In this work we analyse two problems coming from theoretical biology. In the first part we propose a spatially structured population model which is defined on a continuous lattice. In the model individuals disperse at a constant rate v and competition is local and delimitated by the competition radius R. Due to dispersal, the neighborhooh size fluctuates over time. We analyse how these variables affect the adaptive process. While the fixation probabilities of beneficial mutations are roughly the same as in a panmitic population for small and intermediate fitness effects s, a dependence on v and R appears for large s. These quantities also strongly influence fixation times. The model exhibits a dual behavior displaying a power-law growth for the fixation rate and speed of adaptation with the beneficial mutation rate as observed in spatially structured population models, but simultaneously showing a non-saturating behavior for the speed of adaptation with the population size. In the second part we numerically study the dynamics of model imune networks with random and scale-free topologies. We observe that a memory state is reached when the antigen is attached to the most connected sites of the network, where as a percolation state may occur when the antigen attaches to the less connected sites. For increasing values of the connectivity, its population converges exponentially to the asymptotic value of the memory state. On the other hand, the next-nearest populations evolve slowly as power-laws towards the virgin-like state. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, analisamos dois problemas provenientes da biologia teórica. Na primeira parte, propomos um modelo de população espacialmente estruturada, que é definido numa rede contínua. No modelo, indivíduos se dispersam numa taxa constante v e a competição é local e delimitada pelo raio de competição R. Devido à dispersão, o tamanho da vizinhança flutua ao longo do tempo. Analisamos como essas variáveis afetam o processo adaptativo. Embora as probabilidades de fixação de mutações benéficas sejam aproximadamente as mesmas que numa população panmítica para valores de adaptação de pequeno e médio s, uma dependência de v e R aparece para grandes s. Estas quantidades também influenciam fortemente os tempos de fixação. O modelo exibe um comportamento duplo que indica um crescimento em lei de potência para a taxa de fixação e a velocidade de adaptação com a taxa de mutação benéfica como observado em modelos de população espacialmente estruturadas, mas simultaneamente mostra um comportamento não saturante para a velocidade de adaptação com o tamanho da população. Na segunda parte, estudamos numericamente a dinâmica de modelos de redes imunes com topologias aleatória e livre de escala. Observamos que um estado memória é alcançado quando o antígeno é ligado aos sítios mais conectados da rede enquanto que um estado de percolação pode ocorrer quando o antígeno se liga aos sítios menos conectados. Para maiores valores de conectividade, sua população converge exponencialmente para o valor assintótico do estado de memória. Por outro lado, as populações mais próximas evoluem lentamente, como leis de potência para o estado virgem.

Made available in DSpace on 2015-05-14T12:14:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 22318242 bytes, checksum: 4351a310199468e6df013ff385c10c32 (MD5) Previous issue date: 2014-02-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / When one focus a radiation in an atomic vapor, the radiation may undergo absorption and emission several times before the photons leave the cell volume that contains the vapor. As a result of these several scattering occurring inside the cell, the spectral profile of the incident radiation undergoes an evolution, which is governed by the mechanisms of frequency redistribution. There are two kinds of frequency redistribution: a Partial Frequency Redistribution (PFR) and a Complete Frequency Redistribution (CFR). When there is a correlation between the emission and absorption frequencies, we say that a PFR occurred. Otherwise, when there is no correlation between the absorbed and emitted frequencies, we say that a CFR occurred. This frequency redistribution has its origin in the inhomogeneity of the spectral profiles of the incident radiation and the response of the resonant vapor. It may be noted also that this inhomogeneity determines the distribution of step lengths of photons in an atomic vapor. The photons which propagate through this atomic medium perform a random walk between successive processes of absorption and emission, whose step length r is described by a probability distribution so-called "long tail". However, the superdifusive behavior of these photons is characterized by a single step length, which decreases asymptotically following a power law P(r) r with < 3. In this work we study, on a hand, the frequency redistribution in two parts: the first one is for several detunings of the radiation relative to the absorption center and we fix the vapor density, and, at a second part, we fixed the radiation detuning of the radiation and we changed the atomic density. In our numerical model, we studied rubidium atoms, by considering its optically active electronic structure with only two levels of energy and we excited it at the frequency of its D2 line. For the second part of this work, we analyzed numerically the exponent of the power law for the probability distribution of the single step lengths of the photons in an atomic vapor for absorption spectra and modified emission. For the last part of this work, we developed an experimental model to analyze the frequency redistribution, where the emitted photons coming out of the cell volume are collected in a certain solid volume by a lens of a few centimeters, directed through a fiber for analysis by a Fabry-Perot. Furthermore, an experimental setup has been developed to generate the probability distribution of photon steps, where we modified the spectra of the incident radiation or absorption. In the case of the incident radiation, it is guided by a fiber towards a second cell where a CCD camera with high sensitivity allows measuring the length of individual photon steps. / Quando