Estabilização de órbitas periódicas instáveis utilizando controle por modos deslizantes com compensação adaptativa

The chaotic behavior has been widely observed in nature, from physical and chemical phenomena to biological systems, present in many engineering applications and found in both simple mechanical oscillators and advanced communication systems. With regard to mechanical systems, the effects of nonlinearities on the dynamic behavior of the system are often of undesirable character, which has motivated the development of compensation strategies. However, it has been recently found that there are situations in which the richness of nonlinear dynamics becomes attractive. Due to their parametric sensitivity, chaotic systems can suffer considerable changes by small variations on the value of their parameters, which is extremely favorable when we want to give greater flexibility to the controlled system. Hence, we analyze in this work the parametric sensitivity of Duffing oscillator, in particular its unstable periodic orbits and Poincar´e section due to changes in nominal value of the parameter that multiplies the cubic term. Since the amount of energy needed to stabilize Unstable Periodic Orbits is minimum, we analyze the control action needed to control and stabilize such orbits which belong to different versions of the Duffing oscillator. For that we will use a smoothed sliding mode controller with an adaptive compensation term based on Fourier series.

Slow deterministic vector rogue waves

For an erbium-doped fiber laser mode-locked by carbon nanotubes, we demonstrate experimentally and theoretically a new type of the vector rogue waves emerging as a result of the chaotic evolution of the trajectories between two orthogonal states of polarization on the Poincare sphere. In terms of fluctuation induced phenomena, by tuning polarization controller for the pump wave and in-cavity polarization controller, we are able to control the Kramers time, i.e. the residence time of the trajectory in vicinity of each orthogonal state of polarization, and so can cause the rare events satisfying rogue wave criteria and having the form of transitions from the state with the long residence time to the state with a short residence time.

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Comparing the orthogonal and homotopy functor calculi

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.

Analisi della stabilità motoria durante il cammino: come gli indici di variabilità e stabilità dell'accelerazione del centro di massa sono influenzati da processi cognitivi (dual-task)

La valutazione strumentale del cammino è solitamente svolta chiedendo ai soggetti semplicemente di camminare (ST). Tale condizione non rappresenta la quotidianità. Infatti, nella vita di tutti i giorni la locomozione richiede di adattarsi alle necessità individuali e il coinvolgimento di attività cognitive. I paradigmi di Dual-Task (DT) sono utilizzati per valutare i cambiamenti nella strategia di controllo del cammino in situazioni di vita quotidiana. In particolare, gli indici di performance, di variabilità e di stabilità, utilizzati nella valutazione del controllo motorio, potrebbero essere utili per valutare le interferenze cognitive durante il cammino. L’obiettivo del lavoro è di valutare come tali indici cambiano durante il Dual-Task. Sono stati reclutati 16 studenti, giovani e sani, della Facoltà di Ingegneria Biomedica di Cesena, ai quali è stato chiesto di compiere un cammino rettilineo di 250 m, senza ostacoli, all’aperto, in due condizioni: svolgendo la sola attività di cammino (ST); aggiungendo al precedente task, una sottrazione consecutiva di 7 ad alta voce, partendo da un numero casuale (DT). Tramite tre sensori inerziali tri-assiali, posti sul tronco (L5) e sulle caviglie, sono stati acquisiti i segnali di accelerazione e velocità angolare. Dopo aver calcolato, a partire da tali dati, indici di performance (numero di passi, cadence, velocità e tempo di esecuzione del test), di variabilità (Standard Deviation, Coefficient of Variation, Index of the Variance, Nonstationary Index, Poincare 4 Plots) e di stabilità (Harmonic Ratio e Index of Harmonicity), nelle due condizioni (ST e DT), è stata eseguita un’analisi statistica tra i due task. Le analisi statistiche condotte su tali indici hanno evidenziato che il DT influenza prevalentemente gli indici di performance (numero di passi, cadence, velocità e tempo di esecuzione del test) e in grado minore gli indici di variabilità e stabilità.

Vector self-pulsing in erbium-doped fiber lasers

Insight into instabilities of fiber laser regimes leading to complex self-pulsing operations is an opportunity to unlock the high power and dynamic operation tunability of lasers. Though many models have been suggested, there is no complete covering of self-pulsing complexity observed experimentally. Here, I further generalized our previous vector model of erbium-doped fiber laser and, for the first time, to the best of my knowledge, map tunability of complex vector self-pulsing on Poincare sphere (limit cycles and double scroll polarization attractors) for laser parameters, e.g., power, ellipticity of the pump wave, and in-cavity birefringence. Analysis validated by extensive numerical simulations demonstrates good correspondence to the experimental results on complex self-pulsing regimes obtained by many authors during the last 20 years.