Cette thèse est composée de deux parties : l’une traite des propriétés combinatoires de mots infinis et l’autre des problèmes de colorations des graphes.La première partie du manuscrit concerne les structures régulières dans les mots apériodiques infinis, à savoir les sous-séquences arithmétiques et les premiers retours complets.Nous étudions la fonction qui donne la longueur maximale d’une sous-séquence arithmétique monochromatique (une progression arithmétique) en fonction de la différence commune d pour une famille de mots morphiques uniformes, qui inclut le mot de Thue-Morse. Nous obtenons la limite supérieure explicite du taux de croissance de la fonction et des emplacements des progressions arithmétiques de longueurs maximales et de différences d. Pour étudier des sous-séquences arithmétiques périodiques dans des mots infinis, nous définissons la notion d'indice arithmétique et obtenons des bornes supérieures et inférieures sur le taux de croissance de la fonction donnant l’indice arithmétique dans la même famille de mots.Dans la même veine, une autre question concerne l’étude de deux nouvelles fonctions de complexité de mots infinis basées sur les notions de mots ouverts et fermés. Nous dérivons des formules explicites pour les fonctions de complexité ouverte et fermée pour un mot d'Arnoux-Rauzy sur un alphabet de cardinalité finie.La seconde partie de la thèse traite des colorations parfaites (des partitions équitables) de graphes infinis de degré borné. Nous étudions les graphes de Caley de groupes additifs infinis avec un ensemble de générateurs fixé. Nous considérons le cas où l'ensemble des générateurs est composé d'entiers de l'intervalle [-n, n], et le cas où les générateurs sont des entiers impairs de [-2n-1, 2n+1], où n est un entier positif. Pour les deux familles de graphes, nous obtenons une caractérisation complète des colorations parfaites à deux couleurs / The content of the thesis is comprised of two parts: one deals with combinatorial properties of infinite words and the other with graph coloring problems.The first main part of the manuscript concerns regular structures in infinite aperiodic words, such as arithmetic subsequences and complete first returns.We study the function that outputs the maximal length of a monochromatic arithmetic subsequence (an arithmetic progression) as a function of the common difference d for a family of uniform morphic words, which includes the Thue-Morse word. We obtain the explicit upper bound on the rate of growth of the function and locations of arithmetic progressions of maximal lengths and difference d. To study periodic arithmetic subsequences in infinite words we define the notion of an arithmetic index and obtain upper and lower bounds on the rate of growth of the function of arithmetic index in the same family of words.Another topic in this direction involves the study of two new complexity functions of infinite words based on the notions of open and closed words. We derive explicit formulae for the open and closed complexity functions for an Arnoux-Rauzy word over an alphabet of finite cardinality.The second main part of the thesis deals with perfect colorings (a.k.a. equitable partitions) of infinite graphs of bounded degree. We study Caley graphs of infinite additive groups with a prescribed set of generators. We consider the case when the set of generators is composed of integers from the interval [-n,n], and the case when the generators are odd integers from [-2n-1,2n+1], where n is a positive integer. For both families of graphs, we obtain a complete characterization of perfect 2-colorings

Os processos industriais de produção têxtil têm como característica o uso de grandes volumes de água durante as etapas de lavagem e tingimento de tecido, resultando em efluentes com enorme diversidade e complexidade química. A presença de corantes dissolvidos no efluente é bastante visível e problemática, considerando sua recalcitrância e cinética de degradação lenta. Neste trabalho, o fungo ascomiceto L. theobromae MMPI foi avaliado quanto à capacidade de remoção de cor do efluente sintético contendo corante azul reativo e de efluente industrial. Os ensaios com efluente sintético foram realizados em incubadora orbital shaker e em biorreator com cuba de 5 L. O meio foi suplementado com MgSO4.7H2O 2 g L-1, K2HPO4 2 g L-1, autoclavado (121o C/15 min), e acrescido de sacarose, nitrato