Diese Arbeit ist ein erster Versuch, mit Modellbildung und mathematischer Analyse die Experimente zu verstehen, die zeigten, dass die Stimulation eines einzelnen Neurons im Cortex eine Verhaltensreaktion auslösen kann. Dieser Befund stellt die verbreitete Ansicht infrage, dass viele Neurone nötig sind, um Information zuverlässig kodieren zu können. Der Ausgangspunkt der vorliegenden Untersuchung ist die Stimulation einer zufällig ausgewählten Zelle in einem Zufallsnetzwerk exzitatorischer und inhibitorischer Neuronmodelle. Es wird dann nach einem plausiblen Ausleseverfahren gesucht, das die Einzelzellstimulation mit einer mit den Experimenten vergleichbaren Zuverlässigkeit detektieren kann. Das erste Ausleseschema reagiert auf Abweichungen vom spontanen Zustand in der Aktivität einer Auslesepopulation. Die Stimulation wird detektiert, wenn bei der Auswahl der Auslesepopulation denjenigen Neuronen ein Vorzug gegeben wird, die eine direkte Verbindung von der stimulierten Zelle bekommen. Im zweiten Teil der Arbeit wird das Ausleseschema erweitert, indem ein zweites Netzwerk als Ausleseschaltkreis dient. Interessanterweise erweist sich dieses Ausleseschema nicht nur als plausibler, sondern auch als effektiver. Diese Resultate basieren sowohl auf Simulationen als auch auf analytischen Rechnungen. Weitere Experimente zeigten, dass eine konstante Strominjektion einen Effekt auslöst, der kaum von Dauer und Intensität der Stimulation abhängt, der aber bei unregelmäßiger Stimulation zunimmt. Der letzte Teil der Arbeit befasst sich mit einer theoretischen Erklärung für diese Ergebnisse. Hierzu werden die biologischen Eigenschaften des Systems im Modell detaillierter beschrieben. Weiterhin wird die Funktionsweise des Ausleseschemas so modifiziert, dass es auf Veränderungen reagiert, anstatt den Input zu integrieren. Dieser Differenzierdetektor liefert Ergebnisse, die mit den Experimenten übereinstimmen, und könnte bei nichtstationärem Input vorteilhaft sein. / This thesis is a first attempt at developing a theoretical model of the experiments which show that the stimulation of a single cell in the cortex can trigger a behavioral reaction and that challenge the common belief that many neurons are needed to reliably encode information. As a starting point of the present work, one neuron selected at random within a random network of excitatory and inhibitory integrate-and-fire neurons is stimulated. One important goal of this thesis is to seek a readout scheme that can detect the single-cell stimulation in a plausible way with a reliability compatible with the experiments. The first readout scheme reacts to deviations from the spontaneous state in the activity of a readout population. When the choice of readout neurons is sufficiently biased towards those receiving direct links from the stimulated cell, the stimulation can be detected. In the second part of the thesis, the readout scheme is extended by employing a second network as a readout circuit. Interestingly, this new readout scheme is not only more plausible, but also more effective. These results are based both on numerical simulations of the network and on analytical approximations. Further experiments showed that the probability of the behavioral reaction is substantially independent of the length and intensity of the stimulation, but it increases when an irregular current is used. The last part of this thesis seeks a theoretical explanation for these findings. To this end, a recurrent network including more biological details of the system is considered. Furthermore, the functioning principle of the readout is modified to react to changes in the activity of the local network (a differentiator readout), instead of integrating the input. This differentiator readout yields results in accordance with the experiments and could be advantageous in the presence of nonstationarities.

Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to pandemics spreading across continents. Most of such systems are driven by irregular and distributed fluctuating input signals from the environment. Yet how networked dynamical systems collectively respond to such fluctuations depends on the location and type of driving signal, the interaction topology and several other factors and remains largely unknown to date. As a key example, modern electric power grids are undergoing a rapid and systematic transformation towards more sustainable systems, signified by high penetrations of renewable energy sources. These in turn introduce significant fluctuations in power input and thereby pose immediate challenges to the stable operation of power grid systems. How power grid systems dynamically respond to fluctuating power feed-in as well as other temporal changes is critical for ensuring a reliable operation of power grids yet not well understood. In this work, we systematically introduce a linear response theory (LRT) for fluctuation-driven networked dynamical systems. The derivations presented not only provide approximate analytical descriptions of the dynamical responses of networks, but more importantly, also allow to extract key qualitative features about spatio-temporally distributed response patterns. Specifically, we provide a general formulation of a LRT for perturbed networked dynamical systems, explicate how dynamic network response patterns arise from the solution of the linearised response dynamics, and emphasise the role of LRT in predicting and comprehending power grid responses on different temporal and spatial scales and to various types of disturbances. Understanding such patterns from a general, mathematical perspective enables to estimate network responses quickly and intuitively, and to develop guiding principles for, e.g., power grid operation, control and design.

In this work, the structural, electronic, and optical properties of CdS nanoparticles with sizes up to 4nm have been calculated using density-functional theory (DFT). Inaccuracies in the description of the unoccupied states of the applied density-functional based tight-binding method (DFTB) are overcome by a new SCF-DFTB method. Density-functional-based calculations employing linear-response theory have been performed on cadmium sulfide nanoparticles considering different stoichiometries, underlying crystal structures (zincblende, wurtzite, rocksalt), particle shapes (spherical, cuboctahedral, tetrahedral), and saturations (unsaturated, partly saturated, completely saturated). For saturated particles, the calculated onset excitations are strong excitonic. The quantum-confinement effect in the lowest excitation is visible as the excitation energy decreases towards the bulk band gap with increasing particle size. Dangling bonds at unsaturated surface atoms introduce trapped surface states which lie below the lowest excitations of the completely saturated particles. The molecular orbitals (MOs), that are participating in the excitonic excitations, show the shape of the angular momenta of a hydrogen atom (s, p). Zincblende- and wurtzite-derived particles show very similar spectra, whereas the spectra of rocksalt-derived particles are rather featureless. Particle shapes that confine the orbital wavefunctions strongly (tetrahedron) give rise to less pronounced spectra with lower oscillator strengths. Finally, a very good agreement of the calculated data to experimentally available spectra and excitation energies is found.

Η πλειονότητα των ερευνητών/ειδικών του αντισεισμικού σχεδιασμού συμφωνεί πως μια υπολογιστική διαδικασία που θα έχει ως βασική παράμετρο της απόκρισης τις σεισμικές μετακινήσεις θα είναι πιο ορθολογική και πιθανότατα πιο οικονομική απ’ τη συμβατική μεθοδολογία σχεδιασμού βάσει δυνάμεων. Η έλλειψη μιας μεθοδολογίας αντισεισμικού σχεδιασμού γεφυρών βάσει μετακινήσεων που να είναι απλή, εφικτή και συμβατή με την εφαρμοζόμενη πρακτική και η απουσία πρότασης σχεδιασμού των περιοχών του φορέα βάσει μετακινήσεων, αποδεικνύει το γνωστικό κενό που υπάρχει σ’ αυτή την περιοχή του αντισεισμικού σχεδιασμού. Η παρούσα εργασία επιχειρεί να συμβάλλει στην πλήρωση αυτού του κενού και προς τούτο προτείνει μια νέα μεθοδολογία. Αναφέρεται σε (μή-μονωμένες) γέφυρες σκυροδέματος και περιλαμβάνει μια απλή διαδικασία για την εκτίμηση των απαιτούμενων ανελαστικών παραμορφώσεων, τόσο των βάθρων, όσο και των περιοχών του φορέα - κάνοντας χρήση ελαστικής φασματικής ανάλυσης και