K-stability of constant scalar curvature K\"ahler manifolds

We show that a polarised manifold with a constant scalar curvature K\"ahler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S. K. Donaldson.Comment: 14 page

A W-band gyrotron backward wave oscillator with helically corrugated waveguide

This thesis was previously held under moratorium from 9th May 2011 until 9th May 2013.This thesis presents the results of a successful W-band gyrotron backward wave oscillator experiment. Three major achievements presented in this thesis are: 1) The design, simulation, construction and operation of a cusp electron gun; 2) The design, simulation, optimisation, construction and experimental measurement of a W-band helically corrugated waveguide and 3) the operation of the world's first W-band gyro-BWO using both a helically corrugated waveguide and a cusp electron gun. Gyro-BWO interaction with a 2nd cyclotron harmonic axis-encircling annular electron beam was observed. The interaction region was constructed through an accurate electroplating method while the designed dispersion characteristics agreed well to the experimental measurements. The loss through the optimised construction method was low, recorded around 1dB through the frequency range of interest. The following work presents the analytical, numerical and experimental investigation of a proof of principle gyro-BWO experiment. The design, simulation and optimisation of a thermionic cusp electron gun that can generate a 1.5A, 40kV axisencircling electron beam are discussed. Simulations showed a high quality electron beam with ~8% velocity spread and ~10% alpha spread. Experiments were conducted using this electron gun and the accelerating voltage pulse, diode current, transported beam current are presented. The electron beam profile was recorded showing a clear axis-encircling beam image from which the electron beam diameter and alpha values can be measured. Microwave radiation was measured over a frequency range of ~91-100GHz with a approximate maximum power of ~0.37kW. Operating over the magnetic field range 1.79T to 1.9T and measured over a range of alpha values this result was very impressive and proved the successful operation of the gyro-BWO.This thesis presents the results of a successful W-band gyrotron backward wave oscillator experiment. Three major achievements presented in this thesis are: 1) The design, simulation, construction and operation of a cusp electron gun; 2) The design, simulation, optimisation, construction and experimental measurement of a W-band helically corrugated waveguide and 3) the operation of the world's first W-band gyro-BWO using both a helically corrugated waveguide and a cusp electron gun. Gyro-BWO interaction with a 2nd cyclotron harmonic axis-encircling annular electron beam was observed. The interaction region was constructed through an accurate electroplating method while the designed dispersion characteristics agreed well to the experimental measurements. The loss through the optimised construction method was low, recorded around 1dB through the frequency range of interest. The following work presents the analytical, numerical and experimental investigation of a proof of principle gyro-BWO experiment. The design, simulation and optimisation of a thermionic cusp electron gun that can generate a 1.5A, 40kV axisencircling electron beam are discussed. Simulations showed a high quality electron beam with ~8% velocity spread and ~10% alpha spread. Experiments were conducted using this electron gun and the accelerating voltage pulse, diode current, transported beam current are presented. The electron beam profile was recorded showing a clear axis-encircling beam image from which the electron beam diameter and alpha values can be measured. Microwave radiation was measured over a frequency range of ~91-100GHz with a approximate maximum power of ~0.37kW. Operating over the magnetic field range 1.79T to 1.9T and measured over a range of alpha values this result was very impressive and proved the successful operation of the gyro-BWO

Quantum-based security in optical fibre networks

Electronic communication is used everyday for a number of different applications. Some of the information transferred during these communications can be private requiring encryption and authentication protocols to keep this information secure. Although there are protocols today which provide some security, they are not necessarily unconditionally secure. Quantum based protocols on the other hand, can provide unconditionally secure protocols for encryption and authentication. Prior to this Thesis, only one experimental realisation of quantum digital signatures had been demonstrated. This used a lossy photonic device along with a quantum memory allowing two parties to test whether they were sent the same signature by a single sender, and also store the quantum states for measurement later. This restricted the demonstration to distances of only a few metres, and was tested with a primitive approximation of a quantum memory rather than an actual one. This Thesis presents an experimental realisation of a quantum digital signature protocol which removes the reliance on quantum memory at the receivers, making a major step towards practicality. By removing the quantum memory, it was also possible to perform the swap and comparison mechanism in a more efficient manner resulting in an experimental realisation of quantum digital signatures over 2 kilometres of optical fibre. Quantum communication protocols can be unconditionally secure, however the transmission distance is limited by loss in quantum channels. To overcome this loss in conventional channels an optical amplifier is used, however the added noise from these would swamp the quantum signal if directly used in quantum communications. This Thesis looked into probabilistic quantum amplification, with an experimental realisation of the state comparison amplifier, based on linear optical components and single-photon detectors. The state comparison amplifier operated by using the wellestablished techniques of optical coherent state comparison and weak subtraction to post-select the output and provide non-deterministic amplification with increased fidelity at a high repetition rate. The success rates of this amplifier were found to be orders of magnitude greater than other state of the art quantum amplifiers, due to its lack of requirement for complex quantum resources, such as single or entangled photon sources, and photon number resolving detectors

