Understanding the mechanisms that govern hydraulic fracturing applications in unconventional formations, such as gas-bearing shales, is of increasing interest to the petroleum upstream industry. Among such mechanisms, the geomechanical interactions between hydraulic fractures and pre-existing fractures on one hand, and simultaneous multiple hydraulic fractures on the other hand are seen of high importance. Although the petroleum engineering and related literature contains a number of studies that discusses such topics of hydraulic fracture interactions, there still remain some aspects that require answers, validations, or further supporting data. Particularly, experimental evidence is fairly scarce and keenly needed to solidify the understanding of such complex applications. In this work, the investigation methodology uses a series of hydraulic fracturing laboratory tests performed on synthetic rocks made of gypsum-based cements such as hydrostone and plaster in various experimental set ups. Those laboratory tests aim to closely investigate hydraulic fracture intersection with pre-existing fractures by assessing some factors that govern its outcomes. Specifically, the roles of the pre-existing fracture cementation, aperture, and relative height on the intersection mode are examined. The results show dominant effect of the cement-fill type relative to the host-rock matrix in determining whether hydraulic fracture crossing the pre-existing interface may occur. Similarly, hydraulic fracture height relative to the height of the pre-existing fracture may dictate the intersection results. However, the intersection mode seems to be insensitive of the pre-existing fracture aperture. Moreover, simultaneous multi-fracture propagation is examined and found to be impacted by the interference of the stresses induced from each fracturing source on neighboring fracturing sources. Such stress interference increases as the number of the propagating hydraulic fractures increase. While hydraulic fractures initiating from fracturing sources located in the middle of the fracturing stage seem to have inhibited propagation, outer hydraulic fractures may continue propagating with outward curvatures. Overall, the experimental results and analyses offer more insights for understanding hydraulic fracture complexity in unconventional formations. / text

In this thesis we study two clique-cover problems which have interesting applications regarding the k -bend intersection graph representation: the edge-clique-cover-degree problem and the edge-clique-layered-cover problem. We focus on the complexity of these problems and polynomial time algorithms on restricted classes of graphs. The main results of the thesis are NP-completness of the edge-clique-layered-cover problem and a polynomial-time 2-approximation algorithm on the subclass of diamond-free graphs for the same problem as well as some upper bounds on particular graph classes.

[pt] O objetivo deste trabalho é projetar e implementar um algoritmo eficiente, confiável e preciso para a interseção de superfícies triangulares que representam modelos geológicos complexos. A grandeza das coordenadas espaciais desses modelos, em contraste com o relativamente pequeno tamanho médio de seus elementos, levam a problemas numéricos que podem gerar modelos ruins ou a erros graves do modelador geométrico. Além disso, um alto nível de precisão é desejável para se evitar erros de modelagem que possam gerar acidentes no campo de exploração. Neste trabalho, é proposta uma solução para reduzir os problemas numéricos com o uso de algumas estratégias geométricas e da Aritmética Exata. Exemplos demonstram estes problemas de robustez e validam o algoritmo proposto. / [en] The goal of this work is to design and to develop an efficient, reliable, and accurate algorithm for the intersection of triangular surfaces that represent complex geological models. The wide range of these models coordinates in contrast with the relatively small average size of its elements lead up to numerical instability problems, which may generate bad models or crash the geometric modeler. Additionally, a high degree of precision is desired in the model to avoid accidents in the field of oil exploration. In this work, it is proposed a solution to reduce the numerical issues by the use of some geometrical strategies and the Exact Arithmetic. Examples are used to demonstrate these robustness problems and to validate the proposed algorithm.

Bekannte Theoreme von Carlson und Griffiths gestatten es, die Variation von Hodgestrukturen assoziiert zu einer Familie von glatten Hyperflächen sowie das Cupprodukt auf der mittleren Kohomologie explizit zu beschreiben. Wir benutzen M. Saitos Theorie der gemischten Hodgemoduln, um diesen Kalkül auf die Variation der Hodgestruktur der Schnittkohomologie von Familien nodaler Hyperflächen zu verallgemeinern. / Well known theorems of Carlson and Griffiths provide an explicit description of the variation of Hodge structures associated to a family of smooth hypersurfaces together with the cupproduct pairing on the middle cohomology. We give a generalization to families of nodal hypersurfaces using M. Saitos theory of mixed Hodge modules.

