Gegenstand der Dissertation ist die Untersuchung von wiederkehrenden Ausbrüchen (wie z.B. Epidemien) in der Natur. Dies gelang anhand von Modellen, die die Dynamik von Phytoplankton und die Ausbreitung von Krankheiten zwischen Städten beschreiben. Diese beide Systeme bilden hervorragende Beispiele für solche Phänomene. Die Frage, ob die in der Zeit wiederkehrenden Ausbrüche ein Ausdruck chaotischer Dynamik sein können, ist aktuell in der Ökologie und fasziniert Wissenschaftler dieser Disziplin. Wir konnten zeigen, dass sich das Plankton-Modell im Falle von periodischem Antreiben über die Nährstoffe in einem chaotischen Regime befindet. Diese Dynamik wurde als die komplexe Wechselwirkung zweier Oszillatoren verstanden. Ebenfalls wurde die Ausbreitung von Epidemien in Netzwerken wechselwirkender Städte mit unterschiedlichen Grössen untersucht. Dafür wurde zunächst die Kopplung zwischen zwei Städten als Verhältnis der Stadtgrössen eingeführt. Es konnte gezeigt werden, dass das System sich in einem globalen zweijährigen Zyklus, der auch in den realen Daten beobachtet wird, befinden kann. Der Effekt von Heterogenität in der Grösseverteilung ist durch gewichtete Kopplung von generischen Modellen (Zelt- und Logistische Abbildung) in Netzwerken im Detail untersucht worden. Eine neue Art von Kopplungsfunktion mit nichtlinearer Sättigung wurde eingeführt, um die Stabilität des Systems zu gewährleisten. Diese Kopplung beinhaltet einen Parameter, der es erlaubt, die Netzwerktopologie von globaler Kopplung in gerichtete Netzwerke gleichmässig umzuwandeln. Die Dynamik des Systems wurde anhand von Bifurkationsdiagrammen untersucht. Zum Verständnis dieser Dynamik wurde eine effektive Theorie, die die beobachteten Bifurkationen sehr gut nachahmt, entwickelt. / One of the most striking features of ecological systems is their ability to undergo sudden outbreaks in the population numbers of one or a small number of species. The similarity of outbreak characteristics, which is exhibited in totally different and unrelated (ecological) systems naturally leads to the question whether there are universal mechanisms underlying outbreak dynamics in Ecology. It will be shown into two case studies (dynamics of phytoplankton blooms under variable nutrients supply and spread of epidemics in networks of cities) that one explanation for the regular recurrence of outbreaks stems from the interaction of the natural systems with periodical variations of their environment. Natural aquatic systems like lakes offer very good examples for the annual recurrence of outbreaks in Ecology. The idea whether chaos is responsible for the irregular heights of outbreaks is central in the domain of ecological modeling. This question is investigated in the context of phytoplankton blooms. The dynamics of epidemics in networks of cities is a problem which offers many ecological and theoretical aspects. The coupling between the cities is introduced through their sizes and gives rise to a weighted network which topology is generated from the distribution of the city sizes. We examine the dynamics in this network and classified the different possible regimes. It could be shown that a single epidemiological model can be reduced to a one-dimensional map. We analyze in this context the dynamics in networks of weighted maps. The coupling is a saturation function which possess a parameter which can be interpreted as an effective temperature for the network. This parameter allows to vary continously the network topology from global coupling to hierarchical network. We perform bifurcation analysis of the global dynamics and succeed to construct an effective theory explaining very well the behavior of the system.

