This thesis is concerned with the modeling and numerical study of nonsmooth dynamical systems (NSDS). The first part of the thesis deals with the modeling of some DC-DC power converters using the complementarity formalism. This mathematical theoretical framework allows us to ensure existence and uniqueness of solutions in a "natural" and synthetic way. Specifically, it works pretty well in power electronic converters because it incorporates generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM are stated and simulation results, showing a variety of behaviours, such as persistent or re-entering GDCM, are also presented. Furthermore, the analysis and simulation of a parallel resonant converter (PRC), which has four diodes, illustrate the convenience of the complementarity formalism to simulate electrical systems with a large number of ideal diodes. We also present the simulation of a boost converter with a sliding mode control, even though a general control theory for complementarity systems is not still developed.In the second part of the thesis we focus on the bifurcation analysis in NSDS, and in particular, we have studied different mechanical systems which involve impacts and dry-friction. It is known that nonsmooth or discontinuous dynamical systems can exhibit the bifurcations also exhibited by smooth systems. In addition to these, there are also some novel transitions so-called discontinuity-induced bifurcations (DIBs) which are unique to these systems. We have investigated the complex behaviour occurring in an impacting mechanical system. DIBs such as corner impact bifurcations and transitions from complete to uncomplete chattering motions have been analysed in detail. Another type of DIBs recently classified are the so-called sliding bifurcations. Such bifurcations are a characteristic feature of so-called Filippov systems. We present detailed examples of all the different sliding bifurcation scenarios in a dry friction oscillator using a measured friction characteristic firstly introduced by Popp. Furthermore, a codimension-two degenerate switching-sliding bifurcation is displayed. In this case of degenerate switching-sliding bifurcation two curves of codimension-one sliding bifurcations, crossing-sliding and adding-sliding, branch out from the codimension-two point. Also, a cusp smooth codimension-two bifurcation is shown and coexistence of periodic orbits in the region between both fold codimension-one curves is studied.We have also investigated the dynamic behaviour of the two-block Burridge model for earthquake simulations. Previous numerical studies investigated by Ruina verified that, with a friction force of Coulomb type, the system presents only periodic behaviour. We show that chaotic regions can be observed in a symmetric configuration even if a Coulomb friction is considered with the relaxation of one of the assumptions assumed in the seismological literature. Furthermore, we have studied the behaviour of the system with asymmetric configuration. Different periodic solutions and regions of chaos can be observed varying the asymmetry of the system. With respect to the bifurcation point of view, we have analysed several smooth bifurcations (smooth and DIBs) observed in this system.Chapter 6 of this thesis presents the SICONOS software platform dedicated to simulation of NSDS. We give an overview of the SICONOS software and the way NSDS are modeled and simulated within the platform. Routines for analysis (stability, bifurcations, invariant manifolds,.) of NSDS implemented in the platform are explained in detail. To conclude this part, several representative samples are shown in order to illustrate the SICONOS platform abilities.Conclusion and some open problems are presented in the last chapter.

Fractures are the main flow channels in naturally fractured reservoirs. Therefore the fracture permeability is a critical parameter to production optimization and reservoir management. Fluid pressure reduction caused by production induces an increase in effective stress in naturally fractured reservoirs. The change of effective stress induces fracture deformation and changes fracture aperture and permeability, which in turn influences the production. Coupled interactions exist in the fractured reservoir: (i) fluid pressure change induces matrix deformation and stress change; (ii) matrix deformation induces fluid volume change and fluid pressure change; (iii) fracture deformation induces the change of pore pressure and stress in the whole field (the influence disappears at infinity); (iv) the change of pore pressure and stress at any point has an influence on the fracture and induces fracture deformation. To model accurately the influence of pressure reduction on the fracture permeability change in naturally fractured reservoirs, all of these coupled processes need to be considered. Therefore, in this dissertation a fully coupled approach is developed to model the influence of production on fracture aperture and permeability by combining a finite difference method to solve the fluid flow in fractures, a fully coupled displacement discontinuity method to build the global relation of fracture deformation, and the Barton-Bandis model of fracture deformation to build the local relation of fracture deformation. The fully coupled approach is applied to simulate the fracture permeability change in naturally fracture reservoir under isotropic in situ stress conditions and high anisotropic in situ stress conditions, respectively. Under isotropic stress conditions, the fracture aperture and permeability decrease with pressure reduction caused by production, and the magnitude of the decrease is dependent on the initial effective in situ stress. Under highly anisotropic stress, the fracture permeability can be enhanced by production because of shear dilation. The enhancement of fracture permeability will benefit to the production of oil and gas.