O tema central deste trabalho é o estudo de problemas sobre caminhos mais longos em grafos, de pontos de vista tanto estrutural como algorítmico. A primeira parte tem como foco o estudo de problemas motivados pela seguinte questão levantada por T. Gallai em 1966: é verdade que em todo grafo conexo existe um vértice comum a todos os seus caminhos mais longos? Hoje, já se conhecem diversos grafos conexos cuja intersecção de todos os seus caminhos mais longos é vazia. Entretanto, existem classes de grafos para as quais a resposta à pergunta de Gallai é afirmativa. Nessa linha, apresentamos alguns resultados da literatura e duas novas classes que obtivemos: os grafos exoplanares e as 2-árvores. Motivado por esse problema, nos anos 80, T. Zamfirescu formulou a seguinte pergunta que permanece em aberto: é verdade que em todo grafo conexo existe um vértice comum a quaisquer três de seus caminhos mais longos? Apresentamos, além de alguns resultados conhecidos, uma prova de que a resposta é afirmativa para grafos em que todo bloco não trivial é hamiltoniano. Notamos que esse último resultado e o acima mencionado para grafos exoplanares generalizam um teorema de M. Axenovich (2009) que afirma que quaisquer três caminhos mais longos em um grafo exoplanar têm um vértice em comum. Finalmente, mencionamos alguns outros resultados da literatura relacionados com o tema. Na segunda parte, investigamos o problema de encontrar um caminho mais longo em um grafo. Este problema é NP-difícil para grafos arbitrários. Isto motiva investigações em duas linhas a respeito da busca de tais caminhos. Pode-se procurar classes especiais de grafos para as quais existem algoritmos polinomiais, ou pode-se abrir mão da busca de um caminho mais longo, e projetar um algoritmo eficiente que encontra um caminho cujo comprimento esteja próximo do comprimento de um mais longo. Nesse trabalho estudamos ambas as abordagens e apresentamos alguns resultados da literatura. / The central theme of this thesis is the study of problems related to longest paths in graphs, both from a structural and an algorithmic point of view. The first part focuses on the study of problems motivated by the following question raised by T. Gallai in 1966: is it true that every connected graph has a vertex common to all its longest paths? Today, many connected graphs in which all longest paths have empty intersection are known. However, there are classes of graphs for which Gallais question has a positive answer. In this direction, we present some results from the literature, as well as two new classes we obtained: outerplanar graphs and 2-trees. Motivated by this problem, T. Zamfirescu, in the 80s, proposed the following question which remains open: is it true that every connected graph has a vertex common to any three of its longest paths? We present, in addition to some known results, a proof that the answer to this question is positive for graphs in which all non-trivial blocks are Hamiltonian. We note that this result and the one mentioned above for outerplanar graphs generalize a theorem of M. Axenovich (2009) that states that any three longest paths in an outerplanar graph have a common vertex. Finally, we mention some other related results from the literature. In the second part, we investigate the problem of finding a longest path in a graph. This problem is NP-hard for arbitrary graphs. This motivates investigations in two directions with respect to the search for such paths. We can look for special classes of graphs for which the problem is polynomially solvable, or we can relinquish the search for a longest path and design an efficient algorithm that finds a path whose length is close to that of a longest path. In this thesis we study both approaches and present some results from the literature.