This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well. / Diese Arbeit beschäftigt sich mit dem Phänomen der Diffusion in nichtlinearen Systemen. Unter Diffusion versteht man normalerweise die zufallsmäss ige Bewegung von Partikeln durch den stochastischen Einfluss einer thermodynamisch beschreibbaren Umgebung. Dieser Prozess ist mathematisch beschrieben durch die Diffusionsgleichung. In dieser Arbeit werden jedoch abgeschlossene Systeme ohne Einfluss der Umgebung betrachtet. Dennoch wird eine Art von Diffusion, üblicherweise bezeichnet als Subdiffusion, beobachtet. Die Ursache dafür liegt im chaotischen Verhalten des Systems. Vereinfacht gesagt, erzeugt das Chaos eine intrinsische Pseudo-Zufälligkeit, die zu einem gewissen Grad mit dem Einfluss einer thermodynamischen Umgebung vergleichbar ist und somit auch diffusives Verhalten provoziert. Zur quantitativen Beschreibung dieses subdiffusiven Prozesses wird eine Verallgemeinerung der Diffusionsgleichung herangezogen, die Nichtlineare Diffusionsgleichung. Desweiteren wird die mikroskopische Dynamik des Systems mit analytischen Methoden untersucht, und Schlussfolgerungen für den makroskopischen Diffusionsprozess abgeleitet. Die Technik der Verbindung von mikroskopischer Dynamik und makroskopischen Beobachtungen, die in dieser Arbeit entwickelt wird und detailliert beschrieben ist, führt zu einem tieferen Verständnis von hochdimensionalen chaotischen Systemen. Die mit mathematischen Mitteln abgeleiteten Ergebnisse sind darüber hinaus durch ausführliche Simulationen verifiziert, welche teilweise auf einem der leistungsfähigsten Supercomputer Europas durchgeführt wurden, dem sp6 in Bologna, Italien. Desweiteren können die in dieser Arbeit vorgestellten Erkenntnisse und Techniken mit Sicherheit auch in anderen Fällen bei der Untersuchung chaotischer Systeme Anwendung finden.

Notre travail s'élaborera autour d’une hypothèse centrale : L’écho inédit trouvé par la trame narrative et scopique proposée par Daech s'explique par son adéquation avec les affres des subjectivités contemporaines. Il s’agit donc d’étudier les conditions de cette rencontre, qui capte le sujet errant dans les eaux troubles de l’archaïque, avec une offre de mort distillée par le dévoiement d’un pseudo-islam de cruauté semblant apporter l’illusion d’une réponse. Car, d’emblée, chez les jeunes sujets que nous recevons, la « greffe » fantasmatique prend, telle une rencontre passionnelle entre un sujet agonique et une solution miracle qui vient lui offrir la possibilité de s’extraire d’une subjectivité faite d’inconsistance, d’abandonner l’effroi et le vide au profit d’un remplissage lénifiant. Leur terrorisme ne naît pas d'un projet idéologique mais tire sa vigueur d'un désastre subjectif auquel il donne forme. En cela, l'imagerie de Daech vient actualiser le collapsus Réel/Imaginaire (imaginaire grandiose mais de mort) chez ces sujets agoniques. L'obscène est alors exhibé, la pulsion scopique déchainée. Demeure l'archaïque pur qui scandera la vie et les actes d'un sujet de la discontinuité, au titre du retour du clivé, répétition à l'identique du mortifère. Nous proposerons un exposé de la clinique des sujets volontaires au martyr à partir de notre expérience de clinicien en prison, dans le cadre d’une mission dédiée à la prise en charge de sujets revenant de Syrie, ayant voulu s’y rendre, ou témoignant d’une bascule mortifère en détention vers des trajectoires de mort au nom de Dieu. Pour ce faire, nous étudierons l’institution carcérale comme un lieu privilégié de la remise en scène des éprouvés précoces d’agonie et d’effroi chez des sujets aux prises avec un véritable chaos subjectif, toile de fond de toute appétence radicale actuelle selon nous. Nous étudierons ensuite les ressorts psychiques d’un tel processus : l’addiction, le préjudice, leur dialectique avec l’Idéal, pour interroger ces formes de mélancolies contemporaines chez des sujets qui ne parviennent au sentiment d’existence que dans le projet de mort divine. Nous tenterons d’illustrer notre hypothèse selon laquelle la dissolution d’un Moi inconsistant en un Moi Idéal nihiliste est la clé de compréhension de ce que l’on nomme actuellement « radicalisation », dans sa forme la plus extrême, celle des demandeurs de martyre, les chahids. / Our work will be built around a central hypothesis : The unheard echo found by the narrative and scopic plot proposed by ISIS, is explained by its adequacy with the pangs of contemporary subjectivities. It is thus a question of studying the conditions of this encounter which captures the subject, wandering in the troubled waters of the archaic with a death offer distilled by the deviation of a pseudo-Islam of cruelty that seems to bring the illusion of ‘answer. Because from the outset in the young subjects that we receive, the « transplant » fantasy takes, such a passionate meeting between an agonistic subject, and a miracle solution that comes to offer the possibility of getting out of a subjectivity made of inconsistency to abandon fright and emptiness in favor of a lenient filling. Their terrorism is not born of an ideological project but draws its force from a subjective disaster to which it gives shape. In this, the imagery of ISIS comes to actualize the collapse Real / Imaginary (imaginary grandiose but death) in these agonic subjects. The obscene is then exhibited, the impulse scopic unleashed. The pure archaic remains that will punctuate the life and the acts of a subject of discontinuity, in the name of the return of the cleave, a repetition identical to the mortifère. In this paper, we are going to do a clinical study of subjects willing become martyrs based on our experience of a clinical psychologist in detention. The framework of this mission is dedicated to treatement of subjects coming back from Syria, or who has wanted to go there, or else showing a sudden morbid bascule, towards death trajectories in the name of god. We will focuse on the psychic incounscious motivations of such process : addiction, prejudice and their dialectic with the Ideal to interrogate these forms of contemporary melancholia for subjects who can only reach feeling of existence in project of divine death. We will try to illustrate our 3ypothèses according to which the dossilution of an inconsistent Ego in an nihilist Ideal Ego is the key to an understanding of what we currently call radicalization, in its most extreme form, that of people aspiring to martyrdom, wandering in the morbid zone of the archaic, the “chahids”.