de amônio e velocidade de agitação de acordo com delineamento composto central rotacional (DCCR), temperatura 28o C, inóculo padronizado e tempo para retirada das amostras de 72 h. A eficiência de remoção de cor variou de 31,58% até 91,60% e a produção de biomassa de 0,40 g L-1 a 8,70 g L-1. Foi observada ainda, a produção de um exopolissacarídeo (EPS) na ordem de 0,66 g L-1 a 9,70 g L-1. Na análise das estimativas dos efeitos (p<0,05) apenas o efeito linear da concentração de sacarose (p<0,000) e o efeito quadrático da concentração de nitrato de amônio (p<0,018) se mostraram significativos. O modelo obtido foi avaliado através da ANOVA, apresentando coeficiente de regressão elevado considerando um sistema biológico (R2 0,8483). Este modelo foi validado através de experimento a posteriori, indicando excelente correlação entre o valor preditivo (74,8%) e o valor observado (73,8%). Os ensaios em biorreator ratificaram o comportamento observado em incubadora shaker, obtendo-se 86% de descoloração do efluente sintético ao final de 72 horas de tratamento e 91,3% de descoloração ao final de 168 horas de tratamento para o efluente industrial. Após 168 h de incubação observou-se atividade enzimática de lacase (0,0563 U / ml). Os ensaios de toxicidade aguda com Artemia salina indicaram que a CL50 foi de aproximadamente 14,72% (v / v) para o efluente bruto, enquanto que o efluente submetido ao tratamento de oito dias o valor aproximado foi de 4,98% (v / v). Diversos autores relacionam os processos de descoloração a atividade enzimática, no entanto os resultados obtidos sugerem que a remoção de cor está relacionada a adsorção do corante na biomassa produzida. Estudos posteriores devem ser realizados para o melhor entendimento e confirmação de que a remoção de cor não está associada a biossíntese de enzimas degradadoras de estruturas fenólicas como as lacases. / The industrial processes of textile production are characterized by the use of large volumes of water during the steps of washing and dyeing fabric, resulting in effluent with enormous diversity and chemical complexity. The presence of dye dissolved in the effluent is quite noticeable and problematic, considering its recalcitrance and slow degradation kinetics. In this work, the fungus ascomiceto L. theobromae MMPI were evaluated for the ability to color removal from synthetic effluent containing blue dye reactive and industrial effluent. The tests with synthetic effluent were performed in incubator orbital shaker and in bioreactor with tub of 5L. The media was supplemented with MgSO4.7H2O 2 g L-1, K2HPO4 2 g L-1, autoclaved (121 C/15 min), plus sucrose, ammonium nitrate and stirring speed according to central composite design (CCDR), temperature 28 C, inoculum standardized and time to withdrawal of samples 72h. The color removal efficiency ranged from 31.58% to 91.60% and the biomass yield 0.40 g L-1 to 8.70 g L-1. It was still observed the production of an exopolysaccharide (EPS) in the range of 0.66 g L-1 to 9.70 g L-1. In the analysis of estimated effects (p <0.05) only the linear effect of sucrose concentration (p <0.000) and quadratic effect of the concentration of ammonium nitrate (p <0.018) were significant. The model was evaluated by ANOVA, with high regression coefficient considering a biological system (R2 0.8483). This model was validated by experiment retrospectively, indicating excellent correlation between the predictive value (74.8%) and the observed value (73.8%). The tests in bioreactor ratified the behavior observed in an incubator shaker to give 86% decolorization of synthetic effluent at the end of 72 hours of treatment of discoloration and 91.3% at the end of 168 hours of treatment for industrial effluent. After 168 h of incubation was observed laccase enzyme activity (0.0563 U / ml). The acute toxicity tests with brine shrimp showed that the LC50 was approximately 14.72% (v / v) for the raw wastewater, while the effluent subjected to the treatment eight days was approximately 4.98% (v / v). Several authors relate the processes of bleaching enzyme activity, however the results suggest that the color removal is related to the adsorption of the dye in the biomass produced. Further studies should be performed for better understanding and confirmation that the color removal is not associated with the biosynthesis of phenolic structures degrading enzymes such as laccases.

