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It has been known since the 1930’s that protons and neutrons, collectively called as nucleons, are not “point-like” elementary particles, but rather have a substructure. Today, we know from Quantum Chromodynamics (QCD) that nucleons are made from quarks and gluons, with gluons being the elementary force carriers for strong interactions. Quarks and gluons are collectively called as partons. The substructure of the nucleons can be described in terms of parton correlation functions such as Form Factors, (1D) Parton Distribution Functions (PDFs) and their 3D generalizations in terms of Transverse Momentum-dependent parton Distributions (TMDs) and Generalized Parton Distributions (GPDs). All these functions can be derived from the even more general Generalized Transverse Momentum-dependent Distributions (GTMDs). This dissertation promises to provide an insight into all these functions from the point of view of their accessibility in experiments, from model calculations, and from their direct calculation within lattice formulations of QCD. In the first part of this dissertation, we identify physical processes to access GTMDs. By considering the exclusive double Drell-Yan process, we demonstrate, for the very first time, that quark GTMDs can be measured. We also show that exclusive double-quarkonium production in nucleon-nucleon collisions is a direct probe of gluon GTMDs. In the second part of this dissertation, we shift our focus to the “parton quasi-distributions”. Over the last few decades, lattice QCD extraction of the full x-dependence of the parton distributions has always been prohibited by the explicit time-dependence of the correlation functions. In 2013, there was a path-breaking proposal by X. Ji to calculate instead parton quasi-distributions (quasi-PDFs). The procedure of “matching” is a crucial ingredient in the lattice QCD extraction of parton distributions from the quasi-PDF approach. We address the matching for the twist-3 PDFs gT (x), e(x), and hL(x) for the very first time. We pay special attention to the challenges involved in the calculations due to the presence of singular zero-mode contributions. We also present the first-ever lattice QCD results for gT (x) and hL(x) and we discuss the impact of these results on the phenomenology. Next, we explore the general features of quasi-GPDs and quasi-PDFs in diquark spectator models. Furthermore, we address the Burkhardt-Cottingham-type sum rules for the relevant light-cone PDFs and quasi-PDFs in a model-independent manner and also check them explicitly in perturbative model calculations. The last part of this dissertation focuses on the extraction g1T (x,~k2⊥) TMD for the very first time from experimental data using Monte Carlo techniques. This dissertation therefore unravels different aspects of the distribution functions from varied perspectives.

In Computational aeroacoustics, hybrid approaches first resolve the source and nearfield regions of the flow field by employing Reynolds Averaged Navier-Stokes (RANS) equations, Large Eddy Simulations (LES) or Direct Numerical Simulations (DNS).The source region data is used to form source terms, which are, in turn, applied to either empirical models or equations linearized around a mean flow. An acoustic analogy type of model is used to propagate the acoustics to the farfield regions. The aim of this research is twoold: to introduce and test a hybrid acoustic analogy, based on a coupling between the Navier-Stokes equations, applied in the source region, and the Non-linear Euler (NLE) equations applied in the acoustic propagation region; and to test and validate a recently derived generalized acoustic analogy theory in the framework of jet noise with acoustic source information obtained from RANS or LES. In the first part, the coupling between the Navier-Stokes and the NLE equations is accomplished via a buffer region, which is used to interpolate and penalize the flow variables of interest from the source region. The penalized flow variables are then applied as source terms in the NLE equations, to calculate the acoustic propagation. The non-linear Euler equations, discretized using highurate dispersion-relation preserving schemes constitute a very efficient approach for jet noise predictions in complex environments, especially for supersonic and hypersonic jets, where nonlinearities may propagate over long distances. In the second part, a RANS- or LES-informed model, which is used to provide data for Goldstein's generalized acoustic analogy, is presented. The generalized acoustic analogy of Goldstein is considered, wherein the effects of non-parallelism are taken into account and an asymptotic expansion is utilized to simplify the adjoint Green function equations. The use of the adjoint Green's function leads to a simple model for jet noise predictions for low frequencies and small observation angles, in the linear regime. Both approaches are extensively tested and validated against numerous benchmark problems and applications.

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Philosophiae Doctor - PhD / This dissertation explored the degree and distribution of social capital forms-social networks, volunteer associations, generalized trust, particularized trust and norms of reciprocity in rural Ethiopia. It aims to contribute to the academic understanding of social capital formation in Africa. Whereas the extent of literature focused on uncovering difference in the distribution of social capital at macro, meso and micro levels, this dissertation instead unpacks how political and economic conditions in rural Ethiopia shape the extent of the different forms of social capital at different levels. Aresi and Menze are selected for the case-study based on their representation of rural Ethiopia's ecological, language, and ethnicity, historical and religious diversity. A household survey (n = 735) was conducted to uncover the distribution of social capital forms at the individual, regional and aggregate levels. Eight focus group discussions and ten key informant interviews were conducted to unpack why the different forms of social capital unfold the way they do. The qualitative interviews were also used for validating the result of the household survey by uncovering how institutional and structural factors reconstituted and redefined at the local level and translated into social capital formation. The empirical result revealed that social networks and norms of reciprocity are the most important social capital apects in the study areas. At the same time, trust relations and formal networks (volunteer organizations) are the least important aspects of social capital. However, over time, community-organization has become an alternative venue where community members relate and support each other. Thus, network-based and community-based social capital are the principal social capital forms in the study areas. This result is largely inconsistent with the previous studies that have been conducted in developed and democratic countries which have asserted generalized trust and impersonal civic organizations as the major forms of social capital, rather than localized and interpersonal forms of social capital. The fact that different forms of social capital are present in different contexts with different levels of importance shows that forms of social capital do not necessarily articulate together. Moreover, the variation in the relative importance of social capital forms shows that the production of social capital is shaped by the prevailing political and economic conditions. Thus, this dissertation makes the case that it is necessary to distinguish among the different forms of social capital both in theory and practice.

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