Pour réaliser des simulations précises aux temps longs pour des vagues non linéaires, il faut faire appel à des algorithmes d’évolution temporelle précis. En particulier, la combinaison d’un pas de temps adaptatif avec un facteur intégrant est connue pour être très efficace. Nous proposons une modification de cette technique. Le principe consiste à soustraire un certain polynôme à une EDP. Puis, comme pour le facteur intégrant, nous faisons un changement de variable pour retirer la partie linéaire. Mais nous espérons retirer quelque chose de plus afin de rendre l’EDP moins raide pour les calculs numériques. Le polynôme choisi est une expansion de Taylor autour du temps initial de la solution. Afin de calculer les différentes dérivées nécessaires, nous utilisons le Dense Output qui donne la possibilité d’approximer les dérivées de la solution à tout temps. Une fois le facteur intégrant modifié appliqué, nous faisons appel à une avance temporelle classique afin de résoudre l’équation d’évolution. Il a été considéré plusieurs schémas de Runge-Kutta avec pas de temps adaptatif. Nous avons tiré avantage des méthodes emboîtées, afin de ne pas calculer de nouvelles fonctions et perdre du temps de calcul, en utilisant uniquement des données déjà calculées durant l’évolution temporelle. Les résultats numériques montrent que l’efficacité de notre méthode varie selon les cas. Par exemple, nous avons vérifié que plus le profil de l’onde est pentue, plus notre méthode est efficace. Pour le modèle de vagues non linéaires le plus compliqué à notre disposition, le modèle HOS, nous avons pu réduire le nombre de pas de temps de calcul jusqu’à près de 30 % avec un schéma de Runge-Kutta de Dormand-Prince et jusqu’à plus de 99 % pour un schéma de Bogacki-Shampine. / Efficient time stepping algorithms are crucial for accurate long time simulations of nonlinear waves. In particular, adaptive time stepping combined with an integrating factor are known to be very effective. We propose a modification of the existing technique. The trick consists in subtracting a certain-order polynomial to a PDE. Then, like for the integrating factor, a change of variables is performed to remove the linear part. But, here, we hope to remove something more to make the PDE less stiff to numerical resolution. The polynomial is chosen as a Taylor expansion around the initial time of the solution. In order to calculate the different derivatives, we use a dense output which gives a possibility to approximate the derivatives of the solution at any time. The modified integrating factor being applied, a classical time-stepping method can be used to solve the remaining equation. We focus on various Runge-Kutta schemes with a varying step size. We take advantage of embedded methods and use an evolved adaptive step control. We do not need to calculate new functions and loose time of calculation only by using already estimated values during the temporal evolution. Numerical tests show that the actual efficiency of the method varies along cases. For example, we verified that steeper waves profiles give rise to better behaviour of the method. For fully nonlinear water wave simulations with the HOS model, we can save up to 30% of total time steps with a Dormand-Prince Runge-Kutta scheme and we can save up to 99% with the Bogacki-Shampine scheme.