Les codes identifiants ont été introduits en 1998 par Karpovsky, Chakrabarty et Levitin. Un code identifiant est un sous-graphe tel que chaque sommet est identifié de manière unique par les sommets du code qui l'entourent. Il existe plusieurs variantes de ces codes, dont notamment une version colorée dans laquelle les sommets sont identifiés par les couleurs dans leur voisinage. Dans cette thèse, nous cherchons en particulier à construire un cycle le plus grand possible qui admette une coloration identifiante, étant donné un nombre de couleurs fixé. Nous avons aussi étudié le problème des codes identifiants sur une classe particulière de graphes orientés : les tournois. Dans une seconde partie, nous avons aussi étudié deux jeux particuliers. Le premier est une généralisation des jeux octaux - qui se jouent normalement sur un tas - aux graphes. Plus précisemment, le jeu 0.33 ; chaque joueur peut retirer un ou deux sommets voisins d'un graphe, sans déconnecter ce dernier. Le premier qui ne peut plus jouer perd. Nous avons été capable de caractériser les issues de ce jeu dans des classes de graphes particulières, les étoiles subdivisées et les bi-étoiles subdivisées. Le second jeu est appelé le jeu du Pompier (Firefighter). Il consiste à arrêter un feu qui se propage dans un graphe en protégeant des sommets à chaque tour. Nous avons résolu une conjecture sur ce jeu, et introduit la version online, pour laquelle nous avons pu donner des résultats d'approximation. / Identifying codes were introduced in 1998 by Karpovsky, Chakrabarty and Levitin. An identifying code is a subgraph such that each vertex is uniquely identified by the vertices in its neighborhood. There are several variants of these codes, including a colored version where the vertices are identified by the colors in their neighborhood. In this phd, we want to build an identifying coloring of a large cycle, given a fixed number of colors. We also studied identified codes in a certain class of oriented graphs: tournaments. We have also studied some topics in the game theory. The first one is a generalization of octal games, where we play on a graph instead of a heap. More precisely, the 0.33 game; each player can remove one or two vertices in a graph, with no disconnection allowed. The first player who cannot play loses. We studied this game in some graph classes: subdivided stars and subdivided bistars. The other game is called the Firefighter game. It's a one player game, where this one wants to contain a spreading fire in a graph. We solved a conjecture about this game, and introduced the online version of the game, for which we found some approximation results.

A crescente utilização de corantes na indústria gera grande quantidade de resíduos.Estes, quando descartados inadequadamente, tornam-se uma fonte poluidora dos sistemas aquáticos, os quais são indispensáveis à vida e à manutenção do equilíbrio de ecossistemas naturais. Por este motivo, é importante que sejam desenvolvidos métodos de tratamento eficazes para a remoção de corantes. Dentro desse contexto, este trabalho teve por objetivo avaliar a capacidade de adsorção de microesferas magnéticas de quitosana na remoção do corante violeta de metila 2B (VM 2B) em meio aquoso. Inicialmente, preparou-se magnetita (Fe3O4) através da precipitação química dos sais de ferro (II) e (III), em meio alcalino. A etapa seguinte consistiu na preparação das microesferas de quitosana, por meio da técnica de reticulação em suspensão, utilizando glutaraldeído. Com o objetivo de conferir propriedades magnéticas à quitosana, adicionou-se a Fe3O4 anteriormente preparada. Estes materiais foram caracterizados quanto a sua morfologia e características químicas. Os parâmetros experimentais do processo de adsorção foram previamente otimizados, variando-se a massa de adsorvente, a velocidade de agitação do sistema e o pH inicial do meio. A capacidade adsorvente das microesferas magnéticas de quitosana foi avaliada em um sistema em batelada, sob temperatura controlada de 25 °C, sendo a concentração remanescente de VM 2B em solução determinada por espectroscopia de absorção molecular na região do visível. Os resultados revelaram que as microesferas magnéticas de quitosana apresentam potencial para a finalidade proposta, com elevada capacidade de remoção para o corante VM 2B (~86%). Os resultados experimentais mostraram que a cinética de adsorção foi melhor descrita pelo modelo de pseudossegunda ordem. No que se refere ao equilíbrio de adsorção, os resultados experimentais apresentaram um melhor ajuste à isoterma de Freundlich (R2 superior a 0,98). Os dados termodinâmicos revelaram um processo de adsorção espontâneo ( G°= -3,96 kJ mol-1), exotérmico ( H° = -1,70 kJ mol-1), e com S° = -3,73 J mol-1 K-1, o que sugere pequena mudança na aleatoriedade na interface sólido-soluto durante a adsorção. / Submitted by Ana Guimarães Pereira (agpereir@ucs.br) on 2015-07-10T18:02:46Z No. of bitstreams: 1 Dissertacao Luciane Torezan Toaldo.pdf: 2501965 bytes, checksum: 94553f51b724d699cc4be4545b8c718c (MD5) / Made available in DSpace on 2015-07-10T18:02:46Z (GMT). No. of bitstreams: 1 Dissertacao Luciane Torezan Toaldo.pdf: 2501965 bytes, checksum: 94553f51b724d699cc4be4545b8c718c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior. / The increasing use of dyes in the industry generates great quantities of waste. When disposed improperly, they become a source of pollution of aquatic systems which are essential to life and to maintain the equilibrium of natural ecosystems. For this reason, it is important to develop