Η παρούσα εργασία χωρίζεται σε δύο μέρη. Στην εισαγωγή γίνεται μια ιστορική ανασκόπηση. Στο δεύτερο κεφάλαιο παρουσιάζονται όλες εκείνες οι βασικές εισαγωγικές έννοιες που χρησιμοποιούνται από τη θεωρία του χάους και στο τρίτο κεφάλαιο γίνεται μια στοιχειώδης σύνοψη της Κβαντομηχανικής, τονίζονται οι διαφορές από την κλασική θεωρία και επιχειρείται μια πρώτη προσέγγιση στο ερώτημα "μπορεί να υπάρξει κβαντικό χάος"; Επίσης γίνεται μια πρώτη αναφορά για τις στατιστικές κατανομές ιδιοτιμών και ιδιοσυναρτήσεων που παρατηρούνται στα κβαντομηχανικά συστήματα και βγαίνουν τα πρώτα θεωρητικά συμπεράσματα. Το δεύτερο μέρος είναι αφιερωμένο στα κβαντικά μπιλιάρδα. Το τέταρτο κεφάλαιο ασχολείται με τις στατιστικές ιδιότητες των ιδιοτιμών και των ιδιοσυναρτήσεων. Στο πέμπτο κεφάλαιο παρουσιάζεται αναλυτικά η μέθοδος μετασχηματισμού εφελκυσμού η οποία είναι και η μέθοδος που ακολουθήθηκε για την εξαγωγή των ιδιοτιμών στα πειραματικά μας δεδομένα. Επίσης παρουσιάζεται το μπιλιάρδο του Robnik και διάφορα άλλα μπιλιάρδα. Τέλος παρουσιάζονται τα συμπεράσματα από τη στατιστική ανάλυση των ιδιοτήτων των παραπάνω μπιλιάρδων. Επίσης υπάρχουν και τέσσερα παραρτήματα που αφορούν τη Θεωρία τυχαίων μητρών, Θεωρία διαταραχών, Στοιχειώδη τανυστική ανάλυση και άλλες αριθμητικές μεθόδους υπολογισμού των ιδιοτιμών και ιδιοκαταστάσεων κβαντικών μπιλιάρδων. / -

Community college boards of trustees are faced with the awesome responsibility of governing complex systems and responding to conventional organizational challenges. One Texas board of trustees was faced with the inconceivable challenge of regaining the trust of its district and the community after questionable circumstances surrounding the resignation of the chancellor, indictments of two board members and the former chairman of the board, and other behavior that although not illegal, was unethical and morally corrupt. This study looks at the transformation of a community college board over a two-year period, from a state of organizational disarray to seeking community support for a $450 million bond package. The research chronicles the transition by comparing and contrasting the accounts of what transpired, with the principles of chaos theory, transformational leadership and the John Carver Policy Governance® Model. For an entity in organizational chaos, a commitment to transform is needed to ultimately reach the point where it can adopt governance principles to provide the foundation for effective leadership, such as those espoused by the Carver model. Change must occur and the success or failure of an organization or system depends on how effective the leadership is at identifying challenges and working with them to create opportunities. When an organization approaches chaos and the need for changes with trepidation, progress and success are improbable. It is the understanding that order emerges from chaos that leads to a renewed mindset; a mindset that looks beyond traditional structures and embraces flexibility, innovation and creativity. The resolve of the trustees to regain public trust and support has served as the impetus to implement the changes needed to govern the district effectively. / text

In the course Discrete Deterministic Chaos, Dr. Mark Daniels introduces students to Chaos Theory and explores many topics within the field. Students prove many of the key results that are discussed in class and work through examples of each topic. Connections to the secondary mathematics curriculum are made throughout the course, and students discuss how the topics in the course could be implemented in the classroom. This paper will provide an overview of the topics covered in the course, Discrete Deterministic Chaos, and provide additional discussion on various related topics. / text