Cette recherche se focalise sur la posture Neutre face au Chaos. Elle émerge d’une volonté de rompre avec une lecture paradigmatique de l’urbanisation et d’un désir de trouver un rapport apaisé avec le Chaos urbain qui nous entoure, un Chaos qui n’est plus la congestion spectaculaire de la Grande Ville mais un Chaos gris : diffus, silencieux, insignifiant. Ce regard que l’on qualifierait de Neutre est proche d’une certaine quiétude de l’esprit que l’on trouve dans le Zen ou le Taoïsme. Comme dans ces philosophies orientales il exprime une déconnexion et un dé-saisissement.Le Neutre est une expérience immédiate du réel qui implique une destitution du sujet, la sortie du rapport duel sujet-objet pour tenter une expérience indistincte de l’événement, sur un mode fusionnel, de réceptivité totale. Mais le Neutre qui nous intéresse dans cette recherche est un Neutre créatif et non pas purement contemplatif, un Neutre susceptible de ‘faire projet’. Ce Neutre, en tant que récepteur du Chaos, cherche à transformer la vitalité chaotique en processus actif. Notre argument principal se porte sur ce potentiel créatif et productif de la posture Neutre, et de sa manière à se saisir du Chaos comme source intarissable.La recherche s’organise selon des principes de fragmentation, transdisciplinarité, assemblage et redondance. Les onze figures qui la composent sont autonomes mais elles ne sont pas de la même nature. En effet, elles s’organisent en trois chapitres distincts, qui correspondent aux trois temps, ou trois mécanismes de la posture Neutre : (1) l’indiscernabilité (ou le Neutre réceptif), (2) le Désengagement (ou le Neutre passif) et (3) l’Énonciation (le Neutre actif). Ainsi, les trois premières figures (le Bruit, le Conflit et le Noeud), qui composent le premier chapitre, se rapportent à la réalité exogène, à ce qui se situe en dehors de nous et qui nous entoure ; les cinq figures qui suivent (l’Indifférence, le Laissez-faire, l’Idiotie, la Retraite et l’Infirmité) se rapportent toutes à l’attitude du sujet lui-même, à sa posture passive vis-à-vis du monde ; alors que les trois dernières figures (le Gris, le Pathos et l’Acceptation Active) se rapportent aux moyens d’expression et à l’accès au langage, c’est-à-dire à l’énonciation du projet.La recherche révèle que la posture Neutre ne constitue pas une méthode mais une démarche. Certes, une démarche n’a pas la même force transformatrice qu’une méthode. Elle est plus difficile à partager et à décrire. Elle est impossible à appliquer de façon constante et continue. Cependant, elle peut s’avérer tout aussi précieuse en tant que pensée du projet. / This research focuses on a Neutral posture towards Chaos. It comes from the will to break with a paradigmatic reading of urbanisation and from a desire to find a pacified relationship with the urban Chaos surrounding us, a Chaos which is no longer the spectacular congestion of the Großstadt, but a grey Chaos : diffuse, silent, insignificant. This view, that we qualify as Neutral is close to a certain quietude of the mind that might be found in Zen or Taoism. Like in these eastern philosophies, it expresses a form of disconnection and divestiture. The Neutral is an immediate experience of the real which implies a destitution of the subject, an exit from the dual relationship of subject-object to attempt an indistinctive experience of the event, in a fusional mode, of total receptiveness. But the Neutral on which we are focused in this research is a creative Neutral and not a purely contemplative one, a Neutral which is likely to become a means of projection. This Neutral as a receptor of Chaos, tries to transform chaotic vitality into an active process. Our main argument focuses on this creative and productive potential of the Neutral posture and on its way of taking hold of Chaos as an inexhaustible source. The research is organised according to the principles of fragmentation, transdisciplinarity, assembly and redundancy. The eleven figures of which it is composed are autonomous and of various natures. Indeed, they are organised in three distinct chapters, which correspond to three different moments, or three mechanisms of the Neutral posture : (1) Indiscernibility  (or the receptive Neutral), (2) Disengagement (or the passive Neutral),(3) Enunciation (the active Neutral). Thus, the three figures (Noise, Conflict, Node)that make up the first chapter, relate to the exogenous reality, to that which is situated outside of us and that which surrounds us ; the five following figures (Indifference, Laissez-faire, Idiocy, Retreat and Infirmity) all relate to the attitude of the subject himself, to his passive posture towards the world ; whereas the three final figures (Grey, Pathos and Active Acceptance) relate to the ways of expression and to access to language, that is to say the enunciation of the project. The research reveals that the Neutral posture does not constitute a method but an approach. Certainly, an approach does not have the transformative force of a method. It is much more difficult to impart and to describe. It is impossible to apply in a way which is continuous and constant. However, it might turn out to be just as precious as a projective thought.