επεκτείνοντας τον κανόνα των "Ίσων Μετακινήσεων" στο τοπικό επίπεδο. Η διαδικασία αναπτύσσεται και βαθμονομείται βάσει (σχεδόν δύο χιλιάδων) μή-γραμμικών δυναμικών αναλύσεων (με εν χρόνω ολοκλήρωση) αντιπροσωπευτικών γεφυρών, τριών έως πέντε ανοιγμάτων. Όμως για την εφαρμογή της απαιτούνται μόνο ελαστικά εργαλεία. Σε αντίθεση με τις έως τώρα ερευνητικές προσπάθειες, όπου γίνεται η απλουστευτική παραδοχή γραμμικής συμπεριφοράς του φορέα, στην παρούσα έρευνα δίνεται έμφαση στην προσομοίωση των περιοχών του φορέα και λαμβάνονται υπ’ όψιν οι μή-γραμμικότητές του. Από την εφαρμογή του διαπιστώνεται ότι ο προτεινόμενος σχεδιασμός βάσει μετακινήσεων προσφέρει πολύ οικονομικότερα ποσοστά όπλισης (από 1/2 έως 1/7 στο διαμήκη οπλισμό και από 1/1 έως 1/3 στον εγκάρσιο οπλισμό), χωρίς να επιβαρύνει ουσιαστικά την επιτελεστικότητα της γέφυρας - η υπεραντοχή των γεφυρών που σχεδιάζονται με την προτεινόμενη μεθοδολογία είναι πρακτικά ισοδύναμη με την υπεραντοχή των συμβατικά σχεδιασμένων γεφυρών. Η παρουσίαση της μεθοδολογίας περιλαμβάνει την περιγραφή της διαδικασίας σχεδιασμού υπό μορφή αλγόριθμου (Κεφ. 2), του τρόπου εφαρμογής της στην πράξη (διαδικασία προσομοίωσης, παραδείγματα σχεδιασμού: Κεφ. 3), του θεωρητικού υποβάθρου βάσει του οποίου αναπτύχθηκε (Κεφ. 4), των προβλημάτων της συμβατικής μεθοδολογίας (παραδείγματα σχεδιασμού βάσει δυνάμεων: Κεφ. 3) και των κενών που διαπιστώνονται στην τεκμηρίωση της συμβατικής μεθοδολογίας (Κεφ. 4). Η αποτίμηση του σχεδιασμού (Κεφ. 3) δεκαέξι αντιπροσωπευτικών γεφυρών (οκτώ σχεδιασμένων βάσει μετακινήσεων και οκτώ συμβατικά σχεδιασμένων), παρουσιάζεται υπό μορφή παράλληλης σύγκρισης της επιτελεστικότητας και συνηγορεί υπέρ των πλεονεκτημάτων της νέας μεθοδολογίας. Στα Παραρτήματα δίνονται πληροφορίες για τα υπολογιστικά εργαλεία που αναπτύχθηκαν για την προσομοίωση και την ανάλυση των γεφυρών (επέκταση προγράμματος ANSRuop). / The majority of seismic design researchers/specialists concludes that displacement-based design methodologies reduce the uncertainty of the design process and probably lead to less expensive structures. The absence of a simple displacement-based seismic design procedure for bridges that will be feasible and compatible with the current design practice and the nonexistence of a proposal for the displacement-based design of the deck indicate the gap of knowledge in this field of earthquake engineering. This thesis attempts to contribute to the reduction of this gap and for this scope proposes a new methodology. The procedure focuses on bridges with concrete piers monolithically connected to a prestressed concrete continuous deck and comprises simple steps for the estimation of the inelastic/nonlinear deformations of both the piers and the deck - through elastic modal response spectrum analysis, extending the applicability of the "equal displacement" rule to the level of member deformations. About two thousands nonlinear dynamic (time-history) analyses of several representative bridges (with deck of three or five spans) are used for the development and the calibration of the procedure. However, for the application of the methodology only elastic modal response spectrum analysis is needed. Contrary to other current researches, which adopt the hypothesis of deck elastic response, the nonlinearities of the deck are modeled. The proposed displacement-based procedure offers lower reinforcement ratios (from 1/2 to 1/7 for the longitudinal reinforcement and from 1/1 to 1/3 for the transverse reinforcement) at no detriment to the expected seismic performance - the global overstrength of the bridges which are designed with the proposed procedure is practically equivalent to the global overstrength of the conventionally designed bridges (current force-based design). The step by step description of the design algorithm (Chap. 2) is followed by the practical application of the methodology (modeling aspects, design examples: Chap. 3), the conceptual justification (Chap. 4), the deficiencies of the conventional design procedure (force-based design examples: Chap. 3) and the fallacies in the justification of the conventional design methodology (Chap. 4). Comparative performance-based design evaluation (Chap. 3) of sixteen representative bridges (eight bridges subjected to alternative seismic design) indicates the benefits of the proposed procedure. The computational capabilities which were developed for the modeling and the analysis of the bridges are described in the appendices (upgrade of program ANSRuop).