incide-se uma radiação em um vapor atômico, esta pode sofrer processos de absorção e de emissão várias vezes antes que os fótons saiam do volume da célula que contém o vapor. Em consequência destes diversos espalhamentos, que ocorrem no interior da célula, o prol espectral da radiação incidente sofre uma evolução, o qual é regido pelos mecanismos de redistribuição em frequências. Existem dois tipos de redistribuição em frequências, a Redistribuição Parcial em Frequências (PFR) e a Redistribuição Completa em Frequências (CFR). Quando existe correlação entre a frequência de emissão e da absorção, dizemos que ocorreu uma PFR. Caso contrário, quando não há quaisquer correlação entre as frequências absorvidas e emitidas, dizemos que ocorreu CFR. Esta redistribuição em frequências tem sua origem na inomogeneidade dos perfis espectrais da radiação incidente e da resposta do vapor ressonante. Pode-se destacar, também, que esta inomogeneidade determina a distribuição dos comprimentos de passos dos fótons no vapor atômico. Os fótons que propagam-se neste meio atômico executam um passeio aleatório entre sucessivos processos de absorção e emissão, cujo comprimentos dos passos r é descrito por uma distribuição de probabilidade de dita "cauda longa". Contudo, o comportamento superdifusivo destes fótons é caracterizado por um comprimento de passo único, decaindo assintoticamente como uma lei de potência P(r) r com < 3. Neste trabalho estamos estudando, de uma parte, a redistribuição em frequências em duas etapas, sendo a primeira para diversas dessintonizações da radiação em relação ao centro de absorção, mantendo-se fixa a densidade do vapor e, em uma segunda etapa, deixamos fixa a dessintonização da radiação, variando-se a densidade atômica. Em nosso modelo numérico estudamos átomos de rubídio, considerando sua estrutura eletrônica oticamente ativa com apenas dois níveis de energia e excitado na frequência de sua linha D2. Para a segunda parte deste trabalho analisamos, de forma numérica, o expoente da lei de potência para a distribuição de probabilidade dos comprimentos de passos individuais dos fótons em um vapor atômico para espectros de absorção e emissão modificados. Para a última parte deste trabalho, desenvolveu-se um modelo experimental para analisar a redistribuição em frequências, onde os fótons emitidos que saem do volume da célula são coletados em certo volume sólido por uma lente de alguns centímetros, direcionados através de uma fibra para análise por um Fabry-Pérot. Além disso, foi desenvolvido uma técnica experimental para gerar a distribuição de probabilidade de passos dos fótons onde modificamos os espectros da radiação incidente ou de absorção. No caso da radiação incidente, esta é guiada por uma fibra para uma segunda célula, onde uma câmera CCD, de sensibilidade elevada, permite medir o comprimento de passos individuais dos fótons.

Submitted by (ana.araujo@ufrpe.br) on 2016-07-07T15:36:17Z No. of bitstreams: 1 Katiane Silva Conceicao.pdf: 4363127 bytes, checksum: bdfcba6d5b398e4cc048b2d41e232da1 (MD5) / Made available in DSpace on 2016-07-07T15:36:17Z (GMT). No. of bitstreams: 1 Katiane Silva Conceicao.pdf: 4363127 bytes, checksum: bdfcba6d5b398e4cc048b2d41e232da1 (MD5) Previous issue date: 2008-12-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Despite the complexity of factors that influence the growth and dispersion of individuals in species, some general patterns are observed in the study of ecosystems. One of these patterns is the relationship between the number of species and the size of the area occupied by these species (species-area relationship). This relationship is one of the oldest rules of ecology and has been used to estimate population distributions, species diversity of animals and plants.In this work, the main objective was to determine how the habitat fragmentation affects the behavior of the species-area relationship, based on the colonization of an area or region without any existence of life. The model was built to describe the occupation of a determined area by species. Bidimensional lattices, containing sites, represent these areas. For each site is attributed a capacity, which is characterized by the amount of resources available to people who will colonize the area. Each species has been assigned a f itness, which is defined as the sum of the capacities of sites colonized by the same species. In the process of colonization, mutations can occur causing an increase of the diversity of species. The proposed modelwas extended to simulate fragmented habitats as well. In this situation were considered lattices containing a proportion of sites not available for colonization. For the analysis of the pattern of that relationship, it was considered sampled areas in two contexts: different evolutionary histories and continents. It was observed that the sampling procedure changes the shape of the species-area curve. The analysis of the behavior of the system in the context of different evolutionary histories, shows that increasing the proportion of sites that can not be occupied p, there was an increase in the value of the exponent z for the different scale regions in power laws for large a value, indicating faster growth of diversity in relation to the case where the lattice is not fragmented. Considering the context of continents, it was noted that there are three scaling regions described by power laws for some values of a. However, as the proportion p of sites that can not be colonized was increased, there was a reduction in the number of laws for large a value. It was found that the value of exponent z is higher in large areas. Analyzing the distribution of the species size, it appears that the fragmentation increases the frequency of species with smaller populations. / Apesar da complexidade de fatores que influenciam o crescimento e a dispersão de indivíduos em espécies, alguns padrões gerais são observados no estudo de ecossistemas. Um desses padrões é a relação entre o número de espécies e o tamanho da área ocupada por elas (relação espécie-área). Esta relação é uma das regras mais antigas da ecologia,e tem sido utilizada para estimar distribuições populacionais, diversidade de espécies de animais e plantas.Neste