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The major function of the adult kidney is to filter blood. This task requires a complex vasculature that must be accurately assembled during development. To better understand renal endothelial development, I imaged the vascular tree of embryonic kidneys in 3D. From this, I detailed the origins of the first renal blood vessels and demonstrated that endothelia patterned in cycles alongside the splitting of the cap mesenchyme (nephron progenitor population) and branching of the ureteric bud. Notably, endothelia avoided the cap mesenchyme throughout development. Based on their gene expression patterns, I identified the anti-angiogenic molecule, semaphorin-3f, and its receptor, neuropilin-2, as signalling candidates that may control this endothelial patterning; however, these proteins were not required for endothelial avoidance from the cap mesenchyme. I demonstrated how renal vascularisation occurs in synchrony with the two major processes involved in renal organogenesis: branching morphogenesis and nephrogenesis. Moreover, I showed that angiogenesis predominates in kidney vascularisation and that the role of vasculogenesis is minimal (at most). I next investigated whether macrophages may facilitate renal vascularisation. Kidney macrophage origins have been defined, but their functions during development remain largely unknown. Macrophages arrived in the caudal part of the mouse embryo between E9.5-E10.5, as nephron precursors began collecting at the caudal end of the Wolffian duct. From this stage onwards, macrophages largely avoided populations of nephron progenitors. Instead, most mature macrophages interacted with the vasculature in the renal interstitium. Perivascular macrophages wrapped around, but were not carried within, blood vessels. As well as interacting with the vasculature, these macrophages engulfed erythrocytes and apoptotic endothelia during development. I also identified many galectin-3+ (Mac2+) cells within the kidney, which co-expressed the macrophage/monocyte-restricted marker, Csf1r, and were often carried within the vasculature. Mac2+ cells were present in the kidney from E11.5 onwards, dramatically increasing in number later in development. Single cell RNA-sequencing and subsequent gene over-representation testing indicated that mature F4/80hiCD206hi macrophages, but not Mac2hi cells, were enriched for mRNA transcripts linked to vascular development. Accordingly, kidney macrophage-depletion resulted in abnormal renal vascularisation, characterised by fewer endothelial anastomoses. These results suggest that macrophage-endothelial-communication is important for kidney organogenesis.

The first paper of this thesis considers the impact of minimum wages when search frictions are present and firms can substitute away from low skilled workers to both higher skilled workers and to capital. This represents a contribution to the search literature, which typically assumes labour is the only input of production and perfect substitution between labour inputs. I examine whether the model I develop features significant nonlinearities in the impact of the minimum wage on unemployment. I find that the theoretical contribution of this paper, i.e. allowing for search frictions and imperfect substitutability of factor inputs, is quantitatively significant. Specifically, the nonlinear unemployment response in my model does not occur if I use the typical assumptions of the search literature. In my second paper, I develop a structural model that can help to quantify the relative importance of institutions, labour market frictions and technology in explaining wage inequality. This contribution is a complement to the empirical literature on wage inequality, which tends to emphasise either technological explanations or institutional ones but rarely considers the two jointly. I take my model to the data to test whether estimates of capital skill complementarity in \citet{krusellohanianriosrull} are robust to the inclusion of search frictions. I find this is indeed the case: parameter estimates change very little when allowing for search frictions. My final paper returns to the minimum wage model of my first paper and considers how allowing for asset accumulation by workers changes the model's predictions regarding the relationship between the minimum wage and consumption inequality. I find that allowing for asset accumulation by workers suggests the minimum wage is more successful at reducing consumption inequality than models without asset accumulation would indicate.

The aim of this thesis is to provide an investigation toward a rigorous derivation of a stable and consistent numerical method based on the established Smoothed Particle Hydrodynamics method. The method should be suitable for modelling the large deformation transient response of fluids and solids, the interests of the Crashworthiness, Impact and Structural Mechanics group (CISM) at Cranfield University. A literature review of the current state of the art of the SPH method finds that the conventional SPH equations are not derived in a rigorous way, often the equations are manipulated into a mathematically equivalent form in order to preserve conservation of linear momentum, which often leads to different results; the reasons for this are unknown and it is not fully understood how each particular form of the discrete equations effects the solution in terms of stability, accuracy and convergence. This leads to specific objectives being defined which underpin the overall aim of the thesis. The first objective is to develop an understanding of the SPH method and the implementation used at Cranfield University, this is done through a capability study which demonstrates the coupled SPH-FE method and a number of relevant improvements to the MCM code including the addition of a turbulence model and the modification of the SPH contact algorithm to model lateral forces between materials. This is demonstrated through the implementation of a friction model, which suggests that the contact algorithm is suitable for resolving lateral forces based on the relative velocity between materials, with the potential for coupling with a structural FE model ... [cont.].