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In recent decades, computational models have become critical to how engineers and mathematicians understand nature; as a result they have become an integral part of the design process in most engineering disciplines. Moore's law anticipates computing power doubling every two years; a prediction that has historically been realized. As modern computing power increases, problems that were previously too complex to solve by hand or by previous computing abilities become tractable. This has resulted in the development of increasingly complex computational models simulating increasingly complex dynamics. Unfortunately, this has also resulted in increased challenges in fields related to model development, such as model validation and model based control, which are needed to make models useful in the real world. Much of the validation literature to date has focused on spatial and spatiotemporal simulations; validation approaches are well defined for such models. For most time series simulations, simulated and experimental trajectories can be directly compared negating the need for specialized validation tools. In the study of some ship motion behavior, chaos exists, which results in chaotic time series simulations. This presents novel challenges for validation; direct comparison may not be the most apt approach. For these applications, there is a need to develop appropriate metrics for model validation. A major thrust of the current work seeks to develop a set of validation metrics for such chaotic time series data. A complementary but separate portion of work investigates Non-Intrusive Polynomial Chaos as an approach to reduce the computational costs associated with uncertainty analysis and other stochastic investigations into the behavior of nonlinear, chaotic models. A final major thrust of this work focuses on contributing to the control of nonlinear marine systems, specifically the autonomous recovery of an unmanned surface vehicle utilizing motion prediction information. The same complexity and chaotic nature that makes the validation of ship motion models difficult can also make the development of reliable, robust controllers difficult as well. This body of work seeks to address several facets of this broad need that has developed due to our increased computational abilities by providing validation metrics and robust control laws. / Ph. D.

Unusual and challenging ionization processes take place when an atom or molecule is placed in the presence of a super intense, ultra short laser field. One such process is the ionization and subsequent return of an electron to the ionic core. The electron carries with it the energy it has absorbed from the laser field and this energy drives different atomic phenomena such as high harmonic generation or multiple ionization. The mechanism of the electron return is often referred to as the “three-step” model. In this model, an electron is first ionized at the peak amplitude of the laser field. Once ionized, a change in the direction of the laser field forces the electron to return to the parent ion and causes a subsequent recollision. The purpose of this thesis is to examine in great detail the recollision process, its mechanisms, and its dependence on physical parameters (such as laser intensity and ellipticity) for a number of physically interesting scenarios.

International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / According to the advantages of chaotic analog sequences and chaotic binary sequences, this paper proposes a method generating chaotic binary spread-spectrum sequence by multilevel quantifying. This paper proved that even correlation and odd correlation between such sequences of length N are all Gaussian distributed with mean 0 and variance N, the even of mean-square cross-correlation is N, and the variance of mean-square cross-correlation is 2N. The method can increase the number of chaotic sequences, made the spread-spectrum system more secure. The theoretical analyses and the results of simulation show that the performance of such sequence general is as same as traditional spread-spectrum sequence, its number is very large, and can be used in CDMA in future.

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No description available.