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LHC proton-proton collisions at a centre of mass energy of $\sqrt{s} = 7 TeV were observed in 2011. From a 1.68 fb$^{-1}$ sample of the data collected using the ATLAS detector, electron-positron pairs originating from the Drell-Yan process were selected using a cut based analysis. After the selection process, an estimate of the background was determined followed by the selection efficiency, detector resolution, reconstruction efficiency, and kinematic acceptance. Using these, the Drell-Yan differential cross section was calculated as a function of invariant mass between 26 and 66 GeV/c$^2$. This measurement has a precision between 12.4\% and 8.01\% from the lower invariant mass bins to the higher ones. The Drell-Yan cross section in proton-proton collisions depends on empirical quantities known as parton distribution functions which parametrize the structure of the proton. The measurement outlined in this thesis observes a region in parton distribution function phase space previously untouched by experiments. / Graduate

Since the discovery in the 1960's that the proton is not a fundamental particle but instead composed of even smaller particles known as quarks and gluons, there has been a concerted effort to understand the proton's internal structure. There still remain many mysteries about the proton and the theory that describes the interactions within: Quantum Chromodynamics (QCD). The distributions of quarks and gluons are encoded in objects known as parton correlation functions. Physicists use high-energy scattering experiments to access these functions by means of QCD factorization. This process of extracting information is known as a global QCD analysis. Further insight can be gained through first-principles calculations in lattice QCD as well as models for the strong interaction. In this thesis, we will use global QCD analyses to provide information on the one-dimensional (1D) structure of the proton using the latest experimental data available. Among the mysteries that remain within the proton, we provide insight on the non-perturbative nature of the proton's sea quarks, for both cases where the proton is unpolarized and longitudinally polarized. We also bring new information on the "proton spin puzzle," which concerns the delegation of the proton's spin into its constituent quarks and gluons. We shed light on the proton's transversely polarized structure, where current results from global QCD analyses and lattice QCD fail to paint a consistent picture. Our analyses also reveal a new feature of nuclear effects within light, highly asymmetric nuclei such as helium and tritium. Finally, we perform derivations in a spectator diquark model to glean information on the proton's 3D structure, and calculate moments that can be used in future lattice QCD studies. / Physics

The focus of this research is on hypotheses testing involving inequality constraints. In the first chapter of this dissertation, we propose Kolmogorov-Smirnov type tests for stochastic dominance relations between the potential outcomes of a binary treatment under the unconfoundedness assumption. Our stochastic dominance tests compare every point of the cumulative distribution functions (CDF), so they can fully utilize all information in the distributions. For first order stochastic dominance, the test statistic is defined as the supremum of the difference of two inverse-probability-weighting estimators for the CDFs of the potential outcomes. The critical values are approximated based on a simulation method. We show that our test has good size properties and is consistent in the sense that it can detect any violation of the null hypothesis asymptotically. First order stochastic dominance tests in the treated subpopulation, and higher order stochastic dominance tests in the whole population and among the treated are shown to share the same properties. The tests are applied to evaluate the effect of a job training program on incomes, and we find that job training has a positive effect on real earnings. Finally, we extend our tests to cases in which the unconfoundedness assumption does not hold. On the other hand, there has been a considerable amount of attention paid to testing inequality restrictions using Wald type tests. As noted by Wolak (1991), there are certain situations where it is difficult to obtain tests with correct size even asymptotically. These situations occur when the variance-covariance matrix of the functions in the constraints depends on the unknown parameters as would be the case in nonlinear models. This dependence on the unknown parameters makes it computationally difficult to find the least favorable configuration (LFC) which can be used to bound the size of the test. In the second chapter of this dissertation, we extend Hansen's (2005) superior predictive ability (SPA) test to testing hypotheses involving general inequality constraints in which the variance-covariance matrix can be dependent on the unknown parameters. For our test we are able to obtain correct size asymptotically plus test consistency without requiring knowledge of the LFC. Also the test can be applied to a wider class of problems than considered in Wolak (1991). In the last chapter, we construct new Kolmogorov-Smirnov tests for stochastic dominance of any pre-specified order without resorting to the LFC to improve the power of Barrett and Donald's (2003) tests. To do this, we first show that under the null hypothesis if the objects being compared at a given income level are not equal, then the objects at this given income level will have no effect on the null distribution. Second, we extend Hansen's (2005) recentering method to a continuum of inequality constraints and construct a recentering function that will converge to the underlying parameter function uniformly asymptotically under the null hypothesis. We treat the recentering function as a true underlying parameter function and add it to the simulated Brownian bridge processes to simulate the critical values. We show that our tests can control the size asymptotically and are consistent. We also show that by avoiding the LFC, our tests are less conservative and more powerful than Barrett and Donald's (2003). Monte Carlo simulations support our results. We also examine the performances of our tests in an empirical example. / text

This thesis presents the measurement of the inclusive jet cross section using data collected in 2010 by the ATLAS detector, with a particular focus on the reconstruction and calibration techniques used for jets in this measurement and on the estimate of the systematic uncertainty on their energy scale. The inclusive jet cross section measurement is used as input to fits of parton distribution functions. Although the PDF analysis in this thesis is preliminary and its main purpose is to serve as a proof of principle for future studies, improvements in the knowledge of the gluon density are observed thanks to the inclusion of ATLAS data.