Les gaz ou fluides de Coulomb sont composés de particules chargées couplées entre elles par interaction coulombienne à longue portée. De part la nature de ces interactions, la physique du gaz de Coulomb est très riche, comme par exemple dans des électrolytes plus ou moins complexes, mais aussi à travers l'émergence de monopôles magnétiques dans la glace de spin. Dans cette thèse nous nous intéressons au comportement hors d'équilibre des gaz de Coulomb et de la glace de spin. Au centre de cette étude se trouve le deuxième effet de Wien, qui est une croissance linéaire de la conductivité en fonction du champ électrique appliqué à un électrolyte faible. Ce phénomène est une conséquence directe de l'interaction coulombienne qui pousse les charges à se lier par paires ; le champ électrique va alors aider à dissocier ces paires et créer des charges mobiles qui amplifient la conductivité. Le deuxième effet de Wien est un processus hors-équilibre non-linéaire, remarquablement décrit par la théorie de Onsager. Nos simulations sur réseau permettent de découvrir le rôle de l'environnement ionique qui agit contre le deuxième effet de Wien, ainsi que de caractériser la mobilité du système et sa dépendance en fonction du champ externe. Les simulations nous ont aussi donné accès aux corrélations de charges qui décrivent le processus microscopique à la base de l'effet Wien. Enfin, nous regardons plus précisément le gaz émergent de monopôles dans la glace de spin, aussi appelé « magnétolyte », capable de décrire de manière remarquable les propriétés magnétiques de glace de spin. Nous décrivons la dynamique complète hors-équilibre de cette magnétolyte soumise à une forçage périodique ou une trempe dans un champ magnétique en incluant à la fois le deuxième effet de Wien et la réponse du réseau de spins qui est à la base de l'émergence des monopôles magnétiques. Tout au long, nous utilisons une simple extension des simulations de gaz de Coulomb sur réseau pour préciser nos prédictions. Il est très rare de trouver une théorie analytique du comportement hors-équilibre d'un système hautement frustré au-delà de la réponse linéaire. / A Coulomb gas or fluid comprises charged particles that interact via the Coulomb interaction. Examples of a Coulombic systems include simple and complex electrolytes together with magnetic monopoles in spin ice. The long-range nature of the Coulomb interaction leads to a rich array of phenomena.This thesis is devoted to the study of the non-equilibrium behaviour of lattice based Coulomb gases and of the quasi-particle excitations in the materials known as spin ice which constitute a Coulomb gas of magnetic charges. At the centre of this study lies the second Wien effect which describes the linear increase in conductivity when an electric field is applied to a weak electrolyte. The conductivity increases due to the generation of additional mobile charges via a field-enhanced dissociation from Coulombically bound pairs.The seminal theory of Onsager gave a detailed analysis of the Wien effect. We use numerical simulations not only to confirm its validity in a lattice Coulomb gas for the first time but mainly to study its extensions due to the role of the ionic atmosphere and field-dependent mobility. The simulations also allow us to observe the microscopic correlations underlying the Wien effect.Finally, we look more closely at the emergent gas of monopoles in spin ice—the magnetolyte. The magnetic behaviour of spin ice reflects the properties of the Coulomb gas contained within. We verify the presence of the Wien effect in model spin ice and in the process predict the non-linear response when exposed to a periodic driving field, or to a field quench using Wien effect theory. We use a straightforward extension of the lattice Coulomb gas simulations to refine our predictions. It is a highly unusual result to find an analytic theory for the non-equilibrium behaviour of a highly frustrated system beyond linear response.

