Circle and Torus Actions in Exceptional Holonomy

The work in this thesis is an investigation of the geometric structures arising on S 1 and T 2 quotients of manifolds endowed with G2 and Spin(7)-structures. This was motivated by the work of Apostolov and Salamon who studied the circle reduction of G2 manifolds and showed that imposing that the quotient is Kähler leads to a rich geometry. We shall consider the following problems: 1. The S 1 quotient of Spin(7)-structures 2. The Kähler reduction of Spin(7) manifolds with T 2 actions 3. The S 1 -invariant G2 Laplacian flow 4. The SU(2) 2 ×U(1)-invariant G2 Laplacian flow on S 3 ×R 4 Our key results include expressions relating the intrinsic torsion of S 1 -invariant Spin(7)-structures to that of the quotient G2-structures, a new expression for the Ricci curvature of Spin(7)-structures only in terms of the intrinsic torsion, infinitely many new examples of (incomplete) Spin(7) metrics arising as T 2 bundles over Kähler manifolds with trivial canonical bundle, the first example of an inhomogeneous shrinking gradient G2 Laplacian soliton and a local classification of closed SU(2) 2 ×U(1)-invariant G2-structures on S 3 ×R 4

Explicit abelian instantons on S1S^1-invariant K\"ahler Einstein 66-manifolds

We consider a dimensional reduction of the (deformed) Hermitian Yang-Mills condition on $S^1$-invariant K\"ahler Einstein $6$-manifolds. This allows us to reformulate the (deformed) Hermitian Yang-Mills equations in terms of data on the quotient K\"ahler $4$-manifold. In particular, we apply this construction to the canonical bundle of $\mathbb{C}\mathbb{P}^2$ endowed with the Calabi ansatz metric to find explicit abelian $SU(3)$ instantons and we show that these are determined by the spectrum of $\mathbb{C}\mathbb{P}^2$. We also find $1$-parameter families of explicit deformed Hermitian Yang-Mills connections. As a by-product of our investigation we find a coordinate expression for its holomorphic volume form which leads us to construct a special Lagrangian foliation of $\mathcal{O}_{\mathbb{C}\mathbb{P}^2}(-3)$.Comment: v2: 31 pages, added results (the content of section 8.

Examples of deformed Spin(7)-instantons/Donaldson-Thomas connections

We construct examples of deformed Hermitian Yang-Mills connections and deformed Spin(7)-instantons (also called Spin(7) deformed Donaldson-Thomas connections) on the cotangent bundle of $\mathbb{C}\mathbb{P}^2$ endowed with the Calabi hyperK\"ahler structure. Deformed Spin(7)-instantons on cones over 3-Sasakian 7-manifolds are also constructed. We show that these can be used to distinguish between isometric structures and also between Sp(2) and Spin(7) holonomy cones. To the best of our knowledge, these are the first non-trivial examples of deformed Spin(7)-instantons

S¹ -quotient of Spin(7)-structures

If a Spin(7)-manifold N⁸ admits a free S¹ action preserving the fundamental 4-form, then the quotient space M¹ is naturally endowed with a G₂ -structure. We derive equations relating the intrinsic torsion of the Spin(7)-structure to that of the G₂-structure together with the additional data of a Higgs field and the curvature of the S¹-bundle; this can be interpreted as a Gibbons–Hawking-type ansatz for Spin(7)-structures. In particular, we show that if N is a Spin(7)-manifold, then M cannot have holonomy contained in G₂ unless the N is in fact a Calabi–Yau fourfold and M is the product of a Calabi–Yau threefold and an interval. By inverting this construction, we give examples of SU(4) holonomy metrics starting from torsion-free SU(3)-structures. We also derive a new formula for the Ricci curvature of Spin(7)-structures in terms of the torsion forms. We then describe this S¹-quotient construction in detail on the Bryant–Salamon Spin(7) metric on the spinor bundle of S⁴ and on flat R⁸

Expression of monocyte heat shock protein 70 (HSP70) during malaria fever in the presence of antimalarial, anti-inflammatory drugs and β-haematin.