[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los objetivos de la obra en el contexto histórico de la integración numérica. En el Capítulo 2 se introducen los conceptos esenciales y unas herramientas fundamentales utilizadas a lo largo de la tesis. El diseño de los integradores propuestos se basa en los métodos de composición y escisión y en el desarrollo de Magnus. En el Capítulo 3 se describe el primero. Su idea principal consta de una recombinación de unos integradores sencillos para obtener la solución del problema. El concepto importante de las condiciones de orden se describe en ese capítulo. En el Capítulo 4 se hace un resumen de las álgebras de Lie y del desarrollo de Magnus que son las herramientas algebraicas que permiten expresar la solución de ecuaciones diferenciales dependientes del tiempo. La ecuación lineal de Schrödinger con potencial dependiente del tiempo está examinada en el Capítulo 5. Dado su estructura particular, nuevos métodos casi sin conmutadores, basados en el desarrollo de Magnus, son construidos. Su eficiencia es demostrada en unos experimentos numéricos con el modelo de Walker-Preston de una molécula dentro de un campo electromagnético. En el Capítulo 6, se diseñan los métodos de Magnus-escisión para las ecuaciones de onda y de Hill. Su eficiencia está demostrada en los experimentos numéricos con varios sistemas oscilatorios: con la ecuación de Mathieu, la ec. de Hill matricial, las ecuaciones de onda y de Klein-Gordon-Fock. El Capítulo 7 explica cómo el enfoque algebraico y el desarrollo de Magnus pueden generalizarse a los problemas no lineales. El ejemplo utilizado es el problema de Kepler con masa decreciente. El Capítulo 8 concluye la tesis, reseña los resultados y traza las posibles direcciones de la investigación futura. / [CAT] Aquesta tesi tracta de la integració numèrica de sistemes hamiltonians amb potencials explícitament dependents del temps. Els problemes d'aquest tipus són comuns en la física matemàtica, perquè provenen de la mecànica quàntica, clàssica i celest. L'objectiu de la tesi és construir integradors per a uns problemes rellevants no autònoms: l'equació de Schrödinger, que és el fonament de la mecànica quàntica; les equacions de Hill i d'ona, que descriuen sistemes oscil·latoris; el problema de Kepler amb la massa variant en el temps. El Capítol 1 descriu la motivació i els objectius de l'obra en el context històric de la integració numèrica. En Capítol 2 s'introdueixen els conceptes essencials i unes ferramentes fonamentals utilitzades al llarg de la tesi. El disseny dels integradors proposats es basa en els mètodes de composició i escissió i en el desenvolupament de Magnus. En el Capítol 3, es descriu el primer. La seua idea principal consta d'una recombinació d'uns integradors senzills per a obtenir la solució del problema. El concepte important de les condicions d'orde es descriu en eixe capítol. El Capítol 4 fa un resum de les àlgebres de Lie i del desenvolupament de Magnus que són les ferramentes algebraiques que permeten expressar la solució d'equacions diferencials dependents del temps. L'equació lineal de Schrödinger amb potencial dependent del temps està examinada en el Capítol 5. Donat la seua estructura particular, nous mètodes quasi sense commutadors, basats en el desenvolupament de Magnus, són construïts. La seua eficiència és demostrada en uns experiments numèrics amb el model de Walker-Preston d'una molècula dins d'un camp electromagnètic. En el Capítol 6 es dissenyen els mètodes de Magnus-escissió per a les equacions d'onda i de Hill. El seu rendiment està demostrat en els experiments numèrics amb diversos sistemes oscil·latoris: amb l'equació de Mathieu, l'ec. de Hill matricial, les equacions d'onda i de Klein-Gordon-Fock. El Capítol 7 explica com l'enfocament algebraic i el desenvolupament de Magnus poden generalitzar-se als problemes no lineals. L'exemple utilitzat és el problema de Kepler amb massa decreixent. El Capítol 8 conclou la tesi, ressenya els resultats i traça les possibles direccions de la investigació futura. / [EN] The present thesis addresses the numerical integration of Hamiltonian systems with explicitly time-dependent potentials. These problems are common in mathematical physics because they come from quantum, classical and celestial mechanics. The goal of the thesis is to construct integrators for several import ant non-autonomous problems: the Schrödinger equation, which is the cornerstone of quantum mechanics; the Hill and the wave equations, that describe oscillating systems; the Kepler problem with time-variant mass. Chapter 1 describes the motivation and the aims of the work in the historical context of numerical integration. In Chapter 2 essential concepts and some fundamental tools used throughout the thesis are introduced. The design of the proposed integrators is based on the composition and splitting methods and the Magnus expansion. In Chapter 3, the former is described. Their main idea is to recombine some simpler integrators to obtain the solution. The salient concept of order conditions is described in that chapter. Chapter 4 summarises Lie algebras and the Magnus expansion ¿ algebraic tools that help to express the solution of time-dependent differential equations. The linear Schrödinger equation with time-dependent potential is considered in Chapter 5. Given its particular structure, new, Magnus-based quasi-commutator-free integrators are build. Their efficiency is shown in numerical experiments with the Walker-Preston model of a molecule in an electromagnetic field. In Chapter 6, Magnus-splitting methods for the wave and the Hill equations are designed. Their performance is demonstrated in numerical experiments with various oscillatory systems: the Mathieu equation, the matrix Hill eq., the wave and the Klein-Gordon-Fock eq. Chapter 7 shows how the algebraic approach and the Magnus expansion can be generalised to non-linear problems. The example used is the Kepler problem with decreasing mass. The thesis is concluded by Chapter 8, in which the results are reviewed and possible directions of future work are outlined. / Kopylov, N. (2019). Magnus-based geometric integrators for dynamical systems with time-dependent potentials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/118798 / TESIS

