its moments. In the third and fourth chapters, we study the Fokker-Planck equation, and use it to compute the first passage time in the discrete and continuous time random walk cases. In the final chapter, we study sequences of neurons and the change in the density of the waiting time distributions, and hence in the inter spike intervals, as the output spike train from one neuron is considered as the input in the subsequent neuron.

Sinc eancient times,the area we know today as Slovenia has been influenced by the diverse political, economic and cultural impulses that ran from north to south and from west to east. The bustle of activity along these trade routes brought novelties which refined and defined various spheres of everydaylife. It was no coincidence, therefore, that music culture aswell pulsated in various forms – it was unique, yet also tightly bound to other cultures. Throughout history, it was the neighbouring cultural environments that enjoyed the most intense interdependence with the Slovenian lands; the countries within the Austrian Empire and later the Austro-Hungarian Empire were most closely tied.

Inertial measurement units (IMUs) and wearable sensors have enabled athlete monitoring and research to become more ecologically valid due to their small size and low cost. IMUs and accelerometers that are placed on the body close to the point of impact and that record at sufficiently high frequencies have demonstrated the highest validity when measuring temporal gait event moments such as ground contact time (GCT) and flight time (FT) as well as peak forces (PF) during upright running. While the use of IMUs has increased in the sport performance and athlete monitoring realm, the potential of the technology’s ability to estimate running force-time curves utilizing the two-mass model (TMM) remains unexplored. The purpose of this study was two-fold. First, was to determine the validity of measuring temporal gait events and peak forces utilizing a commercially available shank-mounted inertial measurement unit. Second, was to determine the validity of force-time curves generated from the TMM utilizing data from shank-mounted inertial measurement units. Ten subjects voluntarily completed submaximal treadmill tests equipped with a force plate while wearing shank-mounted IMUs on each leg. Using the raw data from the IMUs, GCT, FT, total step time (ST), PF, and two-mass model-based force-time (F-t) curves were generated for 25 steps at 8 different speeds. Paired sample T-tests were performed on the gait events and peak force between the IMU and treadmill with both individual step comparison and averages per each speed. 95% confidence intervals were calculated for each timepoint of the force time curves. No statistically significant differences (p > 0.05) and nearly perfect relationships were observed for the step averages for each speed with FT, ST, and PF. Confidence intervals of the corrected mean difference suggest that F-t curves calculated from the TMM may not be valid when assessing the running population as a whole. When performing a sub-group analysis of skilled runners and recreational runners, F-t curves derived from shank-mounted IMUs may be more valid in skilled runners than recreational runners. In skilled runners, the 95% CI for the mean difference contained zero within the first 60% of the GCT duration, whereas the 95% CI recreational runners contained a zero-value in a smaller percentage of the GCT located only in the middle of the GCT at the curve peak height. The results of this study suggest that interchangeability between shank-mounted IMUs and force plates may be very limited when estimating temporal gait events and kinetics. While agreement was low between F-t curves after the peak in skilled runners, use of shank-mounted IMUs to estimate F-t curves may have several benefits still in skilled runners when assessing peak forces and force development from initial contact until peak force.

Neste trabalho, apresentamos condições suficientes para a existência e a unicidade de soluções periódicas para equações diferenciais funcionais com retardo e impulsos. Os resultados sobre existência estão ancorados num Teorema de Continuação de Jean Mawhin. Por outro lado, as condições que garantem a unicidade de soluções periódicas são condições do tipo Lipschitz / In this work, we present sufficient conditions for the existence and the uniqueness of periodic solutions for retarded functional differential equations with impulses. The results on the existence of periodic solutions are anchored by a Jean Mawhin continuation theorem. Moreover, the conditions that guarantee the uniqueness of the periodic solutions are Lipschitz type

Neste trabalho, apresentamos condições suficientes para a existência e a unicidade de soluções periódicas para equações diferenciais funcionais com retardo e impulsos. Os resultados sobre existência estão ancorados num Teorema de Continuação de Jean Mawhin. Por outro lado, as condições que garantem a unicidade de soluções periódicas são condições do tipo Lipschitz / In this work, we present sufficient conditions for the existence and the uniqueness of periodic solutions for retarded functional differential equations with impulses. The results on the existence of periodic solutions are anchored by a Jean Mawhin continuation theorem. Moreover, the conditions that guarantee the uniqueness of the periodic solutions are Lipschitz type

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Neste trabalho, apresentamos novos critérios para a existência de soluções oscilatórias e não oscilatórias de equações diferenciais funcionais em medida com impulsos, separando-as em duas classes: equações diferenciais funcionais retardadas e equações diferenciais funcionais com argumento avançado. Tratamos das formas integrais destas equações diferenciais usando as integrais de Perron e Perron-Stieltjes. Assim, as funções envolvidas podem ter muitas descontinuidades e/ou podem ser de variação ilimitada. / In this work, we present new criteria for the existence of oscillatory and nonoscillatory solutions of measure functional differential equations with impulses, separating them into two classes: delay differential equations and functional differential equations with advanced argument. We deal with the integral forms of the differential equations using the Perron and the Perron-Stieltjes integrals. Thus the functions involved can have many discontinuities and/or they can be of unbounded variation.