Spain, after successfully joining EC and NATO and consolidating itself as a respected member of the Western bloc, has been seeking to improve its status in the international political arena in the last two decades. However, during its quest to become a major European power like Germany, France and UK, Spain lost the momentum it caught in the early years of its EC membership, after Felipe Gonzalez left the Presidency of Government in 1996. The discord between the two major Parties, the Popular Party (PP) and the Spanish Socialist Workers Party (PSOE) on the broad lines of the Spanish foreign policy - that yielded to discontinuity - has been one of the reasons for this development. The main aim of this dissertation is to elaborate this discontinuity as a case study, in a middle range European power. For this purpose, the foreign policies followed by the Conservative PP Governments headed by J&oacute / se Mar&iacute / a Aznar during 1996-2004 term is compared with the policies followed by the Socialist PSOE Governments headed by J&oacute / se Luis Rodr&iacute / guez Zapatero since 2004. Given that these policies are associated with the decisions, acts and speeches of the Party leaders, the level of analysis in this dissertation is the individual policy makers.

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Although many fracture models are based on two-dimensional plane strain approximations, accurately predicting fracture propagation geometry requires accounting for the three-dimensional aspects of fractures. In this study, we implemented 3-D displacement discontinuity (DD) boundary element modeling to investigate the following intrinsically 3-D natural or hydraulic fracture propagation problems: the effect of fracture height on lateral propagation of vertical natural fractures, joint development in the vicinity of normal faults, and hydraulic fracture height growth and non-planar propagation paths. Fracture propagation is controlled by stress intensity factor (SIF) and its determination plays a central role in LEFM. The DD modeling is used to evaluate SIF in Mode I, II and III at the tip of an arbitrarily-shaped embedded crack by using crack-tip element displacement discontinuity. We examine the accuracy of SIF calculation is for rectangular, penny-shaped, and elliptical planar cracks. Using the aforementioned model for lateral propagation of overlapping fractures shows that the curving path of overlapping fractures is strongly influenced by the spacing-to-height ratio of fractures, as well as the differential stress magnitude. We show that the angle of intersection between two non-coincident but parallel en-echelon fractures depends strongly on the fracture height-to-spacing ratio, with intersection angles being asymptotic for "tall" fractures (large height-to-spacing ratios) and nearly orthogonal for "short" fractures. Stress perturbation around normal faults is three-dimensionally heterogeneous. That perturbation can result in joint development at the vicinity of normal faults. We examine the geometrical relationship between genetically related normal faults and joints in various geologic environments by considering a published case study of fault-related joints in the Arches National Park region, Utah. The results show that joint orientation is dependent on vertical position with respect to the normal fault, the spacing-to-height ratio of sub-parallel normal faults, and Poisson's ratio of the media. Our calculations represent a more physically reasonable match to measured field data than previously published, and we also identify a new mechanism to explain the driving stress for opening mode fracture propagation upon burial of quasi-elastic rocks. Hydraulic fractures may not necessarily start perpendicular to the minimum horizontal remote stress. We use the developed fracture propagation model to explain abnormality in the geometry of fracturing from misaligned horizontal wellbores. Results show that the misalignment causes non-planar lateral propagation and restriction in fracture height and fracture width in wellbore part. / text

