We explore the dynamics of integrable and chaotic quantum many-body systems with a focus on universal structures known as caustics, which are a type of singularity categorized by catastrophe theory. Papers I and II study light cones in quantum spin chains, which we show are caustics and therefore inherits specific functional forms. For integrable systems, the edge of the cone is a fold catastrophe, making the wavefunction locally of Airy form. We also identify the cusp catastrophe in the XY model, thus the secondary light cone is a Pearcey function. Vortex pairs appear in the dynamics, are sensitive to phase transitions, and permit the extraction of critical scaling exponents. In paper II we use a Gaussian wavefront form to distinguish integrable and chaotic models. Writing the wavefront as exp[−m(x)(x − vt)2 + b(x)t], the scaling of coefficients m(x) and b(x) is the diagnostic. The local Airy function description in free models leads to a power-law ∼ x^{−n/3} scaling, while for the chaotic case the scaling is exponential ∼ e^{−cx}. In Paper III, we study the function Fn(t) = <(A(t)B)^n>, a generalization of the four-point out-of-time ordered correlator (OTOC) F2(t), for an integrable system and show that the function Fn(t) can be recast as the return amplitude of an effective time dependent chaotic system, exhibiting signals of chaos such as a positive Lyapunov exponent, spectral statistics consistent with random matrix theory, and relaxation. In Paper IV we perform a comprehensive investigation of caustics in many-body systems in (1+1)- and (2+1)-dimensional Fock space and time. We show how a hierarchy of caustics appear in the dynamics of many-body models, using two- and three-mode Bose-Hubbard models as guiding systems. We show that, in the case of the trimer, high dimensional caustics appear and are organized by the catastrophe X9. / Thesis / Doctor of Philosophy (PhD)

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No / In this paper, we investigate trajectory tracking in a multi-input nonlinear system, where there is little knowledge of the system parameters and the form of the nonlinear function. An identification-based iterative learning control (ILC) scheme to repetitively estimate the linearity in a neighborhood of a desired trajectory is presented. Based on this estimation, the original nonlinear system can track the desired trajectory perfectly by the aid of a regional training scheme. Just like in adaptive control, a singularity exists in ILC when the input coupling matrix is estimated. Singularity avoidance is discussed. A new parameter modification procedure for ILC is presented such that the determinant of the estimate of the input coupling matrix is uniformly bounded from below. Compared with the scheme used for adaptive control of a MIMO system, the proposed scheme reduces the computation load greatly. It is used in a robotic visual system for manipulator trajectory tracking without any information about the camera-robot relationship. The estimated image Jacobian is updated repetitively and then its inverse is used to calculate the manipulator velocity without any singularity.

Constructing and understanding arguments is often difficult but key to both philosophyand other parts of the everyday life. Some methods to ease this task has been developed.One of the methods developed within informal reasoning is argument diagramming, amethod to structure and visualize arguments. This essay takes a complicated argumentabout the fate of the universe, put forward by futurist Ray Kurzweil in his book TheSingularity is Near, as well as some critique published against said argument, as a casestudy for the application of argument diagramming on unstructured arguments fromoutside the field of philosophy. To arrive at a diagram that can be easily grasped andread but still contains all information of the original argument, this essay developsa method of splitting sub-diagrams off of a main diagram. Analysing the resultingdiagrams shows that the plausibility of Kurzweil’s argument is heavily dependent on afew, critical premises at the lower levels of the diagram.

The master thesis is focused on estimation of crack propagation origin from sharp V-notch. Stress distribution around the tip of the V-notch is described on the base of generalized linear elastic fracture mechanics. The change of the stress singularity exponent caused by geometry of the V-notch and the vertex singularity is taken into account. The first part of the work is devoted to the estimation of the stress singularity exponent of the V-notch either from stress distribution around the tip of the V-notch or by using analytical solution. Formerly derived stability criteria are applied in the second part of the work. The origin of the crack propagation is estimated for several experimental specimens. The aim of this thesis is to compare the available experimentally observed data with results obtained using those criteria based on the application of generalized linear elastic fracture mechanics developer at the Institute of Physics of Materials Academy of Sciences of the Czech Republic. The finite element code Ansys and mathematical software Matlab were used for the necessary calculations.

