A Popular Pictorial Introduction to Chaos


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Predicting Climate Tipping Points

by

J Michael T Thompson (1, 2) and Jan Sieber (3)

(1) Dept of Applied Mathematics & Theoretical Physics, Cambridge University,
Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK.

(2) School of Engineering (Sixth Century Professor), Aberdeen University

(3) Dept of Mathematics, University of Portsmouth, Portsmouth, PO1 3HF, UK.

Abstract
There is currently much interest in examining climatic tipping points, to see if it is feasible to predict them in advance. Using techniques from bifurcation theory, recent work looks for a slowing down of the intrinsic transient responses, which is predicted to occur before an instability is encountered. This is done, for example, by determining the short-term autocorrelation coefficient ARC(1) in a sliding window of the time series: this stability coefficient should increase to unity at tipping. Such studies have been made both on climatic computer models and on real paleoclimate data preceding ancient tipping events. The latter employ re-constituted time-series provided by ice cores, sediments, etc, and seek to establish whether the actual tipping could have been accurately predicted in advance. One such example is the end of the Younger Dryas event, about 11,500 years ago, when the Arctic warmed by 7℃ in 50 years. A second gives an excellent prediction for the end of 'greenhouse' Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state, using data from tropical Pacific sediment cores. This prediction science is very young, but some encouraging results are already being obtained. Future analyses, relevant to geo-engineering, will clearly need to embrace both real data from improved monitoring instruments, and simulation data generated from increasingly sophisticated predictive models.

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Prepared as an extra Chapter for a book to be published by Cambridge University Press entitled Geo-Engineering Climate Change, edited by Brian Launder and Michael Thompson, to appear in 2009.
The book is based on the Theme Issue of Phil. Trans. R. Soc., A, Vol 366, No 1882, 2008 entitled Geoscale Engineering to avert Dangerous Climate Change (eds. B. Launder & J.M.T. Thompson).

Full paper (PDF)



Localised buckling, writhing and cutting of the DNA molecule

This section is based on Prof. J.M.T. Thompson's lecture in Budapest, Hungary, recorded in April 2008.

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Press release from the University of Aberdeen

University of Aberdeen - Leading scientist appointed to chair in Engineering



Chaos and Fractals: Understanding the Unpredictable (in two parts)

This section is based on Prof. J.M.T. Thompson's two-part studio lecture at DAMTP, Cambridge, recorded in June 2005.

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Instabilities and Catastrophes

This section is based on Prof. J.M.T. Thompson's lecture which was held at the University of Cambridge on 11th Nov. 2004.

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Golden Medal Lecture - Chaos and Fractals: History and Applications

A lecture on Chaos and Fractals delivered by Prof JMT Thompson at the 40th Anniversary Conference of the Institute of Mathematics and its Applications (IMA) at the University of Manchester on the 2nd of Sept 2004. At the meeting he was awarded a Gold Medal for contributions to mathematics.

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Chaos and Fractals: Understanding the Unpredictable

This section is based on Prof. J.M.T. Thompson's lecture which was held at the University of Cambridge on 22th Jan. 2004.

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The 2nd edition of the textbook about Chaos written by Prof. J.M.T. Thompson and Dr. H.B. Stewart
entitled "Nonlinear dynamics and chaos" is now available.
amazon.co.uk, amazon.com, amazon.co.jp.



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