trabalho, o principal objetivo foi verificar o efeito da fragmentação do habitat sobre o comportamento da relação espécie-área, a partir da colonização de uma área ou região sem nenhuma existência de vida. O modelo foi construído para descrever a ocupação de determinadas áreas por espécies.Estas áreas são representadas por redes bi-dimensionais que contém sítios. A cada sítio associa-se uma capacidade, que é caracterizada pela quantidade de recursos disponíveis às populações que colonizarão a área. A cada espécie foi atribuído um f itness, definido como a soma das capacidades dos sítios colonizados pela mesma espécie. No processo de colonização, mutações podem ocorrer, aumentando a diversidade de espécies.O modelo proposto foi estendido para simular, também, habitats fragmentados, e para esse caso foram consideradas redes contendo uma proporção de sítios não disponíveis para a colonização. Para a análise do comportamento dessa relação, considerou-se áreas amostradas em dois contextos: histórias evolucionárias diferentes e continentes. Observou-se que o procedimento adotado para amostragem da área altera a forma da curva espécie-área. Na análise do comportamento do sistema no contexto de histórias evolucionárias diferentes, observou-se que, com o aumento da proporção de sítios não colonizáveis p, houve um acréscimo no valor do expoente z para as diferentes regiões de escala em leis de potência para valores grandes de a, indicando um crescimento mais rápido da diversidade em relação ao caso onde as redes não são fragmentadas. Já no contexto de continentes, notou-se a existência de três regiões de escala em leis de potência para alguns valores de a. No entanto, à medida que a proporção de sítios não colonizáveis p foi acrescida, houve uma redução no número de leis para valores grandes de a. Verificou-se que o valor do expoente z é maior em áreas grandes. Analisando-se a distribuição de tamanhos das espécies, conclui-se que a fragmentação aumenta a freqüência de espécies com populações menores.

Ces travaux de thèse ont pour but d'obtenir une meilleure connaissance des mécanismes de dégradation, lors de l'exposition à un milieu agressif, de primaires de peinture en phase aqueuse (époxy-polyamino amide) utilisés dans l'industrie aéronautique pour la protection contre la corrosion de l'alliage d'aluminium 2024 à l'aide des techniques d'impédances globale et locale. Deux revêtements formulés soit avec du chromate de strontium soit avec un mélange de pigments non-chromatés ont été comparés. Les diagrammes d'impédance des deux revêtements, mesurés dans des conditions sèches (en contact avec Hg), présentent un comportement proche de celui d'une capacité pure, et ont été analysés à l'aide du modèle en loi de puissance, qui correspond à un comportement CPE (Constant Phase Element). Lors de l'immersion dans une solution chlorurée, le comportement des revêtements s'écarte progressivement de l'idéalité. Les données d'impédance électrochimique obtenues pour différents temps d'immersion ont été analysées avec un modèle qui suppose une variation exponentielle de la résistivité le long de l'épaisseur du revêtement (modèle de Young). Cette analyse a confirmé que la pénétration de l'eau et des ions dans le revêtement ne se fait pas de façon identique. La vitesse de pénétration de l'eau est plus rapide et celle-ci affecte plus fortement la permittivité que la résistivité, alors que la diffusion des ions Na+ et Cl- est plus lente et affecte exclusivement la résistivité du revêtement. L'utilisation de ces modèles permet non seulement d'expliquer les comportements CPE et pseudo CPE observés sur les diagrammes d'impédance mais aussi de déterminer la prise en eau des revêtements durant le test. Celle-ci est en accord avec des mesures gravimétriques. L'effet d'auto-cicatrisation des deux revêtements en présence de blessures artificielles a ensuite été étudié par spectroscopie d'impédance électrochimique locale. Les diagrammes locaux et les cartographies (2D ou 3D) ont permis de suivre les phénomènes d'auto-cicatrisation pour le système chromaté ou bien le développement de la corrosion pour le système non-chromaté. Ce travail de thèse propose une méthodologie qui servira de référence pour développer et caractériser les performances de peintures contenant des inhibiteurs écologiques et en particulier leur processus d'auto-cicatrisation. / The aim of this work is to obtain a better understanding of the degradation mechanisms, as a function of exposition time in an aggressive environment, of commercial coatings (epoxy-polyaminoamide waterborne paint) used in aeronautical industry for corrosion protection of 2024 aluminium alloy by global and local impedance techniques. The coatings formulated with either strontium chromate (SrCrO4) or Cr(VI)-free pigments were compared. The behavior of dry coatings (in contact with Hg) was close to that of an ideal capacitor and could be accurately modelled with the power-law model corresponding to a CPE (Constant Phase Element). Upon immersion in NaCl solution, the behavior of the wet coatings became progressively less ideal, i.e. farther from a capacitive behavior. The impedance data was analyzed with the Young model that take into account the exponential variation of the coating resistivity along its thickness. This analysis confirmed that penetration of water and ions occurs on different time scales. The former process is faster and affects permittivity more strongly than resistivity; the latter is slower and affects almost exclusively resistivity. The models allows to explain not only the CPE or pseudo-CPE behaviors observed on impedance diagrams but also to determine the coatings water uptake during the test which is in good agreement with gravimetric measurements. Then, the self-healing properties of artificially damaged coatings were studied by local electrochemical impedance spectroscopy (LEIS). The local diagrams and the mappings (2D or 3D) allowed self-healing processes for the chromated system or corrosion developments for the unchromated system to be observed. The present work proposed a methodology to develop and to characterize coatings containing environmentally friendly inhibitors, and particularly the self-healing process.