effective treatment methods for the removal of dyes. In this context, this work aimed to evaluate the adsorption capacity of magnetic chitosan microspheres for the removal of methyl violet 2B (MV 2B) dye in aqueous media. Initially, magnetite (Fe3O4) was prepared by chemical precipitation of iron salts (II) and (III). Then, chitosan microspheres were prepared by the suspension crosslinking technique. Finally, Fe3O4 was added to chitosan in order to achieve magnetic properties. These materials were characterized by their morphology and chemical characteristics. The experimental parameters of the adsorption process were optimized by varying the mass of adsorbent, the stirring rate, and the initial pH of the medium. The adsorbent capacity of magnetic chitosan microspheres was evaluated in a batch system at 25 °C. After the adsorption process in an aqueous medium, the remaining concentration of MV 2B solution was determined by molecular absorption spectroscopy in the visible region. The results showed that the magnetic chitosan microspheres present a high potential for the purpose, with a high capacity for removing MV 2B (~86%). The adsorption process followed pseudo-second-order rate kinetics, and the adsorption equilibrium was better described by the Freundlich isotherm (R2 higher than 0.98). The thermodynamic data revealed a spontaneous ( G° = -3.96 kJ mol-1), exothermic ( H° = -1.70 kJ mol-1), and S° = -3.73 J mol-1 K-1, which suggests a small variation in the randomness at the solidsolution interface.

A crescente utilização de corantes na indústria gera grande quantidade de resíduos.Estes, quando descartados inadequadamente, tornam-se uma fonte poluidora dos sistemas aquáticos, os quais são indispensáveis à vida e à manutenção do equilíbrio de ecossistemas naturais. Por este motivo, é importante que sejam desenvolvidos métodos de tratamento eficazes para a remoção de corantes. Dentro desse contexto, este trabalho teve por objetivo avaliar a capacidade de adsorção de microesferas magnéticas de quitosana na remoção do corante violeta de metila 2B (VM 2B) em meio aquoso. Inicialmente, preparou-se magnetita (Fe3O4) através da precipitação química dos sais de ferro (II) e (III), em meio alcalino. A etapa seguinte consistiu na preparação das microesferas de quitosana, por meio da técnica de reticulação em suspensão, utilizando glutaraldeído. Com o objetivo de conferir propriedades magnéticas à quitosana, adicionou-se a Fe3O4 anteriormente preparada. Estes materiais foram caracterizados quanto a sua morfologia e características químicas. Os parâmetros experimentais do processo de adsorção foram previamente otimizados, variando-se a massa de adsorvente, a velocidade de agitação do sistema e o pH inicial do meio. A capacidade adsorvente das microesferas magnéticas de quitosana foi avaliada em um sistema em batelada, sob temperatura controlada de 25 °C, sendo a concentração remanescente de VM 2B em solução determinada por espectroscopia de absorção molecular na região do visível. Os resultados revelaram que as microesferas magnéticas de quitosana apresentam potencial para a finalidade proposta, com elevada capacidade de remoção para o corante VM 2B (~86%). Os resultados experimentais mostraram que a cinética de adsorção foi melhor descrita pelo modelo de pseudossegunda ordem. No que se refere ao equilíbrio de adsorção, os resultados experimentais apresentaram um melhor ajuste à isoterma de Freundlich (R2 superior a 0,98). Os dados termodinâmicos revelaram um processo de adsorção espontâneo ( G°= -3,96 kJ mol-1), exotérmico ( H° = -1,70 kJ mol-1), e com S° = -3,73 J mol-1 K-1, o que sugere pequena mudança na aleatoriedade na interface sólido-soluto durante a adsorção. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior. / The increasing use of dyes in the industry generates great quantities of waste. When disposed improperly, they become a source of pollution of aquatic systems which are essential to life and to maintain the equilibrium of natural ecosystems. For this reason, it is important to develop effective treatment methods for the removal of dyes. In this context, this work aimed to evaluate the adsorption capacity of magnetic chitosan microspheres for the removal of methyl violet 2B (MV 2B) dye in aqueous media. Initially, magnetite (Fe3O4) was prepared by chemical precipitation of iron salts (II) and (III). Then, chitosan microspheres were prepared by the suspension crosslinking technique. Finally, Fe3O4 was added to chitosan in order to achieve magnetic properties. These materials were characterized by their morphology and chemical characteristics. The experimental parameters of the adsorption process were optimized by varying the mass of adsorbent, the stirring rate, and the initial pH of the medium. The adsorbent capacity of magnetic chitosan microspheres was evaluated in a batch system at 25 °C. After the adsorption process in an aqueous medium, the remaining concentration of MV 2B solution was determined by molecular absorption spectroscopy in the visible region. The results showed that the magnetic chitosan microspheres present a high potential for the purpose, with a high capacity for removing MV 2B (~86%). The adsorption process followed pseudo-second-order rate kinetics, and the adsorption equilibrium was better described by the Freundlich isotherm (R2 higher than 0.98). The thermodynamic data revealed a spontaneous ( G° = -3.96 kJ mol-1), exothermic ( H° = -1.70 kJ mol-1), and S° = -3.73 J mol-1 K-1, which suggests a small variation in the randomness at the solidsolution interface.