This work deals with the automatic control of calculations of specialized system. The reader is acquainted with the numerical solution of differential equations by Taylor series method and numerical integrators. The practical aim of this work is to analyze parallel characteristics of Taylor series method, specification of parallel math operations and design of control of this operations.

The thesis deals with the pouring of epoxy materials over LED strips. The research part contains an introduction to photometry and summarizes the types of potting compounds along with their characteristics. The practical part delves into the effect different amount of pigment has on the photometric properties. This is assessed based on verified measurements performed with the help of a goniophotometer on samples with different amounts of pigment, which were created using an integration sphere. Furthermore, a brightness analysis and a long-term outdoor test were performed.

The present thesis is focused on all pass filters. The principle of all pass filters, their properties, the design of nth degree of these circuits will be analysed in succession and then some of functional blocks, by which these structures can be made, will be described. After that, the allpass filters will be designed and simulated in program OrCAD PSpice. First of all, the analysis will be performed with ideal components, then with real components. After that, the sensitivity and tolerance analysis will be made and the influence of parasite effects on circuit parameters will be examined. Once the experiments are finished, the design of Printed Circuit Board's (PCB) will be realized. Circuit showing the best parameters will be chosen for the design.

The aim of this thesis is to design a universal analog oscillator using transconductance amplifiers. For studying behaviour of chaotic dynamical systems can be used systems Class C. Suitable way for the purpose modeling dynamic phenomena arising in these systems is an electronic circuit that exhibits the same behavior as modeled system. After familiarization with the basic principles of synthesis of integrators systems, and studying the involvement of frequently used functional blocks were designed the concept of universal chaotic oscillator using transconductance amplifiers. The functionality of this circuit has been verified by PSpice simulation program. A typical feature of chaotic oscillator is extremely sensitivity to initial conditions. Each small change on the initial parameters can lead to major change in the shape of the attractor. The result of this thesis is a functional sample of a universal chaotic oscillator, which was verified by the dynamic behavior of the given differential equations.

Goal of this doctoral thesis is to focus to understand of behavior of working of basic electronics circuits and to appoint which parameters of these circuits is possible to control using external digital system. Further the examples of some digitally controlled analog circuits are present and the analysis of these circuits is achieved. Some of these blocks are realized and the results of that’s measuring is presented.

<p>Neuromorphic computing endeavors to develop computational systems capable of emulating the brain’s capacity to execute intricate tasks concurrently and with remarkable energy efficiency. By utilizing new bioinspired computing architectures, these systems have the potential to revolutionize high-performance computing and enable local, low-energy computing for sensors and robots. Organic and soft materials are particularly attractive for neuromorphic computing as they offer biocompatibility, low-energy switching, and excellent tunability at a relatively low cost. Additionally, organic materials provide physical flexibility, large-area fabrication, and printability.</p><p>This doctoral dissertation showcases the research conducted in fabricating a comprehensive spiking organic neuron, which serves as the fundamental constituent of a circuit system for neuromorphic computing. The major contribution of this dissertation is the development of the organic, flexible neuron composed of spiking synapses and somas utilizing ultra-low voltage organic field-effect transistors (OFETs) for information processing. The synaptic and somatic circuits are implemented using physically flexible and biocompatible organic electronics necessary to realize the Polymer Neuromorphic Circuitry. An Axon-Hillock (AH) somatic circuit was fabricated and analyzed, followed by the adaptation of a log-domain integrator (LDI) synaptic circuit and the fabrication and analysis of a differential-pair integrator (DPI). Finally, a spiking organic neuron was formed by combining two LDI synaptic circuits and one AH synaptic circuit, and its characteristics were thoroughly examined. This is the first demonstration of the fabrication of an entire neuron using solid-state organic materials over a flexible substrate with integrated complementary OFETs and capacitors.</p>