Esta pesquisa caracterizou o comportamento de motoristas em interseções semaforizadas sob três aspectos: (1) reação frente à mudança do verde para o amarelo; (2) comportamento durante a desaceleração para parar; e (3) comportamento durante a saída do cruzamento semaforizado. Os dados foram coletados em uma interseção localizada em pista de testes no Virginia Tech Transportation Institute, nos EUA. A amostra foi composta por 60 motoristas voluntários igualmente divididos em função do gênero; dos quais 32 tinham idade inferior a 65 anos (\"jovens\"). Foram investigados efeitos da idade, do gênero e da declividade da via sobre as seguintes situações: tomada de decisão entre parar ou prosseguir no amarelo; posição de parada em relação à faixa de retenção; tempo de percepção e reação (TPR) para frenagem e partida do cruzamento; efeito de zonas de opção e de dilema; taxa de desaceleração para parada na interseção; e taxa de aceleração para partida da interseção. As análises indicaram que: (1) os motoristas mais jovens invadiram mais a faixa de retenção que os idosos; (2) mulheres apresentam maiores TPR para decidir partir da interseção; e (3) o TPR é menor no declive tanto para a decisão de frear quanto para a partida do cruzamento. As taxas de desaceleração não apresentaram influência dos fatores avaliados. Por outro lado, constatou-se que a aceleração foi afetada pelo fator declividade. Como resultado final da pesquisa, foram propostos modelos, em função do tempo, que exprimem a desaceleração/aceleração usada pelos motoristas ao frear/acelerar. Foram propostos modelos para o motorista médio e para motoristas desagregados em três grupos em função da agressividade. / The objective of this research was to characterize driver behavior at signalized intersections according to three aspects: (1) reaction at the onset of the amber phase; (2) behavior during the deceleration to stop at the signal; and (3) behavior during the acceleration to leave the intersection at the onset of the green. The data were collected at a signalized intersection on a private highway, at the Virginia Tech Transportation Institute, in the USA. The sample consisted of 60 volunteer drivers, equally divided by gender. The sample was divided into two age groups: younger drivers (age was less than 65) and older drivers. Effects of gender, age group and roadway grade were investigated for the following aspects: decision making at the onset of amber; final stopping position with relation to the stop line; perception/reaction times (PRT) at the onset of the amber and the green lights; effects of dilemma and option zones; and deceleration and acceleration rates used by the drivers. The analyses suggest that: (1) younger drivers tend to stop farther past the stop line, compared to older drivers; (2) women have longer PRT at the onset of the green; and (3) PRT are shorter on downgrade at the onset of both amber and green lights. The observed deceleration rates were not affected by gender, age group or roadway grade. Acceleration rates were found to be influenced by the grade. A set of models that express the acceleration/deceleration rates as a function of time were proposed to represent the average behavior observed for drivers in the sample. Specific models were also proposed for aggressive, non-aggressive and intermediate drivers.

Computational modeling offers better insight into a wide range of bioelectrical and biomechanical problems with improved tools for the design of medical devices and the diagnosis of pathologies. Electromagnetic modeling at low and high frequencies is particularly necessary. Modeling electromagnetic, structural, thermal, and acoustic response of the human body to different internal and external stimuli is limited by the availability of numerically efficient computational human models. This study describes the development to date of a computational full-body human model - Visible Human Project (VHP) - Female Model. Its unique feature is full compatibility both with MATLAB and specialized FEM computational software packages such as ANSYS HFSS/Maxwell 3D. This study also describes progress made to date in using the newly developed tools for segmentation. A visualization tool is implemented within MATLAB and is based on customized version of the constrained 2D Delaunay triangulation method for intersecting objects. This thesis applies a VHP - Female Model to a specific application, transcranial Direct Current Stimulation (tDCS). Transcranial Direct Current Stimulation has been beneficial in the stimulation of cortical activity and treatment of neurological disorders in humans. The placement of electrodes, which is cephalic versus extracephalic montages, is studied for optimal targeting of currents for a given functional area. Given the difficulty of obtaining in vivo measurements of current density, modeling of conventional and alternative electrode montages via the FEM has been utilized to provide insight into the tDCS montage performance. An insight into future work and potential areas of research, such as study of bone quality have been presented too.