The singular solutions for linear elastostatics at corners are essential in both theory and computation. In this thesis, we seek new singular solutions for corners with the fixed (displacement), the free stress (traction) boundary conditions, and their mixed types, and to explore their corner singularity and provide the algorithms and error estimates in detail. The singular solutions of linear elastostatics are derived, and a number of new models of corner and crack singularity are proposed. Effective numerical methods, such as the collocation Trefftz methods (CTM), the method of fundamental solutions (MFS), the method of particular solutions (MPS) and their combinations: the so called combined method, are developed. Such solutions are useful to examine other numerical methods for singularity problems in linear elastostatics. This thesis consists of three parts, Part I: Basic approaches, Part II: Advanced topics, and Part III: Mixed types of displacement and traction conditions. Contents of Parts I and II have been published in [47,82]. In Part I, the collocation Trefftz methods are used to obtain highly accurate solutions, where the leading coefficient has 14 (or 13) significant digits by the computation with double precision. In part II, two more new models (symmetric and anti-symmetric) of interior crack singularities are proposed, for the corner and crack singularity problems, the combined methods by using many fundamental solutions, but by adding a few singular solutions are proposed. Such a kind of combined methods is significant for linear elastostatics with corners (i.e., the L-shaped domain), because the singular solutions can only be obtained by seeking the power £hk of r£hk numerically. Hence, only a few singular solutions used may greatly simplify the numerical algorithms; Part III is a continued study of Parts I and II, to explore mixed type of displacement and free traction boundary conditions. To our best knowledge, this is the first time to provide the particular solutions near the corner with mixed types of boundary conditions and to report their numerical computation with different boundary conditions on the same corner edge in linear elastostatics. This thesis explores corner singularity and its numerical methods, to form a systematic study of basic theory and advanced computation for linear elastostatics.

Aus der Einführung: "Stehen wir am Rande einer bio-nanotechnologischen getriebenen Revolution, die unsere Art zu leben, zu arbeiten und miteinander umzugehen grundlegend verändern wird? Welchem gesellschaftspolitischen, wirtschaftlichen und technologischen Wandel haben wir uns zu stellen? Langfristige Entwicklungszyklen (Kondratieff, Schumpeter) führen zur nachhaltigen Weiterentwicklung der Zivilisation. Mittelfristige Entwicklungen wie die Trends Globalisierung, Urbanisierung, Digitalisierung (Miniaturisierung) und Humanisierung (Individualisierung), die immer stärker unser Umfeld und Handeln beeinflussen führen zu ganzheitlichen, weltumspannenden Grundtendenzen der gesellschaftlichen Weiterentwicklung. Die technologischen "Enabler" Computing, Biotechnology, Artifical Intelligence, Robotik, Nanotechnology, Additive Manufacturing und Design Thinking wirken beschleunigend auf die gesellschaftlichen Entwicklungen ein. Die technologischen Möglichkeiten beschleunigen sowohl gesellschaftspolitische Zyklen und zivilisatorische Anpassungen. Durch rasanten technologischen, wissenschaftlichen Fortschritt, zunehmende Globalisierungswirkungen, beschleunigte Urbanisierung und aber auch politischer Interferenzen sind die Veränderungsparameter eines dynamischen Geschäftsumfelds immer schnellere Transformationen ausgesetzt. Alle diese Richtungen zeigen das unsere gesellschaftliche Entwicklung inzwischen stark durch die Technik getrieben ist. Ob dies auch heißt, dass wir den Punkt der Singularität (Kurzweil) absehbar erreichen ist dennoch noch offen. ..."

<p>I investigate how Baruch de Spinoza and Friedrich Nietzsche conceive of difference as bearing a distinctive normative significance for modern social and political life. Both Spinoza and Nietzsche ascribe special importance to the difference embodied by exceptional individuals, and to the attitudes towards difference that such individuals avow when they interact or cooperate with other individuals in society. I then reanimate this neglected aspect of their writings in my own constructive proposal. In particular, I argue that by inhabiting and harnessing our differences, we can realise new yet unknown possibilities that make for deep and meaningful social change. </p><p>According to Spinoza, exceptional individuals--namely, free men or those who live solely by the guidance of reason--avow the attitude of generosity towards individuals they engage. That is to say, the free man actively seeks to establish close friendships with other individuals in society, so that he may increase their power of acting through direct and dynamic interactions. In such interactions, the free man initiates others to the life of reason by getting them to directly experience what it is like to exercise their own powers of thinking, feeling, and acting. Nietzsche criticises Spinoza for diluting the depth and richness of human experience with the formulas and categories of logic, reason, or conscious thought. For instance, Spinoza credits his own affirmative stance towards all things to logical necessity, thus eliding what Nietzsche takes joyful affirmation to involve, namely, experiencing every moment of one's own existence "as good, as valuable, with pleasure." For Nietzsche, we modern individuals have come to develop ways of thinking and feeling that preclude us from harnessing our own lived experiences, and thus the expanse of difference between any one self and another. We have instead become inclined to affects like envy, pity, vanity, or ressentiment, whereby we gain our sense of well-being or power by placing ourselves on par with the persons with whom we associate. To these affects, he contrasts the pathos of distance, in which the lure or influence of one's value perspectives derives from the depth of one's immersion in one's own lived experiences and from the expanse of the difference between oneself and others. Nietzsche nonetheless believes that the pathos of distance can only thrive in an aristocratic social order, with its living hierarchy of rank and value distinctions. </p><p>I argue that we need not follow Nietzsche in this. I develop an alternative account of the pathos of distance as an affect whereby the difference one embodies engenders neither opposition nor exclusion, but rather triggers the drive for self-overcoming in those who are receptive to it. On my account, exceptional individuals cultivate and embody a way of life that wields a nourishing and life-transfiguring effect on other individuals, albeit only to the extent that they also value one another's singularities or differences. Exceptional individuals still play a distinctive role in society but not through "living structures of domination."</p><p>To illustrate this account, I present and analyse a specific kind of social change, in which people who are disadvantaged and oppressed harness their own lived experiences, with the help of exceptional individuals, to drive deep and creative forms of social change. I call this `organic social change.' Through this analysis, I inaugurate an attitude towards difference that I call `inhabiting difference.' In relation to our own specificity, we inhabit our own difference when we harness the hitherto latent powers and inchoate possibilities that our own lived experiences afford. In relation to the specificity of others, we inhabit their difference to the extent that we avow an attitude of open and abiding patience towards the singularity of their lived experiences, and cultivate direct and dynamic relationships in which they may harness powers and possibilities out of their own lived experiences. To establish the distinctive importance of inhabiting difference, I show how it facilitates empowering modes of social cooperation, and thus helps us realise new yet unknown social and political possibilities.</p> / Dissertation