La composition interne de notre planète est un vaste sujet d’étude auquel participent de nombreuses disciplines scientifiques. Les conditions extrêmes de pression et de température qui règnent à l’intérieur du noyau (constitué principalement de fer et de nickel) et du manteau terrestre (à base de pérovskites) rendent très difficile la détermination de leur compositions exactes. Ce projet de thèse contribue aux études récentes dont l’enjeu est de déterminer plus précisément le chimisme des minéraux présents. Il a pour objet le développement d’un outil de calcul des vitesses de propagation des ondes sismiques a l’aide d’une méthode fondée sur les simulations ab initio. Ces vitesses sont déduites du tenseur élastique complet, incluant la relaxation atomique et les modifications induites du champ cristallin. Nous utilisons l’approche de la théorie de perturbation de la fonctionnelle de la densité (DFPT) qui permet de s'affranchir des incertitudes numériques qu’impliquent les méthodes classiques basées sur des différences finies. Nous combinons cette approche avec le formalisme « Projector Augmented-Wave » (PAW) qui permet, avec un coût de calcul faible, de prendre en compte tous les électrons du système. Nous avons appliqué la méthode sur des matériaux du noyau et du manteau terrestre. Nous avons déterminé les effets de différents éléments légers (Si, S, C, O et H) sur les vitesses de propagation des ondes sismiques dans le fer pur ainsi que celui de l’aluminium dans la pérovskite MgSiO3. / The internal composition of our planet is a large topic of study and involves many scientific disciplines. The extreme conditions of pressure and temperature prevailing inside the core (consisting primarily of iron and nickel) and the mantle (consisting mainly of perovskites) make the determination of the exact compositions very difficult. This thesis contributes to recent studies whose aim is to determine more accurately the chemistry of these minerals. Its purpose is the development of a tool for the calculation of seismic wave velocities within methods based on ab-initio simulations. These velocities are calculated from the full elastic tensor, including the atomic relaxation and induced changes in the crystal field. We use the approach of the density functional perturbation theory (DFPT) to eliminate numerical uncertainties induced by conventional methods based on finite differences. We combine this approach with the « Projector Augmented-Wave » (PAW) formalism that takes into account all the electrons of the system with a low computational cost. We apply the method on core and mantle materials and we determine the effects of various lights elements (Si, S, C, O and H) on the seismic wave velocities of pure iron, as well as the effect of aluminum in the perovskite MgSiO3.

Cold-atom quantum simulators offer unique possibilities to prepare, manipulate, and probe quantum many-body systems. However, despite the high level of control in modern experiments, not all observables of interest are easily accessible. This thesis aims at establishing protocols to measure currently elusive static and dynamic properties of quantum systems. The experimental feasibility of these schemes is illustrated by means of numerical simulations for relevant applications in many-body physics and quantum simulation. In particular, we introduce a general method for measuring dynamical correlations based on non-Hermitian linear response. This enables unbiased tests of the famous fluctuation-dissipation relation as a probe of thermalization in isolated quantum systems. Furthermore, we develop ancilla-based techniques for the measurement of currents and current correlations, permitting the characterization of strongly correlated quantum matter. Another application is geared towards revealing signatures of supersolidity in spin-orbit-coupled Bose gases by exciting the relevant Goldstone modes. Finally, we explore a scenario for quantum-simulating post-inflationary reheating dynamics by parametrically driving a Bose gas into the regime of universal far-from-equilibrium dynamics. The presented protocols also apply to other analog quantum simulation platforms and thus open up promising applications in the field of quantum science and technology. / I simulatori quantistici ad atomi freddi offrono possibilità uniche per preparare, manipolare e sondare sistemi quantistici a molti corpi. Tuttavia, nonostante l'alto livello di controllo raggiunto negli esperimenti moderni, non tutte le osservabili di interesse sono facilmente accessibili. Lo scopo di questa tesi è quello di stabilire protocolli per misurare delle proprietà statiche e dinamiche dei