Soft particle glasses like microgels and compressed emulsions are densely packed, disordered suspensions of deformable particles. Quantitative relationships among the constituent properties and the macroscopic properties of the suspension are determined for their customized design as rheological additives. The microscopic origin of their macroscopic properties is also determined. Advanced characterization techniques like Large Amplitude Oscillatory Shear (LAOS) and microrheology are studied to use them efficiently to characterize these materials. Their microstructure and rheology are investigated through theory, simulations and experiments. Soft particle glasses are used as rheological additives in many applications including coatings, solid inks and textured food and cosmetic products but their formulation is largely empirical. A quantitative connection between their formulation and rheology is critical to enable their rational design. Their microstructure will lead to the microscopic origin of some unique properties in common with other soft crowded materials like intracellular cytoplasm and clays. These are complex fluids and require novel techniques to characterize them. A study of these techniques is essential to efficiently interpret the observations in terms of their macroscopic properties and the microscopic dynamics involved. Particle scale simulations of steady and oscillatory shear flow are developed to predict the nonlinear rheology and microstructure of these glasses. The origin of yielding is determined as escape of particles from their cages giving rise to a shear induced diffusion. Microrheology is studied by developing simulations of a probe particle being pulled at a constant force and the rheological information from microrheology is quantitatively connected to that from bulk rheological measurements. Soft particle glasses develop internal stresses when quenched to a solid state by flow cessation during processing. Experiments are performed to characterize and a priori predict these stresses. Simulations are used to determine the particle scale mechanisms involved in the stress relaxation on flow cessation and the microstructural origin of internal stresses. A pairwise interaction theory is developed for quiescent glasses to quantitatively predict their microstructure and elastic properties. The theory is then extended to sheared glasses to quantitatively predict their nonlinear rheology. The implementation of the pairwise theories is computationally much faster than the full three-dimensional simulations. / text

Homogeneous single C-S-H gels have been prepared for the investigation of alkali binding potential and crystallisation. A distribution coefficient, R_d, was introduced to express the partition of alkali between solid and aqueous phases at 25°C. R_d is independent of alkali hydroxide concentration and depends only on Ca:Si ratio over wide ranges of alkali concentration. The trend of numerical values of R_d indicates that alkali bonding into the solid improves as its Ca:Si ratio decreases. Reversibility is demonstrated, indicating a possibility of constant R_d value of the material. Al has been introduced to form C-A-S-H gels and their alkali sorption properties also determined. Al substituted into C-S-H markedly increases R_d, indicating enhancement of alkali binding. However, the dependence of R_d on alkali concentration is non-ideal with composition. A two-site model for bonding is presented. Crystallisation both under saturated steam and 1 bar vapour pressure has been investigated. It has been shown that heat treatment by saturated steam causes crystallisation of gels. The principal minerals obtained were (i) C-S-H gel and Ca(OH)₂ at ~55°C, (ii) 1.1 nm tobermorite, jennite and afwillite at 85-130°C, and (iii) xonotlite, foshagite and hillebrandite at 150-180°C. Properties of crystalline C-S-H were also reported for reversible phase transformation, pH conditioning ability, seeding effect and solubility. At 1 bar pressure, crystallisation is slower than in saturated steam due to lower water activity. Tobermorite-like nanodomains develop during reaction at low Ca/Si ratios. In some Ca-rich compositions, Ca(OH)₂ is exsolved and occurs as nano-sized crystallites.

Neutral current Drell-Yan production in proton-proton collisions at the LHC was studied with the ATLAS detector. The 20.1 inverse femtobarn data set used in this precision measurement was collected in 2012 during which the LHC collided protons at a centre-of-mass energy of 8 TeV. The production rate or differential cross-section was measured in three-dimensions: invariant mass, absolute rapidity, and cosine of the polar angle in the Collins-Soper frame. A measurement of the forward-backward asymmetry was obtained from the differential cross-section by summing over the forward and the backward events and taking their difference. The three-dimensional differential cross-section measurement presented in this dissertation can be used to constrain the invariant mass- and rapidity-dependent parton distribution functions of the proton and the forward-backward asymmetry results can be used to extract a measurement of the weak mixing angle. / Graduate

The purpose of this thesis is to develop a comprehensive model analysis in a three-dimensional spatial frame for the dynamics of molecular particles in dilute colloidal suspensions in solutions flowing inside pores of variable width, subject to hydrodynamic forces, Brownian motion and diffusive collisions at the rough pore boundaries, by using numerical simulations. The approach by simulations is necessary because it is extremely complex to use analytical tools at present to deal with the problem of diffusive collisions of the particles at the solid pore boundaries. The algorithms which we have developed and the corresponding simulations are sufficiently general and refined to be directly applied to the study of the dynamics of a wide variety of polymer and biological particles in dilute solutions under diverse physical and applicable hydrodynamic conditions inside pores. Moreover, the mechanisms leading to the adhesion of particles of nano sizes under what would be non-equilibrium conditions, due to the conflicting influence of the mechanical diffusive collisions and the attractive Hamaker forces at the boundaries, are of major interest. We have hence investigated a theoretical model to calculate the restitution coefficient from basic physical principles. The objective is to quantify the energy balance during the process of a diffusive collision of a nano particle under the influence of the repulsive forces on one hand, and the attractive Hamaker forces acting on the nano particle on the other. This is done by developing a model, based on the JKR and Hertz theories, to account for the energy losses during collisions, and for the energy gains due to the Hamaker interactions. Adhesion becomes an outcome if the energy balance permits this. Our theoretical model is developed by proposing a special analytic approach based on the Hamaker potential. We derive from the theoretical analysis a characteristic nonlinear equation for the restitution coefficient, and analyze its properties which determine under given physical conditions the outcome for adhesion or not.