This thesis discusses recent advances in precision calculations of quantum chromodynamics and their application to the Large Hadron Collider (LHC) physics program and beyond. The first half of the thesis is dedicated to the study of vector boson fusion Higgs (VBF) production; fully differential at the next-to-next-to-leading order level (NNLO), and inclusively at next-to-next-to-next-to-leading order (N³LO). Both calculations are performed in the structure function approximation, where the VBF process is treated as a double deep inelastic scattering. For the differential calculation a new subtraction method, "projection-to-Born", is introduced and applied. We study VBF production in a number of scenarios relevant for the LHC and for Future Circular Colliders (FCC). We find NNLO corrections after typical cuts of 5-6% while differential distributions show corrections of up to 10-12% for some standard observables. For the inclusive calculation we find N³LO corrections at the order of 1-2‰. The second half of the thesis presents recent results on the matching of fixed order calculations with parton showers. We first present the POsitive Weight Hardest Emission Generator (POWHEG) method for matching next-to-leading order (NLO) calculations with parton showers. We then proceed to apply it to the case of vector boson fusion ZZjj production and discuss the results for scenarios relevant for the LHC and a possible FCC. In order to present the matching of a NNLO calculation with a parton shower, we next discuss the Multi-Scale Improved NLO (MiNLO) procedure. By applying a reweighting procedure to MiNLO improved Drell-Yan production, we obtain a generator which is NNLO accurate when integrated over all radiation while providing a fully exclusive description of the final state phase space. We compare the calculation to dedicated next-to-next-to-leading logarithm resummations and find very good agreement. The generator is also found to be in good agreement with 7 and 8 TeV LHC data.

Chiral phosphoric acids are bifunctional catalysts that have the ability to activate electrophiles and nucleophiles through hydrogen bonding, and they have been successful in catalysing highly enantioselective additions of a wide range of nucleophiles to imines. In most literature reports it is not frequently revealed how these catalysts impart enantioselectivity. Thus, the vast majority of time required for reaction development is expended on the optimisation of the catalyst features. The research described here explores the ability of relating computational derived catalyst parameters to enantioselectivity as a means to assess the catalyst features important for enantioinduction. The proposed features are evaluated computationally and summarised into simple qualitative models to understand and predict outcomes of similar reactions. In Chapter 1, I provide an overview of the progress and challenges in the development of chiral phosphoric acid mediated reactions. I highlight leading computational studies that have enabled a greater understanding of how the catalyst imparts reactivity and selectivity. In general, the studies focus on the most effective catalyst and do not do a detailed investigation into the effects of changing the substituents at the 3,3’ positions. Implicating steric effects from reasonably large groups as a key component in imparting enantioselectivity. However, it is clear that they have a more subtle effect. A large group is required but if it is too large poor or unusual results are obtained, making the correct choice of reaction conditions challenging. In Chapter 2, I develop a quantitative assessment of the substituents at the 3,3’ positions. I show in Chapters 3 and 4 that I can use rotation barriers in combination with a novel steric parameter, AREA(θ), to correlate enantioselectivity. By exploiting this finding, the catalyst features important for enantioselectivity can be identified, and this is validated by QM/MM hybrid calculations. Summarising these detailed calculations into a single qualitative model, guides optimal catalyst choice for all seventy-seven literature reactions reporting over 1000 transformations. These mechanistic studies have guided the design of a new catalyst with increased versatility, which is discussed in Chapter 5. Chapter 6 details my study into the effect of the hydroxyl group on the mechanism of transfer hydrogenation of imines derived from ortho-hydroxyacetophenone. I show, using detailed DFT and ONIOM calculations, that transition states of these reactions involve hydrogen bonding from both the hydroxyl group on the imine and the nucleophile’s proton to the phosphate catalyst. In Chapter 7, computational analysis is used to provide insight into the origins of enantioselectivity in chiral phosphoric acid catalysed Friedel-Crafts and Mannich reactions proceeding through monoactivation mechanisms. The final chapter contains an in-depth look into the stereoelectronic effects altering enantioselectivity in the silver-phosphate mediated spirocyclisation reaction involving aromatic ynones. In this study I show that enantioselectivity is governed by the non-covalent interactions between the aromatic group of the ynone and the 3,3’ substituent. I was able to propose synthetic modifications to the substrate used in this reaction, resulting in an improvement in enantioselectivity.

Logic programming realizes the ideal of "computation as deduction," except when floating-point arithmetic is involved. In that respect, logic programming languages suffer the same deficiency as conventional algorithmic languages: floating-point operations are only approximate and it is not easy to tell how good the approximation is. This dissertation proposes a framework to extend the benefits of logic programming to computations involving floating-point arithmetic. John Cleary incorporated a relational form of interval arithmetic into Prolog so that variables already bound can be bound again. In this way, the usual logical interpretation of computation no longer holds. Based on Cleary's idea, we develop a technique for narrowing intervals. We present a relaxation algorithm for coordinating the applications of the interval narrowing operations to constraints in a network. We incorporate relational interval arithmetic into two constraint logic programming languages: CHIP and CLP(R). We modify CHIP by allowing domains to be intervals of real numbers. In CLP(R) we represent intervals by inequality constraints. The enhanced languages ICHIP and ICLP(R) preserve the semantics of logic so that numerical computations are deductions, even when floating-point arithmetic is used. We have constructed a prototype of ICLP(R) consisting of a meta-interpreter executed by an existing CLP(R) system. We show that interval narrowing belongs to the class of domain restriction operations in constraint-satisfaction algorithms. To establish a general framework for these operations, we use and generalize Ashby's notions of cylindrical closure and cylindrance. We show that Mackworth's algorithms can be placed in our framework. / Graduate