Doctor of Philosophy in Biochemistry. University of KwaZulu-Natal, Pietermaritzburg, 2017.Abstract available in PDF file

A review of in-situ grown nanocomposite coatings for titanium alloy implants

Composite coatings are commonly applied to medical metal implants in order to improve biocompatibility and/or bioactivity. In this context, two types of titanium-based composite coatings have been reviewed as biocompatible and anti-bacterial coatings. The different composites can be synthesised on the surface of titanium using various methods, which have their own advantages and disadvantages. Moving with the smart and nanotechnology, multifunctional nanocomposite coatings have been introduced on implants and scaffolds for tissue engineering with the aim of providing more than one properties when required. In this context, titanium dioxide (TiO2) nanotubes have been shown to enhance the properties of titanium-based implants as part of nanocomposite coatings.University of Plymout

High strain rate effect on tensile ductility and fracture of AM fabricated Inconel 718 with voided microstructures

The paper describes Electromagnetic Ring Expansion Tests (ERET) performed on Laser Melting Powder Bed Fusion (LPBF) Inconel 718 stress relieved test pieces, to establish the effect of a randomly dispersed spherically voided microstructure on tensile ductility, fracture, and fragmentation at high strain rate (10-3 < e < 104 s-1). An empirical model to predict porosity type and growth rates as a function of laser energy density was established, to select the LPBF process parameters to fabricate test pieces under stable conduction and keyhole melting. The size, shape, distribution of macro and keyhole pores in the test pieces obtained for ERET testing were characterised. At high strain rate the number of ring fragments for the highest porosity doubled, accompanied by a reduction in true strain at maximum uniform elongation and fracture strain. The trend for reducing fracture strain with increasing porosity at high strain rate was described by a decaying power law. Overall, there was a significant positive strain rate effect on tensile ductility at lower porosities attributed strain rate hardening (Hart, 1967) [1]. Fracture surfaces containing the highest porosity identified four different void coalescence mechanisms that helped explain the influence of larger pores on the stress state in the alloy.The AM of IN718 and tensile testing was funded by the UoD, College of Science and Engineering Research Excellence Framework (REF) funding for the Director of IISE (P. Wood) and AM Researcher (U. Gunputh). The support of G. Williams for IN718 sample preparation and M. Pawlik for tensile testing is acknowledged. A. Rusinek acknowledges the program UC3M-Santander Chair of Excellence in additive manufacturing. The expanding ring tests investigations were funded by the Polish Ministry of Science and Higher Education, Centre for Research and Development under research grant No. TECHMATSTRATEG2/410049/12/NCBR/2019

No Association Between MTHFR A1298C and MTRR A66G Polymorphisms, and MS in an Australian Cohort

Multiple sclerosis (MS) is a complex neurological disease that affects the central nervous system (CNS) resulting in debilitating neuropathology. Pathogenesis is primarily defined by CNS inflammation and demyelination of nerve axons. Methionine synthase reductase (MTRR) is an enzyme that catalyzes the remethylation of homocysteine (Hcy) to methionine via cobalamin and folate dependant reactions. Cobalamin acts as an intermediate methyl carrier between methylenetetrahydrofolate reductase (MTHFR) and Hcy. MTRR plays a critical role in maintaining cobalamin in an active form and is consequently an important determinant of total plasma Hcy (pHcy) concentrations. Elevated intracellular pHcy levels have been suggested to play a role in CNS dysfunction, neurodegenerative, and cerebrovascular diseases. Our investigation entailed the genotyping of a cohort of 140 cases and matched controls for MTRR and MTHFR, by restriction length polymorphism (RFLP) techniques. Two polymorphisms: MTRR A66G and MTHFR A1298C were investigated in an Australian age and gender matched case-control study. No significant allelic frequency difference was observed between cases and controls at the α = 0.05 level (MTRR χ^2 = 0.005, P = 0.95, MTHFR χ^2 = 1.15, P = 0.28). Our preliminary findings suggest no association between the MTRR A66G and MTHFR A1298C polymorphisms and MS