Estuda-se numericamente uma placa circular homogênea com furo centrado sob estado plano de deformação. A placa está fixa ao longo do contorno interno e está sob compressão radial uniforme ao longo do contorno externo. O material da placa é elástico-linear e anisotrópico. Apresenta-se a solução analítica do problema, a qual satisfaz as equações governantes de equilíbrio, no contexto da elasticidade linear clássica. Esta solução prediz o comportamento espúrio da auto-intersecção em uma região central da placa. Para evitar este comportamento, utiliza-se uma teoria que propõe encontrar um campo de deslocamento que minimize a energia potencial total do corpo sujeito à restrição de injetividade local para o campo da deformação correspondente. Esta teoria, juntamente com o método das penalidades interiores, permite encontrar uma solução numérica que preserva a injetividade. Esta solução corresponde a um campo de deslocamento radialmente simétrico. Estuda-se a possibilidade de encontrar uma solução rotacionalmente simétrica do problema restrito, em que o campo de deslocamento possua as componentes radial e tangencial, ambas funções somente do raio. Os resultados desta última modelagem mostram que a componente tangencial é nula, indicando que o campo de deslocamento é, de fato, radialmente simétrico. Mostra-se também que a solução do problema do anel converge para a solução do problema de um disco sem furo à medida que o raio do furo tende a zero. / This work concerns a numerical study of a homogeneous circular plate with a centered hole that is under a state of plane strain. The plate is fixed at its inner surface and is under uniform radial compression at its outer surface. The plate is linear, elastic, and anisotropic. An analytical solution for this problem, which satisfies the governing equations of equilibrium, is presented in the context of classical linear elasticity. This solution predicts the spurious behavior of self-intersection in a central region of the plate. To avoid this behavior, a constrained minimization theory is used. This theory concerns the search for a displacement field that minimizes the total potential energy of the body, which is a quadratic functional from the classical linear theory, subjected to the constraint of local injectivity for the associated deformation field. This theory together with an interior penalty method and a standard finite element methodology yield a numerical solution, which is radially symmetric, that preserves injectivity. Here, it is investigated the possibility of finding a rotationally symmetric solution to the constrained problem; one for which the associated displacement field has radial and tangential components, which are both functions of the radius only. The numerical results show, however, that the tangential component is zero. It is also shown that, as the radius of the hole tends to zero, the corresponding sequence of solutions tends to the solution of a solid disk.

Using a subsample of emerging adults from the Stepfamily Experiences Project (n = 989), we examine how parents' repartnering choices (nonmarital and premarital cohabitation) influence their emerging adult children's commitment-related relationship attitudes (attitudes about sex in committed relationships) and behaviors (hooking up). We further examine these processes at the intersection of race and gender. In this way, we expand the current emerging adult literature by exploring two understudied populations: emerging adults who grew up in stepfamilies, and emerging adults from diverse racial backgrounds. We divided our sample by race (black, Latino, American Indian, white, and multiracial) and gender, resulting in 10 groups. We compared those 10 groups using structural equation modeling within the Bayesian framework. We found a strong association for all groups between attitudes about sex in committed relationships and hooking up and a connection between parental cohabitation and hooking up, which connection was only explained by attitudes for white men. We also found significant variation at the intersection of race and gender for all but one of our hypothesized associations. These results highlight the importance of examining variation at the intersection of race and gender and also suggest that family of origin factors, such as parental cohabitation, may impact hooking up among emerging adults raised in stepfamilies.

Geometrically representable graphs are extensively studied area of research in contempo- rary literature due to their structural characterizations and efficient algorithms. The most frequently studied class of such graphs is the class of interval graphs. In this thesis we focus on two problems, generalizing the problem of recognition, for classes related to interval graphs. In the first part, we are concerned with adjusted interval graphs. This class has been studied as the right digraph analogue of interval graphs. For interval graphs, there are polynomial algorithms to extend a partial representation by given intervals into a full interval representation. We will introduce a similar problem - the partial ordering extension - and we will provide a polynomial algorithm to extend a partial ordering of adjusted interval digraphs. In the second part, we show two NP-completeness results regarding the simultaneous representation problem, introduced by Lubiw and Jampani. The simultaneous representation problem for a given class of intersection graphs asks if some k graphs can be represented so that every vertex is represented by the same object in each representation. We prove that it is NP-complete to decide this for the class of interval and circular-arc graphs in the case when k is a part of the input and graphs...