With the development of technology and availability of data, it is sometimes easier to learn the control policies directly from the data, rather than modeling a plant and designing a controller. Modeling a plant is not always possible due to the complexity of the plant. Data-enabled predictive control (DeePC) is a recently proposed approach that combines system identification, estimation, and control in a single optimization problem. DeePC is primarily designed for LTI systems. The purpose of this thesis is to extend the application of DeePC to nonlinear systems with a particular focus on a non-holonomic ground robot. To reach this goal, we decompose the system states into different working modes where each mode can be linearly approximated. Furthermore, the data collection policies were also evaluated to conclude how they affect the performance of the DeePC. We identified several key challenges in this direction, namely: data-demanding structure, high computational complexity, and performance deterioration with increased non-linearity. While these challenges prohibited the application of DeePC to the ground robot system; we successfully applied the method to a benchmark non-linear system, the inverted pendulum on cart problem, and studied the effect of various design choices on control performance. Our observations indicate potential areas of improvement toward enabling DeePC for highly nonlinear systems. / Med utvecklingen av teknik och tillgänglighet av data är det ibland enklare att lära sig styrpolicyerna direkt från data, snarare än att modellera ett system och designa en styrenhet. Att modellera ett system är inte alltid möjligt på grund av systemets komplexitet. Data aktiverad prediktiv kontroll (DeePC) är en nyligen föreslagen metod som kombinerar systemidentifiering, uppskattning och kontroll i ett enda optimeringsproblem. DeePC är främst designad för LTI-system. Syftet med denna avhandling är att utöka tillämpningen av DeePC till icke-linjära system med särskilt fokus på en icke-holonomisk markrobot. För att nå detta mål delar vi upp systemtillstånden i olika arbetslägen där varje läge kan approximeras linjärt. Dessutom utvärderades datainsamlingspolicyerna för att dra slutsatser om hur de påverkar DeePCs prestation. Vi identifierade ett antal nyckelutmaningar i denna riktning, nämligen: datakrävande struktur, hög beräkningskomplexitet och prestandaförsämring med ökad icke-linjäritet. Även om de utmaningerna hindrade tillämpningen av DeePC på markrobot systemet; har vi framgångsrikt tillämpat metoden på ett benchmark icke-linjärt system, problemet med inverterad pendel på vagn, och studerade effekten av olika designval på kontrollprestanda. Våra observationer indikerar potentiella förbättringsområden för att möjliggöra DeePC för mycket olinjära system.

This thesis deals with the processing of light technical parameters and performance of key LED chips for their applications in lighting systems. The aim is to create a laboratory model for measuring the qualitative and quantitative parameters of highly luminous light LED emitted depending on the angle, using a spherical integrator 0.3 m, goniometer and fiber spektroradiometr /luxmeters. Goniometer is designed using modular optomechanical parts company Thorlabs. Due to the current passing through the LED chips heat up considerably. To light LED chip parameters tested were not affected by heat from the chip is required to pay the heat generated by a passive radiator. Another part of this thesis is the reconstruction of an older model spherical integrator. Reconstruction must be undertaken so as to ensure sufficient cooling again tested LEDs. Light scattered in the ball of the integrator is led by the optical cable to the spektroradiometr that are subsequently recorded its parameters. The second element used to measure the light produced by the LED source is photocell. Spherical integrator must be appropriately modified to indicate the two measuring elements and also meet the standards of determining the correctness of measurement. At the end of the measurement results will be compared with catalog values provided by the manufacturer.