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Feedback loops in climate systems arise from interactions between various subsystems, such as distinct bodies of water, the atmosphere, land and ice masses. They are prominent features and drive observed behaviour. Any such feedback takes effect only after an inherent time delay, because it takes time to transport water, air and energy across the globe and subsystems require time to react. The goal is to develop new mathematics for the study of delayed feedback loops in conceptual climate models to determine the often unexpected and sometimes unwanted consequences that may ensue. The focus will be on the challenging but very natural case when the delays of the feedback loops are not constant but depend on the present state. The El Niño phenomenon and the Atlantic Meridional Overturning Circulation are two climate systems of immediate relevance in this regard.
The task will be to derive and study appropriate functional forms for climate systems with delayed positive and negative feedback loops to determine the consequences of the different types of feedback loops, individually and in combination. This will include a systematic analysis of how different types of delay terms, including state-dependent and distributed delays, influence the observed behaviour. The work will make use of state-of-the-art methods for the analysis of delay differential equations, in particular, the continuation of invariant objects and their bifurcations. This project offers opportunities for collaborations with Professors Henk Dijkstra (Utrecht University, The Netherlands), Tony Humphries (McGill University, Montreal, Canada) and Jan Sieber (University of Exeter, UK).
The project will be supervised by Professor Bernd Krauskopf at the University of Auckland and will benefit from being part of the vibrant Applied Dynamical Systems group at the Department of Mathematics. Funding will be available to sufficiently highly qualified candidates in the form of University of Auckland PhD Scholarships, which will be awarded competitively. For general information about PhD scholarships and the application process, visit www.math.auckland.ac.nz/future-postgraduates or email phdadvice@math.auckland.ac.nz.
Informal enquiries and expressions of interest should be addressed to b.krauskopf@auckland.ac.nz.
Systems of driven and active optical cavities, such as semiconductor lasers, micro-resonators, fibre loops or photonic crystal cavities all display a wide range of dynamical behaviour due to the interplay of nonlinearity, energy supply and loss, and mutual coupling. This project will focus on how such a system can change from simple to highly complex dynamics as parameter are changed. The emphasis will be on how geometric objects in phase space, known as global invariant manifolds, rearrange and generate new types of behaviour. How such behaviour can be characterised and identified in observations will be an important aspect of the work.
This project will be supervised by Professors Bernd Krauskopf and Neil Broderick at the Dodd-Walls Centre. Sufficiently highly qualified candidates will be able to apply for a PhD Scholarships from the Dodd-Walls Centre and/or the University of Auckland, which will be awarded competitively. For general information about PhD scholarships and the application process, visit www.math.auckland.ac.nz/future-postgraduates or email phdadvice@math.auckland.ac.nz.
Atomic and optical systems, including nanolasers, optical cavities, on-chip microresonators and Bose-Einstein-type atomic ensembles are being designed to work with extremely low numbers of photons and/or atoms. As such, they sit right at the boundary between a description by (semi)classical and quantum theory. The project will investigate via dedicated case studies how dynamical systems methods applied to semiclasical models can give information on statistical properties of observable of the quantum description.
This project will be supervised by Professors Bernd Krauskopf and Scott Parkins at the Dodd-Walls Centre. Sufficiently highly qualified candidates will be able to apply for a PhD Scholarships from the Dodd-Walls Centre and/or the University of Auckland, which will be awarded competitively. For general information about PhD scholarships and the application process, visit www.math.auckland.ac.nz/future-postgraduates or email phdadvice@math.auckland.ac.nz.
Informal enquiries and expressions of interest about these projects should be addressed to b.krauskopf@auckland.ac.nz and/or n.broderick@auckland.ac.nz and/or s.parkins@auckland.ac.nz.
The Dodd-Walls Centre for Photonic and Quantum Technologies was established in 2014 as a multi-institution and multidisciplinary centre of research excellence by the NZ government. Our goal is to pursue world-leading research into all aspects of light-matter interactions from the fundamentals of quantum information theory to sensor development for NZ industry. The University of Auckland as the major research University within NZ is playing a major role in the DWC. This project will be part of the theme Sources and Components at The University of Auckland.
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