Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

A probabilistic approach to assess hydrate formation and design preventive measures

Formation of hydrates is one of the major flow assurance problems faced by the oil and gas industry. Hydrates tend to form in natural gas pipelines with the presence of water and favorable temperature and pressure conditions, generally low temperatures and corresponding high pressures. Agglomeration of hydrates can result in blockage of flowlines and equipment, which can be time consuming to remove in subsea equipment and cause safety issues. Natural gas pipelines are more susceptible to burst and explosion owing to hydrate plugging. Therefore, a rigorous risk-assessment related to hydrate formation is required, which assists in preventing hydrate blockage and ensuring equipment integrity. This thesis presents a novel methodology to assess the probability of hydrate formation and presents a risk-based approach to determine the parameters of winterization schemes to avoid hydrate formation in natural gas pipelines operating in Arctic conditions. It also presents a lab-scale multiphase flow loop to study the effects of geometric and hydrodynamic parameters on hydrate formation and discusses the effects of geometric and hydrodynamic parameters on multiphase development length of a pipeline. Therefore, this study substantially contributes to the assessment of probability of hydrate formation and the decision making process of winterization strategies to prevent hydrate formation in Arctic conditions.