Dans cette thèse nous étudions différents problèmes de graphes et multigraphes arêtes-coloriés tels que la connexité propre, la coloration forte d'arêtes et les chaînes et cycles hamiltoniens propres. Enfin, nous améliorons l'algorithme connu $O(n^4)$ pour décider du comportement d'un graphe sous opérateur biclique, en étudiant les bicliques dans les graphes sans faux jumeaux. Plus précisément, 1) Nous étudions d'abord le nombre $k$-connexité-propre des graphes, noté $pc_k(G)$, ç'est à dire le nombre minimum de couleurs nécessaires pour colorer les arêtes d'un graphe de façon à ce qu'entre chaque paire de sommets, ils existent $k$ chemins intérieurement sommet-disjoints. Nous prouvons plusieurs bornes supérieures pour $pc_k(G)$. Nous énonçons quelques conjectures pour les graphes généraux et bipartis et nous les prouvons dans le cas où $k = 1$. 2) Nous étudions l'existence de chaînes et de cycles hamiltoniens propres dans les multigraphes arêtes-coloriés. Nous établissons des conditions suffisantes, en fonction de plusieurs paramètres tels que le nombre d'arêtes, le degré arc-en-ciel, la connexité, etc. 3) Nous montrons que l'indice chromatique fort est linéaire au degré maximum pour tout graphe $k$-dégénéré où, $k$ est fixe. En corollaire, notre résultat conduit à une amélioration des constantes et donne également un algorithme plus simple et plus efficace pour cette famille de graphes. De plus, nous considérons les graphes planaires extérieurs. Nous donnons une formule pour trouver l'indice chromatique fort exact pour les graphes bipartis planaires extérieurs. Nous améliorons également la borne supérieure pour les graphes planaires extérieurs généraux. 4) Enfin, nous étudions les bicliques dans les graphes sans faux jumeaux et nous présentons ensuite un algorithme $O(n+m)$ pour reconnaître les graphes convergents et divergents en améliorant l'algorithme $O(n^4)$. / In this thesis, we study different problems in edge-colored graphs and edge-colored multigraphs, such as proper connection, strong edge colorings, and proper hamiltonian paths and cycles. Finally, we improve the known $O(n^4)$ algorithm to decide the behavior of a graph under the biclique operator, by studying bicliques in graphs withoutfalse-twin vertices. In particular: 1) We first study the $k$-proper-connection number of graphs, this is, the minimum number of colors needed to color the edges of a graph such that between any pair of vertices there exist $k$ internally vertex-disjoint paths. We denote this number $pc_k(G)$. We prove several upper bounds for $pc_k(G)$. We state some conjectures for general and bipartite graphs, and we prove all of them for the case $k=1$. 2) Then, we study the existence of proper hamiltonian paths and proper hamiltonian cycles in edge-colored multigraphs. We establish sufficient conditions, depending on several parameters such as the number of edges, the rainbow degree, the connectivity, etc. 3) Later, we showthat the strong chromatic index is linear in the maximum degree for any $k$-degenerate graph where $k$ is fixed. As a corollary, our result leads to considerable improvement of the constants and also gives an easier and more efficient algorithm for this familly of graphs. Next, we consider outerplanar graphs. We give a formula to find exact strong chromatic index for bipartite outerplanar graphs. We also improve the upper bound for general outerplanar graphs from the $3\Delta-3$ bound. 4) Finally, we study bicliques in graphs without false-twin vertices and then we present an $O(n+m)$ algorithm to recognize convergent and divergent graphs improving the $O(n^4)$ known algorithm.