Successful creations of multiple hydraulic fractures in horizontal wells are critical for economic development of unconventional reservoirs. The recent advances in diagnostic techniques suggest that multi-fracturing stimulation in unconventional reservoirs has often caused complex fracture geometry. The most important factors that might be responsible for the fracture complexity are fracture interaction and the intersection of the hydraulic and natural fracture. The complexity of fracture geometry results in significant uncertainty in fracturing treatment designs and production optimization. Modeling complex fracture propagation can provide a vital link between fracture geometry and stimulation treatments and play a significant role in economically developing unconventional reservoirs. In this research, a novel fracture propagation model was developed to simulate complex hydraulic fracture propagation in unconventional reservoirs. The model coupled rock deformation with fluid flow in the fractures and the horizontal wellbore. A Simplified Three Dimensional Displacement Discontinuity Method (S3D DDM) was proposed to describe rock deformation, calculating fracture opening and shearing as well as fracture interaction. This simplified 3D method is much more accurate than faster pseudo-3D methods for describing multiple fracture propagation but requires significantly less computational effort than fully three-dimensional methods. The mechanical interaction can enhance opening or induce closing of certain crack elements or non-planar propagation. Fluid flow in the fracture and the associated pressure drop were based on the lubrication theory. Fluid flow in the horizontal wellbore was treated as an electrical circuit network to compute the partition of flow rate between multiple fractures and maintain pressure compatibility between the horizontal wellbore and multiple fractures. Iteratively and fully coupled procedures were employed to couple rock deformation and fluid flow by the Newton-Raphson method and the Picard iteration method. The numerical model was applied to understand physical mechanisms of complex fracture geometry and offer insights for operators to design fracturing treatments and optimize the production. Modeling results suggested that non-planar fracture geometry could be generated by an initial fracture with an angle deviating from the direction of the maximum horizontal stress, or by multiple fracture propagation in closed spacing. Stress shadow effects are induced by opening fractures and affect multiple fracture propagation. For closely spaced multiple fractures growing simultaneously, width of the interior fractures are usually significantly restricted, and length of the exterior fractures are much longer than that of the interior fractures. The exterior fractures receive most of fluid and dominate propagation, resulting in immature development of the interior fractures. Natural fractures could further complicate fracture geometry. When a hydraulic fracture encounters a natural fracture and propagates along the pre-existing path of the natural fracture, fracture width on the natural fracture segment will be restricted and injection pressure will increase, as a result of stress shadow effects from hydraulic fracture segments and additional closing stresses from in-situ stress field. When multiple fractures propagate in naturally fracture reservoirs, complex fracture networks could be induced, which are affected by perforation cluster spacing, differential stress and natural fracture patterns. Combination of our numerical model and diagnostic methods (e.g. Microseismicity, DTS and DAS) is an effective approach to accurately characterize the complex fracture geometry. Furthermore, the physics-based complex fracture geometry provided by our model can be imported into reservoir simulation models for production analysis. / text

This dissertation studies three aspects of the economics of climate change: how rising sea levels will affect coastal homeowners in Florida; how changes in weather will affect the prevalence of crime in the United States; and why skepticism about climate change is so common among the general public. Chapter 1 uses housing market data to estimate the welfare costs of shoreline loss along coastal beaches in Florida. I develop a structural housing market model and use it to provide a welfare interpretation for the coefficients from a new “discontinuity matching” hedonic research design. Using housing sales data, beach width surveys, and historical beach nourishment records, I then estimate Florida homeowners’ willingness to pay for an extra foot of sand. I find that changes in beach width have little impact on housing prices, except possibly at very eroded beaches. Chapter 2 estimates the impact of climate change on the prevalence of criminal activity in the United States. The analysis is based on monthly crime and weather data for 2,972 U.S. counties from 1960 to 2009. The results show that temperature has a strong positive effect on criminal behavior, and that between 2010 and 2099, climate change will cause an additional 35,000 murders, 216,000 cases of rape, 1.6 million aggravated assaults, 2.4 million simple assaults, 409,000 robberies, 3.1 million burglaries, 3.8 million cases of larceny, and 1.4 million cases of vehicle theft. The social cost of these climate-related crimes is between 20 and 68 billion dollars. Chapter 3 develops a model of rational skepticism about policy-relevant scientific questions. Many policy debates have three features: first, individuals initially disagree about some scientific question; second, new evidence about the question becomes available; and third, the evidence may be systematically biased. Under these conditions, Bayesian disagreements persist even in the face of an infinite quantity of new evidence. Furthermore, Bayesian updating based on the new evidence produces “skeptics”, in the sense that individuals whose prior beliefs conflict most with the observable evidence end up with the most extreme posterior beliefs about the degree of bias. These results provide insight into the phenomenon of climate skepticism.

