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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 behind 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, where varying delays arise from the coupling between Pacific Ocean and atmosphere, will serve as a prototypical test-case example of immediate relevance.
Two PhD projects are on offer.
Climate models with variable delays.
The task will be to derive appropriate functional forms for the state dependence of delays associated with positive and negative feedback loops, starting with DDE models of the ENSO system. To this end, we will consider details of the coupled ocean-atmosphere feedbacks, including the thermocline-shape dependence of wave speeds and the spatial dependence of the upwelling phenomena.The consequences of the different types of feedback loops, individually and in combination, will then be determined. This project offers opportunities for collaborations with Professor Jan Sieber (University of Exeter, UK) and Professor Henk Dijkstra (Utrecht University, The Netherlands).
The mathematics of state-dependent DDEs
The task is to perform a systematic analysis of how different types of state-dependent terms influence the observed behaviour of delay differential equation (DDE) models. The classes of DDEs considered take a more fundamental form, but are directly motivated by models arising in climate science, especially those for ENSO. A starting point of the work will be the question how well-known bifurcations are influenced by the presence of state-dependence. This project offers the opportunity for collaboration with Professor Tony Humphries (McGill University, Montreal, Canada).
Both projects 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 for these PhD projects 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 firstname.lastname@example.org.
Informal enquiries and expressions of interest should be addressed to email@example.com.
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 firstname.lastname@example.org.
Informal enquiries and expressions of interest should be addressed to email@example.com and/or firstname.lastname@example.org.
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.
Copyright (c) 2018 by Bernd Krauskopf.