Investigações da dinâmica crítica em modelos de magnetismo, para tempos curtos, têm aparecido com grande freqüência na literatura. Essa técnica foi descoberta por Li, Schülke e Zheng que, inspirados em trabalhos anteriores de Huse e Janssen et al., mostraram que generalizações de grandezas como a magnetização e o cumulante de Binder exibem comportamento universal já no início da simulação. O estudo da criticalidade em tempos curtos proporciona um caminho alternativo para a estimativa do expoente z, além de permitir o cálculo de um novo expoente dinâmico θ, associado ao comportamento anômalo da magnetização. Da mesma forma, simulações dependentes do tempo tornaram-se ferramenta útil para estudar transições de fase em autômatos celulares e modelos de spin. Em particular, as melhores estimativas para o expoente z do Ising bidimensional foram obtidas por meio da técnica de propagação de danos, introduzida por Kauffman no estudo de autômatos e mais tarde generalizada para modelos de spin. Na primeira parte deste trabalho utilizamos o método Monte Carlo em tempos curtos para investigar o modelo de Baxter-Wu, definido em uma rede bidimensional triangular com variáveis do tipo Ising, acopladas por interações de três corpos. Obtivemos os expoentes críticos dinâmicos z e θ além dos índices críticos estáticos ß e Nû. Os resultados não corroboram aqueles recentemente obtidos por Santos e Figueiredo para o expoente z. Na segunda parte do trabalho, investigamos a propagação de danos no modelo de Ising unidimensional submetido a duas dinâmicas propostas por Hinrichsen e Domany (HD). Em particular, nós estudamos o efeito da atualização síncrona (paralela) e assíncrona (dinâmica contínua) sobre o espalhamento do dano. Mostramos que o dano não se propaga quando a segunda dinâmica é implementada de forma assíncrona. Também mostramos que as regras para atualização do dano produzidas por essa dinâmica, quando a temperatura vai a infinito e um certo parâmetro Lambda é igual a zero, são equivalentes àquelas do bem conhecido autômato celular (modelo A) de Grassberger. / Short-time simulations have been used with great frequency in the literature. That technique was discovered by Li, Shülke and Zheng that, inspired in previous works by Huse and Janssen et al., showed that generalizations of quantities like magnetization and the Binder´s cumulant exhibit universal behavior in the beginning of the simulation (early time behavior). The study of criticality in short-times provides an alternative way to estimate the dynamic critical exponent z, besides allowing the calculation of a new dynamic exponent θ, associated to the anomalous behavior of the magnetization. In the same way, time-dependent simulations became a useful tool to study phase transitions in cellular automata and also for spin models. In fact, the best estimates for the exponent z of the two-dimensional Ising model were obtained through the technique of damage spreading, introduced by Kauffman in the study of cellular automata, later widespread for spin models. In the first part of this work we used short-time Monte Carlo simulations to investigate the Baxter-Wu model, defined in a triangular lattice whose variables are Ising-like coupled by triplet interactions. We have obtained estimates for the dynamic critical exponents z and θ besides static exponents ß e Nû. Our results do not corroborate recent estimates by Santos and Figueiredo for the critical exponent z. In the second part of this work, we investigated the damage spreading in the one-dimensional Ising model under two dynamics introduced by Hinrichsen and Domany (HD). In particular, we study the effects of synchronous (parallel) and asynchronous (continuous dynamics) updating on the spreading properties. We showed that the damage does not spread when the second dynamic is implemented in an asynchronous way. We found that the rules for updating the damage produced by this dynamic, as the temperature goes to infinity and a certain parameter Lambda is zero, are equivalent to those of Grassberger’s well-known model A cellular automaton.