During the last decades, the localized failure of massive structures under thermo-mechanical loads becomes the main interest in civil engineering due to a number of construction damaged and collapsed due to fire accident. Two central questions were carried out concerning the theoretical aspect and the solution aspect of the problem. In the theoretical aspect, the central problem is to introduce a thermo-mechanical model capable of modeling the interaction between these two physical effects, especially in localized failure. Particularly, we have to find the answer to the question: how mechanical loading affect the temperature of the material and inversely, how thermal loading result in the mechanical response of the structure. This question becomes more difficult when considering the localized failure zone, where the classical continuum mechanics theory can not be applied due to the discontinuity in the displacement field and, as will be proved in this thesis, in the heat flow. In terms of solution aspect, as this multi-physical problem is mathematical represented by a differential system, it can not be solved by an 'exact' analytical solution and therefore, numerical approximation solution should be carried out. This thesis contributes in both two aspects. Particularly, thermomechanical models for both steel and concrete (the two most important materials in civil engineering), which capable of controling the hardening behavior due to plasticity and/or damage and also the softening behavior due to the localized failure, are carried out and discussed. Then, the thermomechanical problems are solved by 'adiabatic' operator split procedure, which 'separates' the multi-physical process into the 'mechanical' part and the 'thermal' part. Each part is solved individually by another operator split procedure in the frame-work of embbed-discontinuity finite element method. In which, the 'local' discontinuities of the displacement field and the heat flow is solved in the element level, for each element where localized failure is detected. Then, these discontinuities are brought into the 'static condensation' form of the overall equilibrium equation, which is used to solved the displacement field and the temperature field of the structure at the global level. The thesis also contributes to determine the ultimate response of a reinforced concrete frame submitted to fire loading. In which, we take into account not only the degradation of material properties due to temperature but also the thermal effect in identifying the total response of the structure. Moreover, in the proposed method, the shear failure is also considered along with the bending failure in forming the overal failure of the reinforced structure. The thesis can also be extended and completed to solve the behavior of reinforced concrete in 2D or 3D case considering the behavior bond interface or to take into account other type of failures in material such as fatigue or buckling. The proposed models can also be improved to determine the dynamic response of the structure when subjected to earthquake and/or impact.

The thesis considers three-dimensional analyses of fractures and wellbores in low-permeability petroleum/geothermal reservoirs, with a special emphasis on the role of coupled thermo-hydro-mechanical processes. Thermoporoelastic displacement discontinuity and stress discontinuity methods are elaborated for infinite media. Furthermore, injection/production-induced mass and heat transport inside fractures are studied by coupling the displacement discontinuity method with the finite element method. The resulting method is then used to simulate problems of interest in wellbores and fractures for related to drilling and stimulation. In the examination of fracture deformation, the nonlinear behavior of discontinuities and the change in status from joint (hydraulically open, mechanically closed) to hydraulic fracture (hydraulically open, mechanically open) are taken into account. Examples are presented to highlight the versatility of the method and the role of thermal and hydraulic effects, three-dimensionality, hydraulic/natural fracture deformation, and induced micro earthquakes. Specifically, injection/extraction operations in enhanced geothermal reservoirs and hydraulic/thermal stimulation of fractured reservoirs are studied and analyzed with reference to induced seismicity. In addition, the fictitious stress method is used to study three-dimensional wellbore stresses in the presence of a weakness plane. It is shown that the coupling of hydro-thermo-mechanical processes plays a very important role in low-permeability reservoirs and should be considered when predicting the behavior of fractures and wellbores.

This thesis is based on three essays. The first chapter analyses the impact of 27 years of civil war in Angola on human capital, expenditures per adult equivalent and fertility. The prediction of the effects of civil war is done through a neoclassical unitary household model in the tradition of Rosenzweig. Using instrumental variable method, this thesis shows that civil war has a negative and disastrous impact in short-term on health of children, this effect is persistent. Civil war has no impact on expenditures per adult equivalent. It increases enrollment and decreases fertility in the short term. The second chapter ofthis thesis analyzes the effectiveness of a social program in a conflict country such as Angola and explores whether this effectiveness depends on the intensity of the conflict. Our identification strategy is based on the political geography of the deployment of the program based on a model of spatial competition of Hotelling. This thesis shows that the Angola Social Fund had a positive impact on expenditures per adult equivalent and on one of the main anthropometric measurements namely the height for age z-score. The program's effectiveness in function to the intensity of the conflict is analyzed using the local instrumental variable estimator. The thesis shows that the program's effectiveness increases with the intensity of the conflict. The last chapter of this thesis analyzes in the case of Cameroon, the impact of teacher training on HIV/AIDS. The two criteria for selecting participating schools, leads us to choose as identification strategy the regression discontinuity design. This thesis shows that 15 to 17 year old girls in teacher training schools are between 7 and 10 percentage points less likely to have started childbearing. For 12 to 13 year old girls, the likelihood of self-reported abstinence and condom use is also significantly higher in treated schools.