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação Araucária de Apoio ao Desenvolvimento Científico e Tecnológico do Paraná / O setor industrial têxtil gera em seu processo produtivo grande volume de efluentes líquidos, que possuem elevado potencial poluidor devido à presença de corantes. Esses são compostos potencialmente tóxicos e de difícil degradabilidade, dos quais destaca-se o Azul Reativo 5G. O tratamento desses efluentes é geralmente realizado por técnicas convencionais de coagulação e floculação, as quais utilizam grandes quantidades de sais de alumínio e ferro. A substituição de coagulantes químicos por tecnologias alternativas como a eletrofloculação pode trazer grandes vantagens. Este processo consiste na desestabilização de poluentes em meio aquoso por meio da produção in situ de íons coagulantes pela aplicação de corrente elétrica a eletrodos de sacrifício. Embora possua eficiência comprovada, inclusive para efluentes têxteis, a eletrofloculação ainda não é uma técnica consolidada, devido principalmente à ausência de metodologias sistemáticas para o projeto e dimensionamento de reatores, em especial os de fluxo contínuo. Diversas abordagens de modelagem e simulação na literatura buscam resolver esse problema, das quais destaca-se a Dinâmica de Fluidos Computacional (CFD) como a mais promissora, podendo ser acoplada a várias físicas, embora comumente seja acoplada apenas à eletroquímica. O objetivo deste trabalho foi acoplar a técnica de CFD a um modelo cinético ajustado experimentalmente para a remoção do corante Azul Reativo 5G de solução sintética por meio de eletrofloculação, visando predizer o perfil de concentração em um reator de fluxo contínuo. O reator contínuo estudado possui volume útil de 8,5 L, é do tipo monopolar, e possui quatro pares de eletrodos de ferro para o tratamento, dispostos como chicanas. Para obtenção do modelo para a cinética da reação, foram realizados experimentos com o sistema de eletrofloculação em batelada com eletrodos de ferro, em que as variáveis foram concentração inicial de corante (C0) e densidade de corrente (j) aplicada aos eletrodos. Testou-se o ajuste de três tipos de modelos cinéticos aos dados experimentais: modelo com base no balanço molar, modelos de adsorção e modelos sigmoidais, dos quais o modelo sigmoidal logístico, obteve melhor ajuste, com valores de R² acima de 90%. Como o modelo não inclui a espécie ferro, foram feitos ensaios preliminares no módulo de fluxo contínuo, para determinar a influência do fluxo na distribuição de ferro ao longo do reator, bem como o ponto no reator onde a reação tem início. Testou-se as vazões de 0,5 L.min-1 e de 2 L.min-1, e observou-se que para a vazão baixa, há retorno de ferro e acúmulo antes do primeiro eletrodo, o que não ocorre para a vazão mais alta. No modelo para o escoamento no reator considerou-se um fluido incompressível, fluxo laminar e estado estacionário, e desprezou-se a influência dos fenômenos eletroquímicos no fluxo e transporte de partículas, como a geração de bolhas de gás e migração iônica. A simulação para o reator de fluxo contínuo foi realizada no software COMSOL Multiphysics v.5.2®,que utiliza o Método dos Elementos Finitos para resolver as equações diferenciais parciais de escoamento da continuidade e de Navier-Stokes. As variáveis resposta consideradas foram a velocidade do fluido e a concentração de corante, e utilizou-se os módulos de CFD (interface de Fluxo Laminar) e de Transporte de Soluções Diluídas (TDS), com acoplamento fraco entre as físicas. Uma análise de convergência foi realizada para a escolha da malha. Foram realizadas três simulações do perfil de concentração no reator, com condição de densidade de corrente igual a 8,65 mA.cm-2, concentrações iniciais de corante respectivamente iguais a 45, 25 e 40 mg.L-1 e vazões 0,5 L.min-1 para os dois primeiros ensaios e 2 L.min-1 para o terceiro. Ensaios experimentais foram feitos com as mesmas condições, e comparou-se os resultados obtidos com uma malha de amostragem de 23 pontos. Verificou-se que o modelo proposto permitiu predizer o perfil de concentração do reator com razoável sucesso para uma faixa de trabalho de velocidades baixas de fluxo, levando em conta as limitações inerentes a ele, notadamente a ausência da influência das microbolhas. Assim, a metodologia proposta mostra-se muito promissora para que uma vez aperfeiçoado, o modelo possa vir a auxiliar no projeto de reatores caso a caso, bem como fornecer subsídios para preencher a lacuna acerca de uma metodologia sistemática de projeto e ampliação de escala. / The textile industry produces great amounts of wastewater as a byproduct of its productive process, which contain high pollutant potential, due to the presence of dyes. These are potentially toxic and high undegradable compounds, from which the Blue