Made available in DSpace on 2016-12-23T14:04:33Z (GMT). No. of bitstreams: 1 Henery Ferreira Garcao.pdf: 1679065 bytes, checksum: 8e3210947a7d17cb14363973810da116 (MD5) Previous issue date: 2010-08-31 / A modelagem computacional é uma importante ferramenta para estimar a trajetória e destino final de manchas de óleo em diferentes condições ambientais, visto a complexidade dos processos que atuam nesse poluente. O presente trabalho concentrou os esforços no desenvolvimento de um modelo lagrangiano de trajetória de partículas que simule o movimento de manchas de óleo em ambiente marinho. O modelo utilizado é o Modelo Lagrangiano de Partículas com Deslocamento Aleatório (MLPDA), que é baseado na equação de Langevin. Em princípio, o algoritmo da advecção da mancha de óleo devido ao vento é implementado no MLPDA, visto sua importância ao deslocamento das partículas. É considerado que 3% da velocidade do vento a 10 metros de altura permite uma boa representação da deriva de manchas de óleo em ambiente marinho. Os testes para este algoritmo apresentaram resultados satisfatórios. Posteriormente, é implementado um algoritmo que representa o processo físico de espalhamento do óleo, conhecido também por espalhamento mecânico, que é definido como o movimento horizontal devido às forças gravitacionais, viscosas e inerciais. No presente estudo, esse processo é fundamentando nas equações definidas por Lehr et al. (1984), onde os resultados dos testes mostraram que as partículas espalham conforme exposto por esse mesmo autor e são influenciadas até cerca de 100 h de simulação. Ainda neste estudo, é avaliado o módulo de cálculo de área implementado no MLPDA. É advertido que malhas grosseiras podem resultar em áreas superestimadas, sendo aconselhável o uso de malhas mais refinadas para o cálculo dessas áreas. Por fim, três cenários de simulação de um derrame hipotético de óleo na Baía do Espírito Santo, no interior do Porto de Tubarão, são conduzidos para ilustrar uma aplicação do modelo desenvolvido. As simulações expõem que há grandes diferenças entre os resultados obtidos, principalmente entre o cenário que desconsidera o vento e os outros dois com a consideração desta forçante. O primeiro cenário, as partículas tenderam a permanecer na Baía do Espírito Santo, enquanto para os demais cenários as partículas caminharam para os canais do sistema estuarino da Grande Vitória (Canal da Passagem e Canal de Acesso aos Portos). / The computational modeling is an important tool to predict the trajectory and fate of the slick oil in different environmental conditions, since the complexity of processes involving oil spill. Thus, the present study has concentrated efforts on developing of a particle tracking lagrangian model that simulate the oil slick movement in the marine environment. The model used is Lagrangian Particles Random Walk Model (MLPDA), that it is based on the Langevin equation. First, the algorithm of the advection of the oil slick due to wind is implemented in the Random Walk Particle Lagrangian Model (MLPDA), seen its importance to the displacement of particles. It is considered that 3% of the wind velocity at 10 meters height allows a good representation of the drift of the slicks. The tests for this algorithm presented satisfactory results. Posteriorly, is implemented an algorithm that represents the physical process of spreading, also known as mechanic spreading, that is defined as the horizontal movement due to gravitational, viscous and inertial forces. In the present study, this process is based on the equations defined by Lehr et al. (1984), where the results of the tests showed that the particles spread as shown by this author and they are influenced up to 100 hours of simulation. In addition, it is evaluate the module for calculation the area implemented in MLPDA. It is adverted that very coarse grid may result in overrated areas, being advisable to use fine grid for calculation of these areas. Finally, three scenarios of simulation of a hypothetic oil spill at the Espírito Santo Bay, in the Tubarão Port, are conducted to illustrate an application of the model development. The simulations show large differences among the results obtained, mainly among the scenario that neglect the wind and the other two with the consideration of this forcing. The first scenario, the particles tended to remain at the Espírito Santo Bay, while other scenarios the particles walked to the channels of the Great Vitória estuarine system (Passage Channel and Access Channel to Ports).