We study the classical nonlinear dynamics and the quantum vibrational energy eigenstates of the molecule HOCl. The classical vibrational dynamics, at energies below the HO+Cl dissociation energy, contains several saddle-center and period doubling bifurcations. The saddle-center bifurcations are shown to be due to a 2:1, and at higher energies a 3:1, nonlinear resonance between bend and stretch motions in various periodic orbits. The sequence of bifurcations takes the system from nearly integrable at low energies to almost completely chaotic at energies near the HO+Cl dissociation energy. At energies above dissociation we study the chaotic scattering of the Cl atom off the HO dimer. This scattering is governed by a homoclinic tangle formed by the stable and unstable manifolds of a parabolic periodic orbit at infinity. We construct the first three segments of the homoclinic tangle in phase space and use scattering functions to investigate its higher-order structure. For the quantum system we use a discrete variable representation to efficiently calculate the Hamiltonian matrix. We find 365 even and 357 odd parity eigenstates with energies below the dissociation energy. By plotting the eigenstates in configuration space we show that almost every quantum eigenstate can be associated with one or more of the classical periodic orbits. The classical bifurcations that give rise to new periodic orbits are manifest quantum mechanically through the sudden appearance of new classes of eigenstates. Despite the high degree of chaos in the classical dynamics at energies near the dissociation energy most quantum eigenstates remain highly ordered with recognizable nodal patterns. We use R-matrix theory together with a discrete variable representation to calculate quasibound states with energies above the dissociation energy. We find quasibound states with lifetimes ranging over 5 orders of magnitude. Using configuration space plots and Husimi distributions we show that the long-lived quasibound states are supported by unstable periodic orbits in the classical dynamics and medium-lived quasibound states are spread throughout the chaotic region of the classical phase space. Short-lived quasibound states show some similarity to unstable periodic orbits that stretch along the dissociation channel. / text

Το θέμα της διπλωματικής μεταπτυχιακής εργασίας είναι οι συνήθεις μη γραμμικότητες και οι εφαρμογές τους. Σχεδιάζονται, εξομοιώνονται και υλοποιούνται στην πράξη απλοί και σύνθετοι μη γραμμικοί αντιστάτες τμηματικής γραμμικότητας (PieceWise-Linear – PWL). Ιδιαίτερη προσοχή δίνεται στην υλοποίηση της διόδου Chua καθώς και στο σχεδιασμό και υλοποίηση του ίδιου του χαοτικού κυκλώματος Chua. Ταυτόχρονα δίνονται συνοπτικά στοιχεία θεωρίας χάους. Επιπλέον, μελετάται και υλοποιείται υπερχαοτικός ταλαντωτής κατάλληλος για συγχρονισμό και εφαρμογή σε ασφαλείς επικοινωνίες. Αυτός ο υπερχαοτικός ταλαντωτής βασίζεται σε έναν LC ταλαντωτή και το γνωστό Deliyannis SAB συζευγμένα μέσω μιας διόδου. Σε όλα τα παραπάνω πρέπει να προστεθεί η συγκέντρωση όλης της σχετικής βιβλιογραφίας. / The subject of this diploma thesis is to study usual nonlinearities and their applications. Simple and composite nonlinear piecewise-linear resistors have been designed, simulated and implemented. A great care is shown towards implementing the Chua’s diode and designing and implementing the chaotic Chua’s circuit itself. At the same time some basics of chaos theory are given. Moreover, a hyperchaotic oscillator is studied which is suitable for synchronization and application in secure communications. This hyperchaotic oscillator is based on a LC oscillator and the well-known Deliyannis SAB coupled by means of a diode. To all above, one should add the very rich bibliography, which has now been accumulated for the benefit of all concerned in the Electronics Laboratory.

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The central purpose of this study is the integration of modem philosophical thinking with different chaos theory principles and definitions to form relational perspectives. Relations are used in different contexts to base the causes of deterministic chaos (chaost) in the laws of nature which constitutes order. The chaost-attractor is used as subjective conception to investigate the possibilities of hidden order in a seemingly chaotic state of the objective reality. Relevant definitions of the chaos theory were analysed methodically and transcendentally with the aid of concepts of order and relations. Attention is given to the broad associations and analogies from philosophy and other disciplines which relate to the connectivity of objects to form systems. Subjective model development was done which is used to consequentially analyse some statements from published research which applied principles of chaost. It is argued that: the intrinsic properties of objects determine the causality of forces which bind objects to compose systems; a web of interactive bonds functions subjective to laws of nature which determine whether a system is in a state of order, chaost or real chaos; a dynamical transfer of many intrinsic and asymmetric properties via internal bonds constitutes non-linear connectivity which causes a sensitivity for initial conditions. It is found that the chaost of the chaos theory is not the same as real, objective chaos. The random-like evolution of a dynamic system is determined by the occurrence of irregularities and uncertainties in its internal order. A web of interactive bonds distribute small changes self-similar and scale-relevant. The difficulty in describing and explaining the complex behaviour of composed entities is simplified by the proposed web-chaost model. / Thesis (M.A. (Philosophy))--North-West University, Potchefstroom Campus, 2006.

An analog controller has been analyzed and built for an electrostatic micro-cantilever beam. The closed loop MEMS device can be used as both actuator and sensor. As an actuator it will have the advantage of large stable travel range up to 90% of the gap. As a sensor the beam is to be driven into chaotic motion which is very sensitive changes in the system parameters. Two versions of the controller have been analyzed and implemented, one for the actuator and one for the sensor. For the actuator, preliminary experiments show good matching with the model. As for the sensor, the dynamic behavior have been studied and the best operating regions have been determined.

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