http://hdl.handle.net/1721.1/7596 2017-07-09T21:45:00Z 2017-07-09T21:45:00Z Vargas Olguin, Ignacio Javier http://hdl.handle.net/1721.1/109647 2017-06-07T06:17:42Z 2017-01-01T00:00:00Z

Equilibrium characterization for resource allocation games on single-path serial networks Vargas Olguin, Ignacio Javier The Resource Allocation Game we examined in this work is a strategic interaction where a principal distribute an infinitely divisible good among different agents based on their specific valuations of said good. The distribution is done by a particular scheme first studied by Kelly [15] with no price-discrimination. In a further study by Johari and Tsitsiklis [13], they aim to distribute the link capacities of a network among different users. The authors prove existence of a unique Nash equilibrium (NE) for the base case of a single link, but for a general network only existence is proven, leaving open questions about uniqueness. In this study we characterize the NE for a distinct structure of networks, the single-path serial network. The problem is tackled gradually. First, we give explicit solutions for the case with n players with affine utility functions on a single arc. Next for networks with different are capacities and all players interested in the same path within the network, uniqueness of the NE is proved. Moreover the NE is characterized by a variational inequality that correspond to the first-order conditions of an optimization problem. Thereupon, for the case where players might have different origin-destination pairs without arcs in common, uniqueness of the NE in terms of flow is again proved. Last but not least, we propose a sequential extension of the scheme. In this framework, players do not act simultaneously, but in a given order of precedence. For the base case of one arc and two players with linear utilities, we obtained an explicit Subgame Perfect Equilibrium. In addition, we get a price of anarchy better than the one obtained for the simultaneous case. We propose some thoughts about the Transportation analysis application of this type of networks for liner shipping and highways, that is to say situations where there is a single-path of interest for every player. Thesis: S.M. in Transportation, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 67-70).

2017-01-01T00:00:00Z AlDajani, Omar AbdulFattah http://hdl.handle.net/1721.1/109646 2017-06-07T06:17:42Z 2017-01-01T00:00:00Z

Fracture and hydraulic fracture initiation, propagation and coalescence in shale AlDajani, Omar AbdulFattah Even though hydraulic fracturing has been in use for more than six decades to extract oil and natural gas, the fundamental mechanism to initiate and propagate these fractures remains unclear. Moreover, it is unknown how the propagating fracture interacts with other fractures in the Earth. The objective of this research is to gain a fundamental understanding of the hydraulic fracturing process in shales through controlled laboratory experiments where the underlying mechanisms behind the fracture initiation, -propagation, and -coalescence are visually captured and analyzed. Once these fundamental processes are properly understood, methods that allow one to produce desired fracture geometries can be developed. Two different shales were investigated: the organic-rich Vaca Muerta shale from the Neuquén Basin, Argentina and the clay-rich Opalinus shale from Mont Terri, Switzerland, which were shown to vary in mineralogy and mechanical properties. Specimen preparation techniques were developed to successfully dry cut a variety of shales and produce prismatic specimens with pre-existing artificial fractures (flaws). The Vaca Muerta shale specimens were subjected to a uniaxial load which induces fractures emanating from the flaws. Two geometries were tested: a coplanar flaw geometry (2a-30-0) resulting in indirect coalescence and a stepped flaw geometry (2a-30-30) resulting in direct coalescence. These "dry" fracture experiments were analyzed in detail and corresponded well to the behavior observed in the Opalinus shale. This result shows that the fracture behavior in Opalinus shale can be extended to other shales. A test setup capable of pressurizing an individual flaw in prismatic shale specimens subjected to a constant uniaxial load and producing hydraulic fractures was developed. This setup also allows one to monitor internal flaw pressure throughout the pressurization process, as well as visually capture the processes that occur when the shale is hydraulically fractured. Three fracture geometries in Opalinus shale were tested using this developed setup: single vertical flaw (SF-90) for the proof of concept of the test setup, stepped flaw geometry (2a-30-30) which resulted in no coalescence, and stepped flaw geometry (2a-30-60) which resulted in indirect coalescence. Of particular interest were the observed lag between the crack tip and the liquid front as well as the way the hydraulic fracture propagates across and along bedding planes. A systematic difference was observed when comparing crack interaction behavior for "dry" and hydraulic fracture experiments for various flaw geometries. The result of this thesis will add to fundamental knowledge of how fractures behave and interact under various loading conditions, flaw geometries, and materials serving as a basis for predictive fracture models. Thesis: S.M., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 152-154).