This thesis addresses the observed fluorescence intermittency of single semiconductor nanocrystals, so called Quantum Dots (QDs), which is also referred to as blinking. Despite continuous excitation their fluorescence is randomly interrupted by dark periods that can last over several minutes. Especially the extraction of power law dwell time statistics in bright and dark states indicates very complex underlying processes that are not fully understood to date. Here two approaches are followed to reveal the nature of the blinking mechanism. One addresses the common threshold method for extraction of power law dwell times. Its performance is tested with simulations to a broad range of experimentally determined parameters. Strong deviations are found between input and extracted statistics dependent on input parameters themselves. A comparison with experimental data does not support the assignment of power law statistics for the bright state and indicates the existence of distinct blinking mechanisms. The second approach directly aims at the nature of the dark state, which is mostly attributed to charges in the QD or trap states in its vicinity. A method is developed to detect charging processes on single QDs with their fluorescence. Electrochemistry is combined with confocal microscopy also allowing evaluations of excited state lifetimes and emission spectra. Reduction and oxidation of the QD bands are successfully observed as a quenching of QD fluorescence. Single QD observations identify two independent blinking mechanisms, that are assigned to positive and negative charging. Positive charging is not only observed after hole injection but also the extraction of excited electrons. Three additional quenching mechanisms are identified, two of which are assigned to trap relaxation. Differences between two substrate electrodes demonstrate the importance of the substrate material.

Confined particulate systems, particularly powder compacts, are widely used in various applications in industries such as pharmaceutical, automotive, agriculture, and energy production. Due to their extensive applications, characterization of these materials is of great importance for optimizing their performance and manufacturing processes. Modeling approaches capable of capturing the heterogeneity and complex behavior are effective at predicting the macroscopic behavior of granular systems. These modeling approaches utilize information about the microstructure evolution of these materials during compaction processes at the mesoscale (particle-scale). Using these types of modeling depend on accurate contact formulation between inter-particle contacts. The challenge comes in formulating these contact models that accurately predict force-area-deformation relationships. In this work, contact laws are presented for elastic-ideally plastic particles and plastic particles with power-law hardening under unconfined (simple compression) and confined (die and hydrostatic compaction) compression. First, material properties for a set of finite element simulations are obtained using space-filling design. The finite element simulations are used for verification and building an analytical framework of the contact radius and contact pressure which allows for efficient determination of the contact force. Semi-mechanistic contact laws are built for elastic-ideally plastic spherical particles that depend on material properties and loading configuration. Then, rigid-plastic assumption is used to modify the contact laws to consider power-law hardening effects while keeping loading configuration dependency. Finally, after building and verifying the contact laws, they are used to estimate hardening properties, contact radius evolution, and stress response of micro-crystalline cellulose particles under different loading configurations using experimental data from simple compression.

No description available.

The atmospheric boundary layer in the Arctic is essential for the understanding of climate change and improving regional weather prediction. The aim of this study is to investigate to which degree wind speed profiles retrieved in the Arctic agree with well known wind profile concepts and understand which local impact factors influence the wind speed profile. As part of the Nansen Legacy project, scientists from the University Centre in Svalbard and the University of Bergen installed two wind lidars onboard the research vessel “Kronprins Haakon” during the “Winter Process Cruise” in February 2021. Wind speed profiles were collected over a period of two weeks. They were manually classified into three categories based on their shape. The ideally shaped profiles were fitted against the wind profile power law to identify the exponent, α, for use in the Arctic marine boundary layer. α was found to be 4-5 times smaller than the conventionally applied α = 1/7 for profiles retrieved over open water, which was associated with unstable atmospheric conditions. Additionally, α was found to be considerably larger than 1/7 when sea ice was present, which was associated with stable conditions. A dependency on wind speed was also found. These results underline the importance of adjusting the exponent in order to ac- curately model the wind speed in the Arctic marine boundary layer. The results might be important for optimizing potential wind energy production, which is of great interest with the increasing human activ- ity in the Arctic. Reversed profiles (wind speed maxima closest to the surface) were mainly measured over open ocean and during low wind speeds and were speculated to be related to swell conditions. Pro- files containing a maxima in low levels were primarily measured during stable atmospheric conditions when sea ice was present. Future research in Arctic conditions would benefit from extending wind speed measurements to even lower levels and including stability measurements for an even deeper analysis.