abstract: Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva. A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds. Further, a numerical algorithm is described for the simulation of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest is in how the partition of rabid foxes into territorial and diffusing rabid foxes influences the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis to latent periods of fixed length and to exponentially distributed latent periods. The results of the numerical calculations are compared for latent periods of fixed and exponentially distributed length and for various proportions of territorial and wandering rabid foxes. The speeds of spread observed in the simulations are compared to spreading speeds obtained by numerically solving the analytic formulas and to observed speeds of epizootic frontlines in the European rabies outbreak 1940 to 1980. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2018

Mathematical modeling of spreading processes have been largely studied in the literature, and its presented a boom in the past few years. This is a fundamental task on the understanding and prediction of real spreading processes on top of a population and are subject to many structural and dynamical constraints. Aiming at a better understanding of this processes, we focused in two task: the modeling and the analysis of both dynamical and structural aspects of these processes. Initially, we proposed a new and general model that unifies epidemic and rumor spreading. Besides, regarding the analysis of these processes, we extended the classical formalism to multilayer networks, in which the theory was lacking. Interestingly, this study opened up new challenges concerning the understanding of multilayer networks. More specifically, regarding their spectral properties. In this thesis, we analyzed such processes on top of single and multilayer networks. Thus, throughout our analysis, we followed three complementary approaches: (i) analytical, (ii) numerical and (iii) simulations, mainly Monte Carlo simulations. Our main results are: (i) a new unifying model, enabling us to model and understand spreading processes on large systems, (ii) characterization of new phenomena on multilayer networks, such as layer-wise localization and the barrier effect and (iii) an spectral analysis of multilayer systems, suggesting a universal parameter and proposing a new analytical tool for its analysis. Our contributions enable further research on modeling of spreading processes, also emphasizing the importance of considering the complete multilayer structure instead of any coarse-graining. Additionally, it can be directly applied on the prediction and modeling real processes. Thus, aside from the theoretical interest and its mathematical implications, it also presents important social impact. / A modelagem matemática dos processos de disseminação tem sido amplamente estudada na literatura, sendo que o seu estudo apresentou um boom nos últimos anos. Esta é uma tarefa fundamental na compreensão e previsão de epidemias reais e propagação de rumores numa população, ademais, estas estão sujeitas a muitas restrições estruturais e dinâmicas. Com o objetivo de entender melhor esses processos, nos concentramos em duas tarefas: a de modelagem e a de análise de aspectos dinâmicos e estruturais. No primeiro, propomos um modelo novo e geral que une a epidemia e propagação de rumores. Também, no que diz respeito à análise desses processos, estendemos o formalismo clássico às redes multicamadas, onde tal teoria era inexistente. Curiosamente, este estudo abriu novos desafios relacionados à compreensão de redes multicamadas, mais especificamente em relação às suas propriedades espectrais. Nessa tese, analisamos esses processos em redes de uma e múltiplas camadas. Ao longo de nossas análises seguimos três abordagens complementares: (i) análises analíticas, (ii) experimentos numéricos e (iii) simulações de Monte Carlo. Assim, nossos principais resultados são: (i) um novo modelo que unifica as dinâmicas de rumor e epidemias, nos permitindo modelar e entender tais processos em grandes sistemas, (ii) caracterização de novos fenômenos em redes multicamadas, como a localização em camadas e o efeito barreira e (iii) uma análise espectral de sistemas multicamadas, sugerindo um parâmetro de escala universal e propondo uma nova ferramenta analítica para sua análise. Nossas contribuições permitem que novas pesquisas sobre modelagem de processos de propagação, enfatizando também a importância de se considerar a estrutura multicamada. Dessa forma, as nossas contribuições podem ser diretamente aplicadas à predição e modelagem de processos reais. Além do interesse teórico e matemático, nosso trabalho também apresenta implicações sociais importantes.