O início do século XXI trouxe importantes revelações para o autismo. Sua concepção ampliou significativamente e a ideia da causalidade psíquica foi questionada, dando lugar a teorias que privilegiam o aspecto biológico. A genética está no seu auge e representa o grande interesse científico. A psicanálise, por sua vez, tem sido rejeitada em detrimento de abordagens que utilizam técnicas de aprendizagem. Dessa forma, esta pesquisa pretendeu investigar as contribuições da psicanálise de orientação lacaniana e da genética no que diz respeito ao autismo na atualidade, a fim de sustentar a posição de que a psicanálise tem algo a contribuir no tratamento desses casos. A discussão sobre os embates entre a supremacia de saberes em relação ao autismo e como o viés político pode justificar essas ações, torna-se importante. Primeiro retratamos os autismos hoje, na tentativa de percorrer seu campo de abrangência: o mercado, os manuais de classificação, os debates atuais, o gozo autista e o seu percurso histórico. Em seguida, foram revisadas as contribuições da psicanálise de orientação lacaniana, no sentido de marcar a distinção entre autismo e psicose, a partir do advento do sujeito no campo da linguagem. Por último, discorremos sobre as novas pesquisas genéticas, com a finalidade de propor uma interlocução possível entre esses campos. A concepção de investigação que embasa esta dissertação é o modelo de pesquisa em psicanálise, que permite compreender os fenômenos em profundidade. Referente à coleta de dados, foram utilizadas a pesquisa bibliográfica e a de campo. A pesquisa de campo seguiu os moldes da entrevista em psicanálise. Foram realizadas duas entrevistas com uma geneticista envolvida com o Projeto Genoma Humano na área do autismo, com o intuito de complementar o escopo teórico deste estudo, bem como identificar um possível encontro entre psicanálise e genética. Concluímos que há um encontro possível, que é, justamente, o retorno do particular, o olhar para a singularidade. O aporte teórico de Lacan sobre o objeto a, traz importantes balizas de como conduzir esses casos na clínica. Esta pesquisa aponta para o compromisso do psicanalista em se posicionar frente aos debates contemporâneos, para procurar desmistificar algumas das principais críticas à psicanálise, que procuram afastá-la das opções dos tratamentos possíveis do autismo / The early 21st century has brought important breakthrough when it comes to autism. Its conception expanded significantly and the idea of psychical causality was questioned, opening precedents to theories which favor the biological aspect. Genetics is at its peak and represents the greatest scientific interest. Psychoanalysis, as an alternative, has been rejected at the expense of propositions that use learning techniques. Along these lines, this research focused on investigating the contributions from Lacanian psychoanalysis and genetics regarding autism at this moment in time, in order to support the viewpoint that psychoanalysis has something to contribute in the treatment of these cases. The argumentation about the dispute between the dominance of knowledge in relation to autism and how the political bias can justify such actions becomes important. We start depicting the contemporary autisms, in an attempt to cover its range field: the market, classification manuals, current debates, autistic jouissance and its historical background. Subsequently, the Lacanian psychoanalysis contributions were elaborated, in order to differentiate between autism and psychosis, deriving out of the introduction of the subject in the language field. Lastly, we discuss about the recent genetic research, intending to propose a possible exchange between the aforementioned fields. The genesis of the investigation that guides this essay is the psychoanalysis research model, that endorses an in-depth understanding of the phenomena. In the matter of data collection, bibliographical and field research have been practiced. The field research followed the interview standards in psychoanalysis. Two interviews with a geneticist involved with the Human Genome Project in the area of autism were carried out, in order to complement the theoretical scope of this study, as well as to identify a possible concurrence between psychoanalysis and genetics. Its been deduced that there is, in fact, a possible encounter, which is, precisely, the return to the particular, the attention to the singularity. Lacans theoretical contribution on object a, bears important landmarks of how to conduct such cases within the practice. This examination acknowledges the psychoanalyst\'s commitment to take a stance in the face of contemporary debates, in an attempt to disparage some of the main criticisms towards psychoanalysis, that ultimately seek to deviate it from the options of possible treatments for autism