Im Vergleich zu Stahlseilen haben hochfeste Faserseile vorteilhafte Eigenschaften. Insbesondere die bei gleicher Bruchlast um den Faktor 7 bis 10 reduzierte Eigenmasse ermöglicht neue Anwendungen. Die Nachteile von hochfesten Faserseilen gegenüber Stahlseilen , wie beispielsweise Druckempfindlichkeit und Empfindlichkeit gegenüber Wärmeeintrag , behindern den Einsatz von hochfesten Faserseilen in zahlreichen Anwendungsgebieten. Mit der vorliegenden Arbeit soll dieses Problem behoben werden. Dazu wurden die Grundlagen zur Auslegung einer neuen Winde für hochfeste Faserseile , welche die Nachteile dieser Zugmittel kompensiert, erarbeitet. Diese sogenannte Hüllandruckwinde vereint die Eigenschaften von hoher Treibkraft und Seilschonung auf kompaktem Bauraum. Eine Hüllandruckwinde ist eine Treibscheibenwinde, bei der das Seil durch ein umlaufendes, sogenanntes Hüllandruckelement in eine seilschonende Rundrille gedrückt wird. Das Hüllandruckelement kann als Zahnriemen mit Rundrille ausgeführt werden. Sowohl Treibscheibe als auch Hüllandruckelement sind angetrieben. Zur Auslegung von Hüllandruckwinden ist die Kenntnis der Treibkraft und des Systemverhaltens erforderlich. Bei der Überprüfung des Stands der Forschung auf geeignete Treibkraftmodelle stellte sich heraus, dass bislang kein geeignetes Modell existierte. Somit erfolgte die Erarbeitung des sogenannten verallgemeinerten nichtlinearen Modells zur Beschreibung der Treibkraft von Hüllandruckwinden. Dieses wurde validiert und mit einem Benchmark-Modell des Stands der Forschung verglichen. Das verallgemeinerte nichtlineare Modell weist im Vergleich zum Benchmark-Modell für den Zustand Haften einen im Durchschnitt 70 % und für den Zustand Gleiten einen im Durchschnitt 36 % niedrigeren mittleren relativen Fehler auf. Das verallgemeinerte nichtlineare Modell sagt in Bezug zu den Messdaten im Durchschnitt einen um 3,5 % erhöhten Wert vorher. Außerdem wurde das Systemverhalten von Hüllandruckwinden untersucht. Dabei konnte nachgewiesen werden, dass das Verhältnis der Winkelgeschwindigkeiten zwischen Treibscheibe und Hüllandrucklement im Bereich des Umschlingungswinkels des Hüllandruckelements auf dem Seil keinen Einfluss auf die Treibkraft hat. In Verspannversuchen mit einer Last unterhalb der Treibkraft konnten ein um 800 % überhöhtes virtuelles Antriebsdrehmoment des Hüllandruckelements und ein um 538 % überhöhtes Antriebsdrehmoment der Treibscheibe gemessen werden. Als Abhilfemaßnahme für diese überhöhten Antriebsdrehmomente erfolgte die Vorstellung eines lastabhängigen Vorspannmechanismus des Hüllandruckelements, welcher in der Nullserie der Hüllandruckwinde „HERO 1000“ angewendet wird. Aus der Gesamtheit der Erkenntnisse wurden Gestaltungshinweise für Hüllandruckwinden abgeleitet.:Kurzfassung VII Abstract IX 1 Einleitung 11 1.1 Problemstellung und Motivation 11 1.2 Zielsetzung und Forschungsfragen 13 1.3 Aufbau der Arbeit 15 2 Stand der Technik 17 2.1 Definitionen und Erläuterungen 17 2.2 Hochfeste Faserseile 21 2.3 Ablegereife und Zustandsüberwachung 23 2.4 Trommelwinden 25 2.5 Durchlaufwinden 27 2.5.1 Einfach umschlungene Treibscheibenwinden mit glatter Rille 28 2.5.2 Einfach umschlungene Treibscheibenwinden mit profilierten Rillen 30 2.5.3 Mehrfach umschlungene, mehrrillige Treibscheibenwinden 31 2.5.4 Spillwinden 35 2.6 Bandscheibenabzüge 37 3 Stand der Forschung 43 4 Mathematische Modellierung 51 4.1 Betriebssituationen 51 4.2 Vereinfachungen 52 4.3 Festlegungen 55 4.4 Modellierung der Treibkraft 56 4.4.1 Herleitung 56 4.4.2 Lösungen Treibkraftfall C 62 4.4.3 Lösungen Treibkraftfall A 63 4.4.4 Lösungen Treibkraftfall B 64 4.4.5 Lösung Treibscheibenbetrieb ohne HAE 65 4.5 Modellierung der Synchronisation 65 5 Experimentelle Untersuchungen 69 5.1 Versuchsstand 69 5.1.1 Parameter 69 5.1.2 Mechanischer Aufbau 72 5.1.3 Steuerung des Versuchsablaufs 75 5.1.4 Kalibrierung der Frequenzumrichter 76 5.1.5 Erfassung der Messgrößen 78 5.1.6 Auswertung der Messergebnisse 79 5.2 Auswahl der Materialpaarungen 84 5.3 Versuchsplanung 86 5.3.1 Treibkraft 87 5.3.2 Systemverhalten 90 5.4 Versuchsdurchführung 91 5.4.1 Treibkraft 91 5.4.2 Systemverhalten 95 6 Diskussion der Ergebnisse 97 6.1 Vorgehensweise 98 6.2 Treibkraft 99 6.2.1 Treibscheibenbetrieb ohne HAE 99 6.2.2 Treibkraftfall A 109 6.2.3 Treibkraftfall B 114 6.2.4 Treibkraftfall C 120 6.2.5 Kritische Betrachtung des Treibkraftmodells 130 6.3 Systemverhalten 132 6.3.1 Verspannversuche 132 6.3.2 Synchronisationsversuche 139 6.3.3 Fazit Systemverhalten 143 6.4 Gestaltungshinweise