L’industrie aéronautique travaille sur l’amélioration des systèmes propulsifs parl’introduction de composites dans la fabrication des aubes de soufflante afin d’alléger lastructure et ainsi de réduire la consommation en carburant des avions. Ces pièces réaliséesen tissage 3D présentent généralement des irrégularités de surface. Une manière d’optimisercet aspect est d’ajouter un pli additionnel de surface : nos travaux de thèse portent sur ledéveloppement de ce pli sous la forme d’un renfort « Non Crimp Fabric » (NCF) biaxial extrafinen fibre de carbone de module intermédiaire (IM), inférieur à 100 g/m², régulier et ayant unebonne déformabilité. Lors de nos travaux de thèse, nous avons utilisé la méthode des plans d’expériencepour améliorer la technologie d’étalement afin de répondre aux exigences demandées. Nousavons pu définir la configuration optimale d’étalement permettant d’atteindre la cible d’un pliinférieur à 50 g/m² en fibre de carbone IM. Pour réaliser un NCF extra-fin, après étalement,les plis sont assemblés par couture afin d’assurer la tenue du renfort. La combinaison decouture choisie (armure, tension, longueur, jauge …) conditionne l’aspect du NCF et sacapacité à être manipulée et déformée. Nous avons donc optimisé les paramètres de coutureafin d’obtenir les propriétés souhaitées. Après avoir optimisé l’étalement des fibres et l’assemblage des plis, nous avons réalisé et caractérisé les renforts NCF extra-fins pour valider leurs propriétés. Nous sommesfinalement parvenus à mettre au point un renfort NCF en fibre de carbone IM, inférieur à50 g/m² par pli ayant un taux de couverture supérieur à 98 % et une bonne capacité à sedéformer. / Aircraft manufacturers are working on the improvement of their engines bymanufacturing fan blades with advanced composite materials to reduce fuel consumption.However, fan blades are made from 3D woven fabrics which often have surface irregularities.It can be minimized by an additional thin layer on the surface : our thesis work is focused onthe development of a new textile structure based on ultra-thin biaxial “Non Crimp Fabric” (NCF)technology. This spread NCF made from intermediate modulus (IM) carbon fibers must belighter than 100 gsm, regular and deformable.During our thesis work, we used Design of Experiments (DOE) methodology to improvethe spreading technology used by Chomarat to make ultra-light NCF materials and meet theestablished requirements. We were able to reach the ultra-thin ply target of less than 50 gsmper ply. After optimizing the spreading process these thin ply tapes are stitched together tocreate NCF. Stability, visual aspect, handling and deformability are dependent on the stitchingsettings (stitching pattern, tension, length, gauge, etc.). Therefore we optimized the stitchingparameters to get the desired properties.After the spreading and stitching process had been optimized, the NCF weremanufactured and tested to validate the desired properties had been achieved. The testingconfirmed that we were able to develop a new carbon fiber NCF that was less than 50 gsm perply, had a coverage rate of higher than 98 % and had good deformability characteristics.

L’épizootie de fièvre aphteuse de 2001 telle qu’elle s’est déroulée en Grande-Bretagne a montré les limites de certains des systèmes de surveillance, d’intervention, d’anticipation et d’aide à la décision actuellement en place. Parallèlement, l’assouplissement des modalités d’utilisation de la vaccination a enrichi la palette des outils utilisables par le gestionnaire de risque. Une réévaluation pour la France a semblé ainsi opportune. Pour cela, le projet de recherche s’est proposé tout d’abord d’étudier l’organisation des différentes filières d’animaux de rente en France. L’analyse du réseau d’élevages français par la méthode d’analyse des réseaux sociaux a permis de caractériser les relations entre établissements et d’estimer une vulnérabilité structurale constante face à la diffusion de maladies apportées essentiellement par le réseau d’échanges bovins.Dans une deuxième partie, la diffusion de la maladie dans ce réseau d’élevages a été étudiée en s’appuyant sur des simulations générées par un modèle spécifiquement construit. L’efficacité et les coûts de différentes stratégies de lutte envisageables (combinaisons d’abattage sanitaire, abattage préventif et vaccination) ont été ensuite comparés. Les résultats obtenus ont montré l’absence d’une stratégie unique optimale à la fois sur le plan épidémiologique et économique et la nécessité de s’adapter au contexte local. En effet, la nature de la stratégie optimale varie selon la région concernée et l’acteur considéré. Ces travaux ont permis de créer un outil de réflexion pour aider à la décision, mais également un outil d’entraînement et de formation collective pour se préparer à une telle gestion de crise. / The 2001 Foot-and-mouth disease epizootic in the United Kingdom has illustrated limits in some