Challenges for the implementation of the renewable heat incentive : an example from a school refurbishment geothermal scheme

The Government run UK Renewable Heat Incentive (RHI) scheme allows cash back payments to be made to producers of renewable heat. As a world first for renewable heat, it aims to tackle head on the issues surrounding emissions, energy use, and climate change targets. However, whilst the scheme goes a long way towards meeting these climate change targets, issues have been identified that may compromise its effectiveness. This paper aims to examine the progress of the RHI since its launch in November 2011, and avenues towards a more effective deploymen

Singularities and K-semistability

In this paper we extend the notion of Futaki invariant to big and nef classes in such a way that it defines a continuous function on the \K\ cone up to the boundary. We apply this concept to prove that reduced normal crossing singularities are sufficient to check $K$-semistability. A similar improvement on Donaldson's lower bound for Calabi energy is given.Comment: Major revision of previous upload. 18 page

Time-resolved photoelectron imaging of excited state relaxation dynamics in phenol, catechol, resorcinol and hydroquinone

Time-resolved photoelectron imaging was used to investigate the dynamical evolution of the initially prepared S1 (\u3c0\u3c0*) excited state of phenol (hydroxybenzene), catechol (1,2-dihydroxybenzene), resorcinol (1,3-dihydroxybenzene), and hydroquinone (1,4-dihydroxybenzene) following excitation at 267 nm. Our analysis was supported by ab initio calculations at the coupled-cluster and CASSCF levels of theory. In all cases, we observe rapid (<1 ps) intramolecular vibrational redistribution on the S1potential surface. In catechol, the overall S1 state lifetime was observed to be 12.1 ps, which is 1\u20132 orders of magnitude shorter than in the other three molecules studied. This may be attributed to differences in the H atom tunnelling rate under the barrier formed by a conical intersection between the S1 state and the close lying S2 (\u3c0\u3c3*) state, which is dissociative along the O\u2013H stretching coordinate. Further evidence of this S1/S2 interaction is also seen in the time-dependent anisotropy of the photoelectron angular distributions we have observed. Our data analysis was assisted by a matrix inversion method for processing photoelectron images that is significantly faster than most other previously reported approaches and is extremely quick and easy to implement.Peer reviewed: YesNRC publication: Ye

Measurements of B± Meson production at LHCb and characterisation of hybrid photon detectors

LHCb is an experiment designed to make precision measurements of Charge- Parity violation in the B meson system. We report a measurement of the B± crosssection and production asymmetry, using B± → J/u K± decays collected at the LHCb detector in 2010 and 2011. Using 27.6 pb-1 of pp collisions at a centre-of-mass energy 7 TeV, we obtain a B± cross-section of [41.6 ± 0.6 (stat.) ± 3.0 (sys.) ± 4.2 (lumi.)] μb in the rapidity region 2 to 4.5. Using 371.1 pb-1 of pp collisions at a centre-of-mass energy 7 TeV, we obtain a B± production asymmetry of [-2.09 ± 1.20 ± 0.8 (CP) ]% in the same rapidity region. The Ring Imaging Cherenkov system of LHCb uses Hybrid photon detectors (HPDs) for single photon detection. This thesis summarises the use of ion feedback measurements as indicators of HPD vacuum quality

Does cancer type influence the impact of recurrence? : a review of the experience of patients with breast or prostate cancer recurrence

Objective: Patients will experience a plethora of issues when faced with a recurrence of their cancer. It is unclear if cancer type is a significant factor in how recurrence is experienced by an individual. The aim of the current review is to explore the evidence base and summarise the experiences of patients specifically with a recurrence of breast or prostate cancer (the most common for women and men, respectively) and then provide a comparison of these experiences. These experiences include the physical, psychological and psychosocial issues that arise at this time.  Methods: A systematic search was conducted of studies published between January 1994 and April 2019. Due to the mix of research designs used previously in the literature, this review was conducted in an integrative manner; allowing for inclusion of diverse research designs. Results were synthesised narratively, with data categorised according to physical, psychological, and psychosocial indices of quality of life. The review protocol was registered in the international database of prospective systematic reviews in health and social care- (CRD42019137381).  Results: Fifteen breast cancer and six prostate cancer articles were identified, each reporting one relevant study. Patients reported several negative issues at the time of a breast or prostate cancer recurrence. Similarities were found between cancer types, with physical problems such as fatigue, psychological issues including anxiety and depressive symptoms, and psychosocial concerns such as issues with healthcare professionals common in both cancers. Certain findings were inconsistent across studies, with some experiences differing between studies rather than due to cancer type.  Conclusions: Differences in the experience of recurrent cancer appear to be more heavily influenced by individual factors, rather than cancer type. Findings are confounded by gender; and should be considered preliminary. Effects of recurrence should be studied in samples where cancer type and gender are not confounded. Concerns are raised about available study quality and differing outcome measures in this interpretation. Care and support of the individual at the time of a cancer recurrence is a key focus. Future research suggestions with implications for clinical practise are included.Publisher PDFPeer reviewe