Reactive 5G is one of the most used. The treatment of such wastewaters is generally accomplished through conventional coagulation and flocculation techniques, which make use of great amounts of aluminum and iron salts. As such, the substitution of these chemical coagulants for alternative technologies such as electrocoagulation may bring great advantages. The process consists in the destabilization of pollutants in aqueous medium by means of the in situ production of coagulant ions by applying electrical current to sacrificial electrodes. Although the process' efficiency is proven, even for the treatment of textile wastewaters, electrocoagulation is still not a consolidated technique, due mainly to the lack of systematic methodologies for the project and scale up of reactors, especially continuous flow ones. Several approaches for modeling and simulation in scientific literature aim to solve this problem, the most promising of which being the Computational Fluid Dynamics (CFD), which may be coupled to several physics, although it is usually coupled only to electrochemistry. The goal of this study was to couple the CFD technique to a kinetic model, experimentally adjusted, for the removal of the Blue Reactive 5G dye from synthetic wastewater through the electrocoagulation technique, aiming to predict the concentration profile in a continuous flow reactor. The reactor is a 8,5 L tank with monopolar connections and four pairs of iron electrodes, which also work as baffles. In order to obtain the kinetic model of the reaction, experiments were carried out in a batch electrocoagulation system with iron electrodes, in which the variables were initial dye concentration (C0) and current density (j) applied to the electrodes. Three kinds of kinetic models were test for the adjust: model based on molar balance, adsorption models and sigmoidal models, from which the logistic sigmoidal model obtained the best adjustment, presenting R² above 90%. Since the model does not include the iron species, preliminary tests were made in the continuous flow reactor, in order to determine the flux influence on the iron distribution through the reactor, as well as the local, in the reactor, were the reaction starts. The flow rates of 0,5 L.min-1 and 2 L.min-1 were tested, and it was noted that, for the low flow rate, there is a reflux of iron, which accumulated before the first electrode, which does not happen for the higher flow rate. For the fluid flow model in the reactor, considerations were made for a incompressible laminar flow and stationary state, and the effect of electrochemical phenomena in the flow and transport of substances, such as gas bubbles and ironic migration, were not considered. The simulation for the continuous flow reactor was performed in the software COMSOL Multiphysics v.5.2®, which makes use of the Finite Elements Method to solve the partial differential equations of continuity and Navier-Stokes. The response variables considered were fluid velocity and dye concentration, and the modules CFD (laminar flow interface) and Transport of Diluted Species (TDS) were used, with weak coupling between the physics. A convergence study was carried out in order to choose the appropriate mesh for the simulation. Three simulations of the concentration profile in the reactor were carried out, with a current density of 8,65 mA.cm-2, respective initial dye concentrations of 45, 25 and 40 mg.L-1 and flow rates of 0,5 L.min-1 for the two first studies and 2 L.min-1 for the third. Experiments were performed with the same conditions as the simulations, samples were collected with mesh of 23 points in the reactor and the results of predicted and observed concentration were compared. The results showed that the proposed model allowed to predict the concentration profile in the reactor with reasonable success, within a low velocity flow range, taking into account the limitations inherent to the model. Therefore, the proposed methodology appears very promising for that, once perfected, the model may assist in the reactor design case to case, as well as aid filling the gap regarding a systematic methodology for reactor project and scale-up, which is the main barrier in expanding the technology.

