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Applications are invited from outstanding early-career researchers in Applied Mathematics or Mathematical Physics to work on the research project Understanding self-organisation in multi-scale systems. The Postdoctoral Fellowship is a two-year appointment and funded via the Science Core Self-Organisation of The Dodd-Walls Centre for Photonic and Quantum Technologies.
Self-organisation is a manifestation of emergent behaviour that arises from the coupling between the different parts of a complex system. This project will investigate such emergent behaviours from a fundamental point of view, examining their dependence on parameters that control the coupling as well as the underlying topology. The main focus will be on the case studies driving the development of new mathematical tools for understanding diverse self-organisation phenomena in contemporary photonic and quantum systems, providing new understanding and insights. The successful candidate has the skills and potential to contribute significantly to one of the following principal research directions:
(1) Coupling of excitable and pulsing multiple-timescale systems into a networked optical micro-device leads to synchronisation and locking properties in the presence of different time scales and spatial separation between subsystems. New tools will be needed to identify qualitative changes of the dynamics, including those due to creation and rearrangements of global dynamical objects, such as periodic and transient solutions.
(2) Mode-locking and synchronisation are organised by isochronal manifolds that depend on the coupling and scale parameters. Advanced computational tools for the study of isochrons have recently been used successfully to explain complex dynamics in low-dimensional systems. These tools will be adapted to understand synchronisation properties in larger-dimensional systems. Specifically, isochronal information can be used implicitly to extract changes and bifurcations in the phase-dynamics of optical systems.
(3) Pulse generation and other excitability phenomena are mediated by the crossing of a critical boundary, which is typically given by a globally invariant separatrix. In the presence of different time scales, which occur, e.g., in microlasers, this threshold can also be formed by a so-called transient manifold. Mechanisms involving transient manifolds are a current and active area of research that straddles developments of new theory as well as new computational methods.
The Fellowship is available immediately and the exact, feasible start date is to be agreed with the successful candidate as appropriate.
Contact
The successful candidate will join the research team led by Professors Hinke Osinga, Bernd Krauskopf and Neil Broderick at the Dodd-Walls Centre.
Informal enquiries and expressions of interest are welcome by email addressed to h.m.osinga@auckland.ac.nz, b.krauskopf@auckland.ac.nz and/or n.broderick@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 leading role in the DWC. This project will be part of the Science Core Self-Organisation at the University of Auckland.
How to apply
Applications should be sent by email to Professor Hinke Osinga; those received by 15 May 2022 will be given full consideration. Your application should include your CV, a research statement of no more than 1000 words that outlines your suitability as a candidate, and the names and email addresses of three academic referees who may be contacted in support of your application.
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.
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.
Copyright (c) 2022 by Bernd Krauskopf.