für HAW 144 7 Zusammenfassung und Ausblick 147 7.1 Zusammenfassung 147 7.2 Ausblick 150 Abkürzungen 153 Symbole 155 Abbildungsverzeichnis 161 Tabellenverzeichnis 165 Literaturverzeichnis 169 Anlagenverzeichnis 182 / Compared to steel ropes, high-strength fibre ropes have advantageous properties. In particular, the reduction in dead weight by a factor of 7 to 10 for the same breaking load makes new applications possible. The disadvantages of high-strength fibre ropes compared to steel ropes, such as pressure sensitivity and sensitivity to heat input, hinder the use of high-strength fibre ropes in numerous areas of application. The present work is intended to eliminate this problem. For this purpose, the basic principles for the development of a new winch for high-strength fibre ropes, which compensates for the disadvantages of high-strength fibre ropes, were worked out. This so-called belt wrap capstan combines the properties of high driving force and rope protection in a compact design. A belt wrap capstan is a traction sheave winch in which the rope is pressed into a round groove by a so-called belt wrap capstan. The enveloping pressure element can be designed as a toothed belt with a round groove. Both the traction sheave and the enveloping pressure element are driven. The design of belt wrap capstans requires knowledge of the driving force and the system behaviour. When reviewing the state of research for suitable driving force models, it was found that no suitable model existed so far. Therefore, a so-called generalised non-linear model was developed to describe the driving force of belt wrap capstans. This was validated and compared with a benchmark model of the state of the art. Compared to the benchmark model, the generalised nonlinear model has a 70 % lower mean relative error for the sticking condition and a 36 % lower mean relative error for the sliding condition. The generalised non-linear model predicts a 3.5 % higher value on average. The system behaviour of belt wrap capstans was also investigated. It was demonstrated that the ratio of angular velocities between the drive sheave and the enveloping pressure element within the wrap angle of the enveloping pressure element on the rope has no influence on the driving force. In tensioning tests with a load below the driving force, an 800 % excessive virtual driving torque of the sheath pressure element and a 538 % excessive driving torque of the traction sheave could be measured. As a remedy for the tensioning, a load-dependent pretensioning mechanism of the belt wrap capstan was presented, which is used in the zero series of the belt wrap capstan 'HERO 1000'. Design recommendations for belt wrap capstans were derived from all the findings.:Kurzfassung VII Abstract IX 1 Einleitung 11 1.1 Problemstellung und Motivation 11 1.2 Zielsetzung und Forschungsfragen 13 1.3 Aufbau der Arbeit 15 2 Stand der Technik 17 2.1 Definitionen und Erläuterungen 17 2.2 Hochfeste Faserseile 21 2.3 Ablegereife und Zustandsüberwachung 23 2.4 Trommelwinden 25 2.5 Durchlaufwinden 27 2.5.1 Einfach umschlungene Treibscheibenwinden mit glatter Rille 28 2.5.2 Einfach umschlungene Treibscheibenwinden mit profilierten Rillen 30 2.5.3 Mehrfach umschlungene, mehrrillige Treibscheibenwinden 31 2.5.4 Spillwinden 35 2.6 Bandscheibenabzüge 37 3 Stand der Forschung 43 4 Mathematische Modellierung 51 4.1 Betriebssituationen 51 4.2 Vereinfachungen 52 4.3 Festlegungen 55 4.4 Modellierung der Treibkraft 56 4.4.1 Herleitung 56 4.4.2 Lösungen Treibkraftfall C 62 4.4.3 Lösungen Treibkraftfall A 63 4.4.4 Lösungen Treibkraftfall B 64 4.4.5 Lösung Treibscheibenbetrieb ohne HAE 65 4.5 Modellierung der Synchronisation 65 5 Experimentelle Untersuchungen 69 5.1 Versuchsstand 69 5.1.1 Parameter 69 5.1.2 Mechanischer Aufbau 72 5.1.3 Steuerung des Versuchsablaufs 75 5.1.4 Kalibrierung der Frequenzumrichter 76 5.1.5 Erfassung der Messgrößen 78 5.1.6 Auswertung der Messergebnisse 79 5.2 Auswahl der Materialpaarungen 84 5.3 Versuchsplanung 86 5.3.1 Treibkraft 87 5.3.2 Systemverhalten 90 5.4 Versuchsdurchführung 91 5.4.1 Treibkraft 91 5.4.2 Systemverhalten 95 6 Diskussion der Ergebnisse 97 6.1 Vorgehensweise 98 6.2 Treibkraft 99 6.2.1 Treibscheibenbetrieb ohne HAE 99 6.2.2 Treibkraftfall A 109 6.2.3 Treibkraftfall B 114 6.2.4 Treibkraftfall C 120 6.2.5 Kritische Betrachtung des Treibkraftmodells 130 6.3 Systemverhalten 132 6.3.1 Verspannversuche 132 6.3.2 Synchronisationsversuche 139 6.3.3 Fazit Systemverhalten 143 6.4 Gestaltungshinweise für HAW 144 7 Zusammenfassung und Ausblick 147 7.1 Zusammenfassung 147 7.2 Ausblick 150 Abkürzungen 153 Symbole 155 Abbildungsverzeichnis 161 Tabellenverzeichnis 165 Literaturverzeichnis 169 Anlagenverzeichnis 182

[EN] In this thesis, we consider two problems: we first explore the application of visibility graphs for describing the orbits of a discrete dynamical system that is governed by a fractional version of the logistic equation. We also study how to use this type of graphs to study response time series from the perspective of psychology. The preliminaries and introduction of these visibility graphs are presented in Chapter 1, where we revisit some basic facts from network science related to them. In the first part of this thesis, we analyze a phenomenon of mathematical nature. Wu and Baleanu introduced a fractional discrete dynamical system inspired by the fractional difference logistic equation. In order to study the trajectories of this model under this perspective of network science, in Chapter 2, we first review the most used fractional derivatives (Riemann-Liouville, Caputo, and Gründwald-Letnikov). Later, we show how to consider discrete fractional derivatives. Within our work, we present an alternative way of deducing the governing equation with respect to the one shown by Wu and Baleanu. We revisit the Wu-Baleanu equation in Chapter 3, focused on the visibility graphs of trajectories generated under different values of the scaling factor and the fractional exponent. We also study the existing connections between these parameters and the fitting with the degree distribution of the corresponding visibility graphs. When chaos is present, we link them with the exponent obtained when fitting the degree distribution to a power-law of the form x^(¿¿). With this approach, we provide an integrated vision of the dynamics of a family of fractional discrete dynamical systems that cannot be obtained from single Feigenbaum diagrams computed for each scaling factor and fractional exponent. We also connect the power-law exponent of the degree distribution fitting with the Shannon entropy of the visibility graphs degree distribution. In the second part, we analyze the response times of students to a binary decision task from the perspective of network science. We analyze the properties of the natural visibility graphs associated with their reaction time series. We observe that the degree distribution of these graphs usually fits a power-law distribution p(x) = x^(¿¿). We study the range in which parameter ¿ occurs and the changes of this exponent with respect to the age and gender of the students. Besides, we also study the links between the parameter ¿ and the ex-Gaussian distribution parameters that best fits each subject's response times. Finally, we outline some conclusions and perspectives of future research in both parts in Chapter 6. / [ES] En esta tesis, hemos considerado dos problemas: primero exploramos la aplicación de los grafos de visibilidad para describir las órbitas de un sistema dinámico discreto que está gobernado por una versión fraccionaria de la ecuación logística. Además, también estudiamos cómo usar este tipo de grafos para estudiar series temporales de tiempos de respuesta desde una perspectiva psicológica. Los preliminares, así como una introducción a estos grafos de visibilidad, se presentan en el Capítulo 1, donde revisitamos algunos hechos básicos de la ciencia de redes relacionados con dichos grafos. En la primera parte de esta tesis, analizamos un fenómeno de naturaleza matemática. Wu y Baleanu introdujeron un sistema dinámico discreto fraccionario inspirado en la ecuación logística con derivadas fraccionarias. Con el propósito de estudiar las trayectorias de este modelo desde la perspectiva de la ciencia de redes, en el Capítulo 2, primero revisamos las derivadas fraccionarias más utilizadas (Riemann-Liouville, Caputo y Gründwald-Letnikov). Posteriormente, mostramos cómo considerar derivadas fraccionarias discretas. En nuestro trabajo, presentamos una forma alternativa de deducir la ecuación gobernante con respecto a la presentada por Wu y Baleanu. Revisitamos la ecuación de Wu-Baleanu en el Capítulo 3, centrado en los grafos de visibilidad de trayectorias generadas a partir de distintos valores del factor de escala y del exponente fraccionario. También estudiamos la existencia de conexiones entre estos parámetros y el ajuste de la distribución de los grados de los correspondientes grafos de visibilidad. Cuando el caos está presente, los enlazamos con el