established surveillance, control, anticipation and decision-making systems. At the same time, the relaxation of vaccination procedures has enhanced the set of usable tools by risk managers. A reassessment in France seemed needed.For this purpose, the research project firstly proposed to study the organization of the different livestock industries in France. The analysis of French holding network by using the method of social network analysis has led to characterize the relationships between holdings and to determine a constant structural vulnerability to diseases spread especially due to bovine trade network.Secondly, the disease spread in the holding network has been studied with simulations generated by a specifically built model. The cost-effectiveness of different control strategies (combining infected herd depopulation, pre-emptive culling and vaccination) were then compared. Results showed that no single epidemiological and economical optimal strategy existed and local context must be taken into account. Indeed, the cost-effective strategy changed according to the concerned area and the considered players.This research work allowed creating a thinking tool for decision-making but also a training tool for crisis management preparation.

The dynamics wetting of fiber is of crucial importance in the fields, such as composites, optical fiber or textile industries. It is therefore valuable to acquire a clear understanding of the fundamental physical mechanisms which govern this phenomenon. In the case of partial wetting, it is assumed that the loss of energy due to the change in shape of the liquid-fluid interface (surface tension) is balanced by two channels of dissipation. One is associated with the viscosity of the liquid (hydrodynamics), whereas the other is due to the friction between the liquid and the solid (molecular-kinetic theory). Translated into equations, this original approach leads to the conclusion that the friction regime should precede the hydrodynamic one for a low viscosity liquid. The crossover time between the two regimes is calculated and shown to be material dependent. To validate these theoretical predictions, both experiments and large scale molecular dynamics simulations of the spontaneous spreading of a liquid along a fiber are run. The experiments consist in capturing images of meniscus formation around the fiber via a high speed camera. For each image, the liquid-air profile is extracted and fitted to a solution of the Laplace equation yielding the contact angle and the height of the meniscus as a function of the time. For low viscosity liquid it is found that the measured dynamic contact angle follows the friction regime, whereas for higher viscosity liquid the viscous regime is recovered as presented theoretically. The same kind of procedure is followed to study the wetting of a nanofiber by molecular dynamics. The properties of the liquid are first assessed (viscosity, shape of the molecule, molecular volume). Because of the very low viscosity of the model liquid, it is expected that the friction between the liquid and the solid is the dominant channel. Indeed, the data from the simulation validates this assumption. Moreover, according to the results of the simulation, it is also confirmed that for a given equilibrium contact angle, a maximum of speed wetting occurs. Actually, a low (or high) equilibrium contact angle involves both a strong (or weak) driving force and adhesion of the liquid molecules to the solid atoms. These opposite effects do not simply cancel out and therefore lead to the existence of a maximum rate at which a liquid can wet a solid. To examine in detail this last statement, the forced wetting of fiber is studied by molecular dynamics. The fiber, at a constant velocity, goes through the meniscus of a liquid which is consequently elongated. Stationary receding and advancing contact angles are then measured as a function of the fiber velocity. It is found that the contact angle dependence on the fiber velocity follows the molecular-kinetic theory, thereby confirming the existence of a maximum. Moreover, a comparison between the values of the microscopic parameters obtained via the adjustement of the theory and a direct measurement of these parameters permits us to check the validity of the chosen theory as well as the reliability of the simulation tool. Finally in order to study the wetting of fibrous materials like fabrics, an effective system is studied via molecular dynamics. It is shown that the measurements of capillary imbibition and droplet spreading are well modelled by a set of equations taking into account the conservation of the volume of the liquid, the influence of a dynamic contact angle inside the pore and the spreading on top of the surface. This single pore geometry is extended theoretically to the case of multiple non-interconnected pores. The time required to absorb the droplet completely is then calculated.