Cette thèse étudie la coloration d'arcs et de cycles dans les graphes orientés. Elle se concentre sur les sujets suivants : la coloration propre d'arcs avec des sommet-distingué dans les graphes orientés, les cycles courts dans les graphes orientés avec des sous-graphes interdits, les cycles sommet-disjoints dans dans les tournois bipartis, les cycle-facteurs dans les tournois bipartis régulier et les arcs universels dans les tournois. La thèse est basée sur cinq articles originaux publiés ou présentés dans des journaux. Les principaux résultats sont les suivants. Nous introduisons la coloration propre d'arcs avec des sommet-distingué dans les graphes orientés. Nous avons proposé une conjecture sur le nombre arc-chromatique sommet-distingué et nous avons aussi donné quelque résultats partiels. Nous avons étendu un résultat de Razborov en prouvant que la conjecture de Caccetta-Häggkvist est vraie pour certains graphes orientés avec des sous-graphes interdits. Nous avons montré que chaque tournoi biparti avec degré sortant minimum au moins qr-1 contient r cycles de sommets-disjoints de toutes longueurs possibles. Le cas spécial q=2 confirme le cas du tournoi biparti de la conjecture de Bermond-Thomassen. Nous avons montré que chaque tournoi biparti k-régulier avec k>2 que l'on notera B a deux cycles complémentaires de longueurs 6 et |V(B)-6|, à moins que B soit isomorphe à un graphe spécifique, étayant ainsi une conjecture sur des 2-cycles-facteurs dans les tournois bipartis. En outre, nous montrons que tous les tournois bipartis réguliers ont un k-cycle-facteur. Nous donnons une condition nécessaire et suffisante pour l'existence d'un arc universel dans un tournoi et nous caractérisons tous les tournois où chaque arc est universel. / In this thesis, we study arc colorings and cycles in digraphs. The following topics are considered: vertex-distinguishing proper arc colorings in digraphs, short cycles in digraphs with forbidden subgraphs , disjoint cycles in bipartite tournaments, cycle factors in regualr bipartite tournaments and universal arcs in tournaments. The main results are contained in five original articles published or submitted to an international journal. We introduce vertex-distinguishing proper arc colorings of digraphs. A conjecture on the vertex-distinguishing arc-chromatic number is given and some partial results are obtained. We extend a result of Razborov by proving that the Caccetta-Häggkvist conjecture is true for digraphs with certain induced forbidden subgraphs or with certain forbidden subgraphs. We show that every bipartite tournament with minimum outdegree at least qr-1 has r vertex disjoint cycles of any given possible lengths. The special case q=2 of the result verifies the bipartite tournament case of the Bermond-Thomassen conjecture. As a partial support of a conjecture on 2-cycle-factors in bipartite tournaments, we prove that every k-regular bipartite tournament B with k>2 has two complementary cycles of lengths 6 and |V(B)|-6, unless B is isomorphic to a special digraph. Besides, we show that every k-connected regular bipartite tournament has a k-cycle-factor. We also give a sufficient and necessary condition for the existence of a universal arc in a tournament and characterize all the tournaments in which every arc is universal.

Dans cette thèse, nous nous intéressons à la résolution exacte de problèmes NP-difficiles sur les graphes et les hypergraphes. Les problèmes que nous étudions regroupent dans un premier temps des variantes du problème classique du nombre chromatique. Les variantes de ce problème se distinguent par la difficulté introduite par les relations entre les classes de couleurs, ou la difficulté de reconnaissance des classes de couleurs elles-mêmes. Puis nous ferons le lien avec les problèmes de transversaux sur les hypergraphes. Plus particulièrement, il s’agira de s’intéresser à l’énumération de transversaux minimaux dans un hypergraphe de rang borné. Outre la résolution exacte, nous nous intéressons à la résolution à paramètre fixe. Le problème de racine carrée de graphe est un problème important en théorie des graphes. Nous proposons et montrons la solubilité à paramètre fixe de deux problèmes d’optimisation reliés. Finalement, nous nous intéresserons à la résolution de problèmes de graphe, soit en lien avec les problèmes de colorations, soit pour montrer les performances possibles de différents algorithmes en fonction de l’espace mémoire disponible. Dans cette thèse, nous aurons à cœur d’appliquer judicieusement la grande majorité des techniques essentielles en algorithmique exacte exponentielle. Principalement, nous appliquerons la programmation dynamique ou le principe d’inclusion-exclusion pour les problèmes de coloration. La technique de programmation dynamique se retrouvera pour d’autres problèmes de cette thèse, aux côtés d’autres méthodes comme la technique de branchement ou de mesurer et conquérir / In this thesis, we are interested in the exact computation of np-hard problems on graphs and hypergraphs. Firstly, we study several variants of colorings. Those variants appear harder than the famous chromatic number problem, by adding difficulty in recognizing the color classes, or more often by introducing various relationships between them. Then we link to problems of transversals in hypergraphs. More precisely, we are interested in enumerating minimal transversals in bounded ranked hypergraphs. Besides the exact computation, we are also interested in fixed parameter tractability. For this area, we study two optimization versions of the famous square root of graphs problem. Finally, we will be interested in solving other problems of graphs related to colorings, or in order to compare efficiencies of algorithms depending on the memory space available. In this thesis, we will apply most of major techniques in designing exact exponential algorithms. The main techniques we use are dynamic programming, inclusion-exclusion, branching, or measure and conquer