exponente obtenido al ajustar la distribución de los grados a una ley de potencias de la forma x^(¿¿). A través de este enfoque, proporcionamos una visión integrada de la dinámica de una familia de sistemas dinámicos discretos fraccionarios que no se pueden obtener a partir de diagramas de Feigenbaum individuales calculados para cada factor de escala y exponente fraccionario. Además, relacionamos el exponente de la ley de potencias del ajuste de la distribución de grados con la entropía de Shannon de la distribución de grados de los grafos de visibilidad. En la segunda parte, analizamos el tiempo de respuesta de un grupo de estudiantes que realizaron una tarea de decisión binaria desde la perspectiva de la ciencia de redes. Estudiamos las propiedades de los grafos de visibilidad natural asociados con sus correspondientes series de tiempos de respuesta. Observamos que la distribución de los grados de estos grafos normalmente sigue una distribución ley de potencias p(x) = x^(¿¿). Analizamos el rango en el cual el parámetro ¿ se mueve y los cambios de este exponente con respecto a la edad y el sexo de los estudiantes. Por otro lado, también estudiamos la relación entre el parámetro ¿ y los parámetros de la distribución ex-Gaussiana que mejor se ajusta al tiempo de respuesta de cada sujeto. Finalmente, destacamos algunas conclusiones y perspectivas de investigación futura en ambas líneas de trabajo en el Capítulo 6. / [CAT] En aquesta tesi, hem considerat dos problemes: primer explorem l'aplicació dels grafs de visibilitat per a descriure les òrbites d'un sistema dinàmic discret que està governat per una versió fraccionària de l'equació logística. A més a més, també estudiem com emprar aquest tipus de grafs per a analitzar sèries temporals de temps de resposta des d'una perspectiva psicològica. Els preliminars, així com una introducció a aquests grafs de visibilitat, es presenten al Capítol 1, on revisitem alguns fets bàsics de la ciència de xarxes relacionats amb ells. En la primera part d'aquesta tesi, analitzem un fenomen de naturalesa matemàtica. Wu i Baleanu van introduir un sistema dinàmic discret fraccionari inspirat en l'equació logística amb derivades fraccionàries. Amb el fi d'estudiar les trajectòries d'aquest model des d'una perspectiva de la ciència de xarxes, en el Capítol 2, primer revisem les derivades fraccionàries més utilitzades (Riemann-Liouville, Caputo i Gründwald-Letnikov). Posteriorment, mostrem com considerar derivades fraccionàries discretes. Al nostre treball, presentem una forma alternativa de deduir l'equació governant respecte a la presentada per Wu i Baleanu. Revisitem l'equació de Wu-Baleanu al Capítol 3, focalitzat en els grafs de visibilitat de trajectòries generades a partir de valors diferents del factor d'escala i de l'exponent fraccionari. També estudiem l'existència de connexions entre aquests paràmetres i l'ajust de la distribució dels graus dels corresponents grafs de visibilitat. Quan el caos hi és, els enllacem amb l'exponent que hem obtés en ajustar la distribució dels graus a una llei de potències de la forma x^(¿¿). Des d'aquesta perspectiva, proporcionem una visió integrada de la dinàmica d'una família de sistemes dinàmics discrets fraccionaris que no es poden obtenir a partir de diagrames de Feigenbaum individuals calculats per a cada factor d'escala i exponent fraccionari. A més a més, relacionem l'exponent de la llei de potències de l'ajust de la distribució de graus amb l'entropia de Shannon de la distribució de graus dels grafs de visibilitat. A la segona part, analitzem el temps de resposta d'un grup d'estudiants que realitzaren una tasca de decisió binària des del punt de vista de la ciència de xarxes. Estudiem les propietats dels grafs de visibilitat natural associats amb les seues corresponents sèries temporals de temps de resposta. Observem que la distribució dels graus d'aquests grafs normalment segueix una distribució llei de potències p(x) = x^(¿¿). Analitzem el rang en què el paràmetre ¿ es mou i els canvis d'aquest exponent respecte a l'edat i el sexe dels estudiants. D'altra banda, també estudiem la relació entre el paràmetre ¿ i els paràmetres de la distribució ex-Gaussiana que millor fita el temps de resposta de cada subjecte. Finalment, destaquem algunes conclusions i perspectives d'investigació futura en ambdues línies de treball en el Capítol 6. / Mira Iglesias, A. (2021). Applications of Visibility Graphs for the representation of Time Series [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176012