Dagens samhälle är präglat av ett enormt reklamutbud och reklamstrategier. I denna djungel av marknadsföring har företag ibland valt en annan strategi, en relativt outnyttjad strategi, som baseras på rykten om produkten, tjänsten eller företaget och är det som används som marknadsföring. Denna strategi kallas för word of mouth. Ena syftet har varit att undersöka hur word of mouth definieras av olika författare. Genom att göra en jämförelse av teorier av begreppet word of mouth har ett försök gjorts att skapa en definition av begreppet, som tillämpas på vårt andra syfte med undersökningen. Det andra syftet är att undersöka om kommunikationen på det utvalda internetforum prisjakt.nu kan liknas vid vår definition av word of mouth. Genom vår undersökning ville vi exemplifiera vad word of mouth är och vilket som är dess användningsområde. Forskningen har därför genomförts genom en litteraturstudie där word of mouth som begrepp har kartlagts och förklarats. Genom litteraturstudien utvecklades sedan en jämförelse av teorier av begreppet word of mouth. Dessa jämförelser av begreppet gjorde det möjligt för oss att kunna applicera begreppet på det tidigare nämnda utvalda internetforum. När slutdefinitionen fanns tillhanda, utfördes studien på Internetforumet Prisjakt.nu, med inriktning på en produkt som det pratades mycket om på detta Internetforum. Denna produkt valdes strategiskt då vi ansåg att det var väsentligt för undersökningen att produkten ännu inte fanns på marknaden, då tidigare teorier om word of mouths beteende tydde på att frekvensen på kommunikation om produkten var som högst innan produkten släppts. Denna produkt var Apple Iphone, som då ännu inte lanserats i Sverige. Därefter genomfördes studien med vår definition av traditionell och generaliserad word of mouth som teoretisk utgångspunkt, och studien resulterade i att förekomsten var positiv för word of mouth-baserad kommunikation på internetforumet prisjakt.nu. Vår definition av begreppet word of mouth lyder så som följer: “Word of mouth är interpersonell kommunikation, där självgenererande ryktesspridning om personer, företag, produkter eller tjänster kan ske via telefon, Internet eller mun-till-mun-kommunikation”. Kommunikationen på det undersökta forumet innehåller en hög grad av interpersonell kommunikation, självgenererande ryktesspridning och har en kommersiell karaktär på dess kommunikation, och uppfyller således de tre delar som enligt vår definition behövs för att kalla det en word of mouth-baserad kommunikation. / Today’s society is characterized by an enormously large advertising range and commercial strategies. In this jungle of marketing companies often chosen another strategy, a comparatively unknown strategy based on rumors about a product, service or company as marketing. That strategy is called word of mouth. The purpose of examine word of mouth as concept is important, because today the concept is defined on various manner of several different authors. By making a theory comparison of the conception word of mouth it is possible to create a good definition of the concept, this because that the concept word of mouth lacks a definite definition, that can be applied on our second purpose. The second purpose is to examine if the communication on the selected internet forum prisjakt.nu is word of mouth. In earlier cases this would been examined according to electronic word of mouth that is an adjustment to the internet, but we felt that the concept almost was identical to other word of mouth-theories we choose to make a theory comparison of the concept as described above. Through our examination we wanted to exemplify what word of mouth is and what it can be used for. A literature study was done as a replacement for the earlier research, the earlier research missed an evident significance of the conception word of mouth, and it handled its usage. The research had therefore been made through a literature study where the concept has been plotted and explained. Through the literature study the theory comparison of the concept word of mouth developed. . The theory comparison made it possible for us to apply the concept on the earlier mentioned internet forum. When the finished definition was at hand, the study was made on the internet forum prisjakt.nu, with the concentration on a product that had a big talk about it on this internet forum. This product was strategically selected as we considered it as an essential part for the research as the product didn’t even exist on the market; this due to the earlier theory’s about word of mouths behaviour that indicated that the frequency of the communication about the product was highest just before the product was released in the USA. The product was the Apple Iphone, and has after this research not yet been released in Sweden.The result shows that our definition of word of mouth can be applied on internet forums and that a separate concept for word of mouth on the internet is unnecessary. Our definition of word of mouth is as follows: “Word of mouth is an interpersonal communication, where self generating rumour spreading about people, companies, products or services can be made via telephone, internet or by mouth-to-mouth-communication“. The communication on the studied forums contain a high pitch of interpersonal communication, self generating rumour spread and have a commercialized character on it’s communication and fulfil the three parts that according of our theory comparison is needed for being called word of mouth-based communication.

In this work, a source term model for estimating the rate of spreading and vaporization of LNG on land and sea is introduced. The model takes into account the composition changes of the boiling mixture, the varying thermodynamic properties due to preferential boiling within the mixture and the effect of boiling on conductive heat transfer. The heat, mass and momentum balance equations are derived for continuous and instantaneous spills and mixture thermodynamic effects are incorporated. A parameter sensitivity analysis was conducted to determine the effect of boiling heat transfer regimes, friction, thermal contact/roughness correction parameter and VLE/mixture thermodynamics on the pool spreading behavior. The aim was to provide a better understanding of these governing phenomena and their relative importance throughout the pool lifetime. The spread model was validated against available experimental data for pool spreading on concrete and sea. The model is solved using Matlab for two continuous and instantaneous spill scenarios and is validated against experimental data on cryogenic pool spreading found in literature.

LEDs are being developed as the next generation lighting source due to their high efficiency and long life time, with a potential to save $15 billion per year in energy cost by 2020. State of the art LEDs are capable of emitting light at ~115 lm/W and have lifetime over 50,000 hours. It has already surpassed the efficiency of incandescent light sources, and is even comparable to that of fluorescent lamps. Since the total luminous flux generated by a single LED is considerably lower than other light sources, to be competitive the total light output must be increased with higher forward currents and packages of multiple LEDs. However, both of these solutions would increase the junction temperature, which degrades the performance of the LED--as the operating temperature goes up, the light intensity decreases, the lifetime is reduced, and the light color changes. The word "junction" refers to the p-n junction within the LED-chips. Critical to the temperature rise in high powered LED sources is the very large heat flux at the die level (100-500 W/cm2) which must be addressed in order to lower the operating temperature in the die. It is possible to address the spreading requirements of high powered LED die through the use of power electronic substrates for efficient heat dissipation, especially when the die are directly mounted to the power substrate in a chipon- board (COB) architecture. COB is a very attractive technology for packaging power LEDs which can lead improved price competiveness, package integration and thermal performance. In our work high power LED-chips (>1W/die) implementing COB architectures were designed and studied. Substrates for these packaging configurations include two types of power electronic substrates; insulated-metal-substrates (IMS) and direct-bonded-copper (DBC). To lower the operating temperature both the thermal impedance of the dielectric layer and the heat spreading in the copper circuit layers must be studied. In the analysis of our architectures, several lead free solders and thermal interface materials were considered. We start with the analysis of single-chip LED package and extend the result to the multi-chip arrays. The thermal resistance of the system is only a function of geometry and thermal conductivity if temperature-independent properties are used. Thus through finite element analysis (ANSYS) the effect of geometry and thermal conductivity on the thermal resistance was investigated. The drawback of finite element analysis is that many simulations must be conducted whenever the geometry or the thermal conductivity is changed. To bypass same of the computational load, a thermal resistance network was developed. We developed analytical expressions of the thermal resistance, especially focusing on the heat spreading effect at the substrate level. Finally, multi-chip LED arrays were analyzed through finite element analysis and an analytical analysis; where die-spacing is another important factor to determine the junction temperature. With this thermal analysis, critical design considerations were investigated in order to minimize device temperatures and thereby maximizing light output while also maximizing device reliability.