title: Matrix operator symmetries of the Dirac equation and separation of variables

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: The set of all matrix-valued first-order differential operators that commute with the Dirac equation in n-dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix-valued second-order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first-order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].

text: Matrix operator symmetries of the Dirac equation and separation of variables The set of all matrix-valued first-order differential operators that commute with the Dirac equation in n-dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix-valued second-order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first-order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].

year: 1986-07

title: The Art of Coffee Roasting: Investigations into Sensor Development for the Application of Controlling Coffee Roasting

authors: Kelly, Cameron Brian Desmond

subjects: Coffee

abstract: In this thesis, I investigate novel methods of sensing change in roasting coffee. Coffee roasting is a vital step in coffee’s supply chain. It is the process that takes green coffee and transforms it via a series of many chemical and physical reactions to produce the flavours for which coffee is recognised. As of today, correctly roasted coffee has been an art. My work applies different methods of sensing to track various changes in coffee as it roasts with the end goal of automating the art.
The goal was to find an event or measurable phenomenon that could be used to detect when the roasting coffee has reached an ideal point, beyond which the beans would start to taste burnt. My investigations looked at various sensing methods. I expanded on three different areas of test: bean temperature, online moisture measurement using microwave resonance, and surface chemistry using Raman spectrometry. Using these different methods, I was able to produce novel and interesting measurements. 
Each of the measurement methods performed satisfactorily and produced novel results. These results however did not produce the desired measurable event or independent characteristics. This meant that they were not able to individually solve the problem. However, their uniqueness and application flexibility would allow them to be used as elements in future roasting sensor systems.

text: The Art of Coffee Roasting: Investigations into Sensor Development for the Application of Controlling Coffee Roasting In this thesis, I investigate novel methods of sensing change in roasting coffee. Coffee roasting is a vital step in coffee’s supply chain. It is the process that takes green coffee and transforms it via a series of many chemical and physical reactions to produce the flavours for which coffee is recognised. As of today, correctly roasted coffee has been an art. My work applies different methods of sensing to track various changes in coffee as it roasts with the end goal of automating the art.
The goal was to find an event or measurable phenomenon that could be used to detect when the roasting coffee has reached an ideal point, beyond which the beans would start to taste burnt. My investigations looked at various sensing methods. I expanded on three different areas of test: bean temperature, online moisture measurement using microwave resonance, and surface chemistry using Raman spectrometry. Using these different methods, I was able to produce novel and interesting measurements. 
Each of the measurement methods performed satisfactorily and produced novel results. These results however did not produce the desired measurable event or independent characteristics. This meant that they were not able to individually solve the problem. However, their uniqueness and application flexibility would allow them to be used as elements in future roasting sensor systems.

year: 2018

title: A core phyllosphere microbiome exists across distant populations of a tree species indigenous to New Zealand

authors: Noble, Anya S.

subjects: Science & Technology

abstract: The phyllosphere microbiome is increasingly recognised as an influential component of plant physiology, yet it remains unclear whether stable host-microbe associations generally exist in the phyllosphere. Leptospermum scoparium (mānuka) is a tea tree indigenous to New Zealand, and honey derived from mānuka is widely known to possess unique antimicrobial properties. However, the host physiological traits associated with these antimicrobial properties vary widely, and the specific cause of such variation has eluded scientists despite decades of research. Notably, the mānuka phyllosphere microbiome remains uncharacterised, and its potential role in mediating host physiology has not been considered. Working within the prevailing core microbiome conceptual framework, we hypothesise that the phyllosphere microbiome of mānuka exhibits specific host association patterns congruent with those of a microbial community under host selective pressure (null hypothesis: the mānuka phyllosphere microbiome is recruited stochastically from the surrounding environment). To examine our hypothesis, we characterised the phyllosphere and associated soil microbiomes of five distinct and geographically distant mānuka populations across the North Island of New Zealand. We identified a habitat-specific and relatively abundant core microbiome in the mānuka phyllosphere, which was persistent across all samples. In contrast, non-core phyllosphere microorganisms exhibited significant variation across individual host trees and populations that was strongly driven by environmental and spatial factors. Our results demonstrate the existence of a dominant and ubiquitous core microbiome in the phyllosphere of mānuka, supporting our hypothesis that phyllosphere microorganisms of mānuka exhibit specific host association and potentially mediate physiological traits of this nationally and culturally treasured indigenous plant. In addition, our results illustrate biogeographical patterns in mānuka phyllosphere microbiomes and offer insight into factors contributing to phyllosphere microbiome assembly.

text: A core phyllosphere microbiome exists across distant populations of a tree species indigenous to New Zealand The phyllosphere microbiome is increasingly recognised as an influential component of plant physiology, yet it remains unclear whether stable host-microbe associations generally exist in the phyllosphere. Leptospermum scoparium (mānuka) is a tea tree indigenous to New Zealand, and honey derived from mānuka is widely known to possess unique antimicrobial properties. However, the host physiological traits associated with these antimicrobial properties vary widely, and the specific cause of such variation has eluded scientists despite decades of research. Notably, the mānuka phyllosphere microbiome remains uncharacterised, and its potential role in mediating host physiology has not been considered. Working within the prevailing core microbiome conceptual framework, we hypothesise that the phyllosphere microbiome of mānuka exhibits specific host association patterns congruent with those of a microbial community under host selective pressure (null hypothesis: the mānuka phyllosphere microbiome is recruited stochastically from the surrounding environment). To examine our hypothesis, we characterised the phyllosphere and associated soil microbiomes of five distinct and geographically distant mānuka populations across the North Island of New Zealand. We identified a habitat-specific and relatively abundant core microbiome in the mānuka phyllosphere, which was persistent across all samples. In contrast, non-core phyllosphere microorganisms exhibited significant variation across individual host trees and populations that was strongly driven by environmental and spatial factors. Our results demonstrate the existence of a dominant and ubiquitous core microbiome in the phyllosphere of mānuka, supporting our hypothesis that phyllosphere microorganisms of mānuka exhibit specific host association and potentially mediate physiological traits of this nationally and culturally treasured indigenous plant. In addition, our results illustrate biogeographical patterns in mānuka phyllosphere microbiomes and offer insight into factors contributing to phyllosphere microbiome assembly.

year: 2020