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>Magister Scientiae - MSc / Most stable and extremely low abundance neutron deficient nuclei with Z ≥ 34 are referred to as p-nuclei. Nearly all p-nuclei with A < 110 are most likely produced in the rp-process while almost all A > 110 are thought to be produced by the photodisintegration of s- and r- process seed nuclei. However, for some nuclear systems, these processes are not sufficient to explain their observed solar abundance. Results from calculations in ¹⁸ᴼTa generally provoke debates since several processes are able, sometimes exclusively, to reproduce the observed ¹⁸ᴼTa abundance in the cosmos, making it a unique case study. Some of the main sources of errors in the predicted reaction rates of ¹⁸ᴼTa arise due to the absence of nuclear data or due to large uncertainties in the nuclear properties such as the nuclear level densities (NLD) and gamma-ray strength functions (γSF) of ¹⁸ᴼ,¹⁸¹Ta. The NLD and γSF are primary ingredients for astrophysical reaction rate calculations based on the Hauser-Feshbach approach. These parameters need to be well understood to improve our understanding of ¹⁸ᴼTa production in astrophysical environments. In this thesis, new experimental data for the low-energy part of the γSF and NLD in ¹⁸ᴼ,¹⁸¹Ta were extracted, using the so-called Oslo method. An experiment was performed and the NaI(Tl) gamma-ray array and silicon particle telescopes at the Oslo cyclotron laboratory were utilized to measure particle-γ coincidence events from which the NLDs and γSFs are extracted below the neutron separation energy threshold Sn. A beam of ³He was used to populate excited states in ¹⁸ᴼ,¹⁸¹Ta through the inelastic scattering (³He,³He’𝛾) and the transfer reaction (³He,𝜶𝛾). Based on results from this measurements, the Maxwellian averaged (n, 𝛾) cross sections for the 179Ta(n, γ) and ¹⁸ᴼTa(n, 𝛾) reactions, at the s-process thermal energy of kT = 30 keV (i.e. a temperature of T = 3.5 × 10⁸ K) and p-process thermal energy of 215 keV (T = 2.5 × 10⁹ K), respectively, were computed with the TALYS reaction code. These results can be used to place the nuclear physics aspects of the large network abundance calculations on a solid footing and have potential to improve our understanding of the astrophysical processes and sites involved in the production of nature’s rarest isotope ¹⁸ᴼTa. / National Research Foundation (NRF)

In 1854 Cayley proposed an interesting sequence 1,1,3,13,75,541,... in connection with analytical forms called trees. Since then there has been various combinatorial interpretations of the sequence. The sequence has been interpreted as the number of preferential arrangements of members of a set with n elements. Alternatively the sequence has been interpreted as the number of ordered partitions; the outcomes in races in which ties are allowed or geometrically the number of vertices, edges and faces of simplicial objects. An interesting application of the sequence is found in combination locks. The idea of a preferential arrangement has been extended to a wider combinatorial object called barred preferential arrangement with multiple bars. In this thesis we study barred preferential arrangements combinatorially with application to resistance of certain electrical circuits. In the process we derive some results on cyclic properties of the last digit of the number of barred preferential arrangements. An algorithm in python has been developed to find the number of barred preferential arrangements.

An Othmer recirculating still and a standard packed column fractionating unit were used in determining the equilibrium flash vaporization and true boiling point curves respectively, for eight samples of crude oils from producing oil-fields in Alberta. The EFV curves, at 10 mm. absolute pressure were also obtained for these samples. Determinations at atmospheric pressure were used for modifying Okamoto and Van Winkle's correlation, which allows the prediction of the EFV curves from the TBP curves, for application to crude oils. The correlation relates the 50 percent points and the slopes of the two curves. In spite of its simplicity, it results in predicted curves of good accuracy. It is believed that this method is suitable for a large number of crudes and can give dependable phase equilibrium data. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

A summary of the work done in the field of analytic differentiation by computer is presented. It is shown that there exists a need for an analytic differentiation routine whose output can be processed by a regular algebraic compiler. An algorithm is presented which will transform a FORTRAN FUNCTION subprogram into a FORTRAN SUBROUTINE subprogram that evaluates both the original function and its first derivative with respect to one independent variable. Implementation of this algorithm and possible extensions to it are discussed. / Science, Faculty of / Computer Science, Department of / Graduate

A method is presented for linear control system design using functional relations between system parameters and system response. The functional relations are obtained by frequency domain evaluation of an integral performance criterion. The performance criterion is defined as a correlation measure between the responses of a known reference system and the system to be designed. A method is also presented for obtaining algebraic expressions relating the time-domain response of linear and piece-wise linear systems with system parameters. By means of a rational fraction approximation to the exponential e and through use of a known technique for evaluating time-domain convolution integrals, it becomes possible to obtain the time-domain response without the necessity of first having to determine the poles of the system. The time-domain response is obtained as a ratio of polynomials in t with the coefficients as algebraic functions of the system parameters. The extension of the linear design theory to cover non-linear and multivariable systems is given. Several examples are given to illustrate the usefulness of the proposed techniques. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate