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The impact of the 2016 EU referendum result on UK politics was as dramatic as it was unexpected. Instead of endorsing the status quo, it forced a significant change in policy direction that most of the political class disagreed with. However, this rare example of direct delegation to UK voters did little to alter the strong and persistent perceptions among them that their MPs do not care what they think. On the contrary, it appeared to exacerbate such sentiments and reinforce the beliefs of voters that their representatives are primarily motivated by other factors. The academic literature suggests that when deciding on what policies to support MPs face a trade-off between three main influences: the demands of their constituents, their party leadership and their own consciences. Within the UK studies regularly suggest that the party line is the most reliable predictor of how an MP will vote. However, the referendum presents a unique opportunity to comprehensively test the extent of these influences that has yet to be sufficiently realised. While there have been numerous academic studies focusing on either explaining why people voted as they did at the referendum or how Parliament handled the withdrawal process in the years that followed, the extent to which the former may have influenced the latter remains understudied. This is an important area of study given the aforementioned declining public faith in their representatives and the rarity of direct delegation to voters within the UK. This research therefore addresses this gap in the literature while also contributing to broader debates about democracy and representation within the UK. Using a mixed methods approach, the study develops and tests a tripartite model of the potential influences on MPs to determine the effect they can have on how they vote in Parliament. The findings suggest that voter perceptions of their elected representatives are not all that far off the mark: most MPs were not directly responsive to constituency opinion and their voting behaviour was instead primarily motivated by their own beliefs and evaluations of what needed to happen. These in turn could be heavily influenced by the evaluations of MPs as to what was best for their party and their position within it. However, despite having little observable impact on how they voted in Parliament, most MPs were still responsive to constituency opinion in other ways, notably in how they framed their policy positions and actions. In contributing these findings to the academic literature, this study therefore proposes a broader framework within which to conceptualise and test the responsiveness of MPs to constituent desires. While the findings of this research do reinforce some of the negative views voters hold about their representatives, it does offer them a broader understanding of how their opinions play into the legislative process and what influence they can actually have. This situation still raises important questions about UK democracy and the ability of political elites to effectively engage with voters and govern the country, but the findings of this study can go some way towards helping academics and practitioners better address and engage with these problems and public perceptions of them.

In this work probability density function (PDF) models are used as a method for studying the statistical distribution of particles in turbulent flows, which is of interest in many industrial and environmental processes. This approach involves derivation of a transport equation for describing the evolution of the joint PDF of particle variables. In different flow configurations the PDF approach identifies various contributions to the particle phase mass flux that act as additional drift and diffusion terms. These terms, which are critical in the formulation of two-fluid models, require closure. In order to evaluate the effect of the different flux contributions arising in the various flow configurations, these terms are considered in the context of both homogeneous and inhomogeneous flows. In the case of homogeneous flows the enhancement of the settling rate of inertial particles under an applied body force, specifically gravity, is investigated. Inhomogeneous turbulence is used to study the clustering of particles in a framework associated with the behaviour of particle pair dynamics in homogeneous flows. Existing closures based on simple local approximations are shown to neglect the contributions of interest to the particle phase mass flux, and an improved methodology is proposed which takes into account underlying physical mechanisms behind the observed behaviour, and consists of modelling various correlations that arise from the PDF formulation. The performance of this closure strategy is evaluated making use of particle trajectory simulations in a synthetic flow field generated using Kinematic Simulation (KS). The Eulerian two-point, two-time fluctuating velocity correlations for the continuous phase are central to the modelling, and these are determined in the specification of the flow field. Similarly the particle response tensor to perturbations in the continuous phase is computed allowing for exact evaluation of the unclosed terms. A linear drag law is used in the particle equation of motion, and the influence of both Stokes number and applied body forces on the increase in particle settling rate and clustering is investigated. In agreement with previous work it is seen that the mechanism responsible for these effects can be quantified in terms of the preferential sampling of strain over rotation by inertial particles due to interaction with the structures in the flow field.