2017-01-01T00:00:00Z Al-Mulla, Talal http://hdl.handle.net/1721.1/109645 2017-06-07T06:17:40Z 2017-01-01T00:00:00Z

Rational manipulation of substrate-supported graphene by heterogeneity of substrate surface and material composition Al-Mulla, Talal In many graphene-based devices graphene is adhered to a substrate that influences its performance, rather than being present in a free standing form. The interaction of graphene with these substrates can lead to deformations that give rise to out-of-plane architectures with new properties such as superhydrophobicity, opened electronic band gap, and higher in-plane rigidity. Earlier experiments and simulations with graphene-substrate interfaces demonstrating reversible and repeatable stacking of out-of-plane buckled graphene to create ridges, which are stacked protrusions of graphene, warrant a detailed understanding of the underlying mechanisms of graphene ridge formation, especially for design of tailored nanostructures. Ridges are created through substrate-mediated compression of graphene, therefore, these ridges should be related to the graphene-substrate interface. It is unknown what the direct effect of the substrate on ridge formation is besides the work done studying graphene's mechanical response to compression. It is necessary to understand how the substrate affects graphene deformation in order to fully utilize the range of accessible graphene deformation shapes. To systematically study the formation of ridges in graphene, molecular dynamics simulations are performed to characterize the deformation of graphene on substrate during and after axial compression of graphene nanoribbons, high aspect ratio (10:1) single layer sheets of graphene in this work. This is done to investigate the hypothesis that graphene deformation depends on the underlying substrate in terms of corrugation wavelength and amplitude and graphene-substrate adhesion energy. In the first part of this thesis a quantitative scheme is formulated to characterize and predict these deformations. A critical value of interfacial adhesion energy marks a transition point that separates two deformation regimes of graphene on substrate under uniaxial compression; the deformation regimes are binary featuring the stacking of graphene after buckling in one case and no stacking, otherwise. These ridges are a product of the graphene limit point buckling, where growing out-of-plane folds of graphene stack and self-adhere. In the second part of this thesis, after establishing the role of substrate and key interfacial properties, the atomistic mechanisms underlying the formation, evolution, and localization of graphene ridges are investigated using fracture mechanics theory and molecular dynamics simulations. It is shown that there is no intrinsic characteristic length scale over which to achieve certain graphene shapes or see any repeated shapes as suggested in previous experiments, but instead these shapes can be tuned by substrate selection and design, a novel approach presented in this thesis. Moreover, a major result of this work is that the location and density of surface features in graphene-substrate systems can be controlled by substrate engineering at nanoscale resolutions, which could be used for developing graphene-based devices with a more efficient use of material, or with tailored distribution of surface futures that lead to specific applications. Efficiency gains can be made through use of less material and more controlled spacing of graphene ridges. The immediate impact of this work is most clearly realized in large scale manipulation of graphene where targeted deformations of different regions of the same graphene sheet can be executed using a single rationally designed substrate. Shifting the mindset from using the substrate as a stage, but as a tool, opens up the potential for more intricate graphene deformations at the nanoscale. Thesis: S.M. in Civil and Environmental Engineering, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 95-104).

2017-01-01T00:00:00Z Zhao, Benzhong http://hdl.handle.net/1721.1/109644 2017-06-07T06:17:39Z 2017-01-01T00:00:00Z

Multiphase flow in porous media: the impact of capillarity and wettability from field-scale to pore-scale Zhao, Benzhong Multiphase flow in the context of this Thesis refers to the simultaneous flow of immiscible fluids. It differs significantly from single-phase flow due to the existence of fluid-fluid interfaces, which are subject to capillary forces. Multiphase flow in porous media is important in many natural and industrial processes, including geologic carbon dioxide (CO₂) sequestration, enhanced oil recovery, and water infiltration into soil. Despite its importance, much of our current description of multiphase flow in porous media is based on semi-empirical extensions of single-phase flow theories, which miss key physical mechanisms that are unique to multiphase systems. One challenging aspect of solving this problem is visualization-flow typically occurs inside opaque media and hence eludes direct observation. Another challenging aspect of multiphase flow in porous media is that it encompasses a wide spectrum of length scales-while capillary force is active at the pore-scale (on the order of microns), it can have a significant impact at the field-scale (on the order of kilometers). In this Thesis, we employ novel laboratory experiments and mathematical modeling to study multiphase flow in porous media across scales. The field-scale portion of this Thesis focuses on gravity-driven flows in the subsurface, with an emphasis on application to geological CO₂ storage. We find that capillary forces can slow and stop the migration of a CO₂ plume. The meso-scale portion of this Thesis demonstrates the powerful control of wettability on multiphase flow in porous media, which is manifested in the markedly different invasion protocols that emerge when one fluid displaces another in a patterned microfluidic cell. The pore-scale portion of this Thesis focuses on the impact of wettability on fluid-fluid displacement inside a capillary tube. We show that the contact line movement is strongly affected by wettability, even in regimes where viscous forces dominate capillary forces. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 95-104).

2017-01-01T00:00:00Z