sistemi quantistici attualmente inaccessibili. La fattibilità sperimentale di questi schemi è illustrata mediante simulazioni numeriche per applicazioni rilevanti nella fisica a molti corpi e nella simulazione quantistica. In particolare, introduciamo un metodo generale per misurare le correlazioni dinamiche basato su una risposta lineare non hermitiana. Ciò consente test imparziali della famosa relazione fluttuazione-dissipazione come sonda di termalizzazione in sistemi quantistici isolati. Inoltre, sviluppiamo tecniche basate su ancilla per la misura di correnti e correlazioni di corrente, consentendo la caratterizzazione della materia quantistica fortemente correlata. Un'altra applicazione è orientata a rivelare l'impronta della supersolidità nei gas Bose con accoppiamento spin-orbita eccitando il corrispondente modo di Goldstone. Infine, esploriamo uno scenario per la simulazione quantistica della dinamica di riscaldamento post-inflazione modulando parametricamente un gas Bose e portandolo nel regime della dinamica universale lontana dall'equilibrio. I protocolli presentati si applicano anche ad altre piattaforme di simulazione quantistica analogica e aprono quindi applicazioni promettenti nel campo della scienza e della tecnologia quantistica. / Quantensimulatoren auf Basis ultrakalter Atome eröffnen einzigartige Möglichkeiten zur Präparation, Manipulation und Untersuchung von Quanten-Vielteilchen-Systemen. Trotz des hohen Maßes an Kontrolle in modernen Experimenten sind jedoch nicht alle interessanten Observablen auf einfache Weise zugänglich. Ziel dieser Arbeit ist es, Protokolle zur Messung aktuell nur schwer erfassbarer statischer und dynamischer Eigenschaften von Quantensystemen zu etablieren. Die experimentelle Realisierbarkeit dieser Verfahren wird durch numerische Simulationen anhand relevanter Anwendungen in der Vielteilchenphysik und Quantensimulation veranschaulicht. Insbesondere wird eine allgemeine Methode zur Messung dynamischer Korrelationen basierend auf der linearen Antwort auf nicht-hermitesche Störungen vorgestellt. Diese ermöglicht unabhängige Tests des berühmten Fluktuations-Dissipations-Theorems als Indikator der Thermalisierung isolierter Quantensysteme. Darüber hinaus werden Verfahren zur Messung von Strömen und Strom-Korrelationen mittels Kopplung an einen Hilfszustand entwickelt, welche die Charakterisierung stark korrelierter Quantenmaterie erlauben. Eine weitere Anwendung zielt auf die Enthüllung spezifischer Merkmale von Supersolidität in Spin-Bahn-gekoppelten Bose-Einstein-Kondensaten ab, indem die relevanten Goldstone-Moden angeregt werden. Schließlich wird ein Szenario zur Quantensimulation post-inflationärer Thermalisierungsdynamik durch die parametrische Anregung eines Bose-Gases in das Regime universeller Dynamik fern des Gleichgewichts erschlossen. Die dargestellten Protokolle lassen sich auch auf andere Plattformen für analoge Quantensimulation übertragen und eröffnen damit vielversprechende Anwendungen auf dem Gebiet der Quantentechnologie.

In this work, the structural, electronic, and optical properties of CdS nanoparticles with sizes up to 4nm have been calculated using density-functional theory (DFT). Inaccuracies in the description of the unoccupied states of the applied density-functional based tight-binding method (DFTB) are overcome by a new SCF-DFTB method. Density-functional-based calculations employing linear-response theory have been performed on cadmium sulfide nanoparticles considering different stoichiometries, underlying crystal structures (zincblende, wurtzite, rocksalt), particle shapes (spherical, cuboctahedral, tetrahedral), and saturations (unsaturated, partly saturated, completely saturated). For saturated particles, the calculated onset excitations are strong excitonic. The quantum-confinement effect in the lowest excitation is visible as the excitation energy decreases towards the bulk band gap with increasing particle size. Dangling bonds at unsaturated surface atoms introduce trapped surface states which lie below the lowest excitations of the completely saturated particles. The molecular orbitals (MOs), that are participating in the excitonic excitations, show the shape of the angular momenta of a hydrogen atom (s, p). Zincblende- and wurtzite-derived particles show very similar spectra, whereas the spectra of rocksalt-derived particles are rather featureless. Particle shapes that confine the orbital wavefunctions strongly (tetrahedron) give rise to less pronounced spectra with lower oscillator strengths. Finally, a very good agreement of the calculated data to experimentally available spectra and excitation energies is found.