scholarly journals Reporting on the Research Track on ‘Pricing and Optimization of Intraday/Day-Ahead Electricity and Futures Contracts’ Mathematics for Energy Systems Program Isaac Newton Institute

2019 ◽  
Author(s):  
Florentina Paraschiv
Keyword(s):  
Energy Systems ◽  
Futures Contracts ◽  
Isaac Newton ◽  
Isaac Newton Institute ◽  
Research Track

scholarly journals Introduction: the mathematics of energy systems

2021 ◽  
Vol 379 (2202) ◽  
pp. 20190425
Author(s):  
Pierluigi Mancarella ◽  
John Moriarty ◽  
Andy Philpott ◽  
Almut Veraart ◽  
Stan Zachary ◽  
...  
Keyword(s):  
Time Scales ◽  
Interdisciplinary Research ◽  
Energy Systems ◽  
Energy Markets ◽  
Theme Issue ◽  
Isaac Newton ◽  
Isaac Newton Institute ◽  
Mathematical Sciences ◽  
Power And Energy Systems ◽  
Power And Energy

The urgent need to decarbonize energy systems gives rise to many challenging areas of interdisciplinary research, bringing together mathematicians, physicists, engineers and economists. Renewable generation, especially wind and solar, is inherently highly variable and difficult to predict. The need to keep power and energy systems balanced on a second-by-second basis gives rise to problems of control and optimization, together with those of the management of liberalized energy markets. On the longer time scales of planning and investment, there are problems of physical and economic design. The papers in the present issue are written by some of the participants in a programme on the mathematics of energy systems which took place at the Isaac Newton Institute for Mathematical Sciences in Cambridge from January to May 2019—see http://www.newton.ac.uk/event/mes . This article is part of the theme issue ‘The mathematics of energy systems’.

scholarly journals Algebraic Properties of Chromatic Roots

10.37236/6578 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Peter J. Cameron ◽  
Kerri Morgan
Keyword(s):  
Algebraic Integer ◽  
Tutte Polynomial ◽  
Chromatic Polynomial ◽  
Galois Groups ◽  
Algebraic Numbers ◽  
Isaac Newton ◽  
Isaac Newton Institute ◽  
Chromatic Root ◽  
The Subject ◽  
Chromatic Roots

A chromatic root is a root of the chromatic polynomial of a graph.  Any chromatic root is an algebraic integer. Much is known about the location of chromatic roots in the real and complex numbers, but rather less about their properties as algebraic numbers. This question was the subject of a seminar at the Isaac Newton Institute in late 2008.  The purpose of this paper is to report on the seminar and subsequent developments.We conjecture that, for every algebraic integer $\alpha$, there is a natural number n such that $\alpha+n$ is a chromatic root. This is proved for quadratic integers; an extension to cubic integers has been found by Adam Bohn. The idea is to consider certain special classes of graphs for which the chromatic polynomial is a product of linear factors and one "interesting" factor of larger degree. We also report computational results on the Galois groups of irreducible factors of the chromatic polynomial for some special graphs. Finally, extensions to the Tutte polynomial are mentioned briefly.

scholarly journals Developments in turbulence research: a review based on the 1999 Programme of the Isaac Newton Institute, Cambridge

2001 ◽  
Vol 436 ◽  
pp. 353-391 ◽  
Author(s):  
J. C. R. HUNT ◽  
N. D. SANDHAM ◽  
J. C. VASSILICOS ◽  
B. E. LAUNDER ◽  
P. A. MONKEWITZ ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Numerical Simulations ◽  
Turbulent Flows ◽  
Small Scale ◽  
Isaac Newton ◽  
Eddy Simulation ◽  
Isaac Newton Institute ◽  
Large Eddy ◽  
Eddy Structures

Recent research is making progress in framing more precisely the basic dynamical and statistical questions about turbulence and in answering them. It is helping both to define the likely limits to current methods for modelling industrial and environmental turbulent flows, and to suggest new approaches to overcome these limitations. Our selective review is based on the themes and new results that emerged from more than 300 presentations during the Programme held in 1999 at the Isaac Newton Institute, Cambridge, UK, and on research reported elsewhere. A general conclusion is that, although turbulence is not a universal state of nature, there are certain statistical measures and kinematic features of the small-scale flow field that occur in most turbulent flows, while the large-scale eddy motions have qualitative similarities within particular types of turbulence defined by the mean flow, initial or boundary conditions, and in some cases, the range of Reynolds numbers involved. The forced transition to turbulence of laminar flows caused by strong external disturbances was shown to be highly dependent on their amplitude, location, and the type of flow. Global and elliptical instabilities explain much of the three-dimensional and sudden nature of the transition phenomena. A review of experimental results shows how the structure of turbulence, especially in shear flows, continues to change as the Reynolds number of the turbulence increases well above about 104 in ways that current numerical simulations cannot reproduce. Studies of the dynamics of small eddy structures and their mutual interactions indicate that there is a set of characteristic mechanisms in which vortices develop (vortex stretching, roll-up of instability sheets, formation of vortex tubes) and another set in which they break up (through instabilities and self- destructive interactions). Numerical simulations and theoretical arguments suggest that these often occur sequentially in randomly occurring cycles. The factors that determine the overall spectrum of turbulence were reviewed. For a narrow distribution of eddy scales, the form of the spectrum can be defined by characteristic forms of individual eddies. However, if the distribution covers a wide range of scales (as in elongated eddies in the ‘wall’ layer of turbulent boundary layers), they collectively determine the spectra (as assumed in classical theory). Mathematical analyses of the Navier–Stokes and Euler equations applied to eddy structures lead to certain limits being defined regarding the tendencies of the vorticity field to become infinitely large locally. Approximate solutions for eigen modes and Fourier components reveal striking features of the temporal, near-wall structure such as bursting, and of the very elongated, spatial spectra of sheared inhomogeneous turbulence; but other kinds of eddy concepts are needed in less structured parts of the turbulence. Renormalized perturbation methods can now calculate consistently, and in good agreement with experiment, the evolution of second- and third-order spectra of homogeneous and isotropic turbulence. The fact that these calculations do not explicitly include high-order moments and extreme events, suggests that they may play a minor role in the basic dynamics. New methods of approximate numerical simulations of the larger scales of turbulence or ‘very large eddy simulation’ (VLES) based on using statistical models for the smaller scales (as is common in meteorological modelling) enable some turbulent flows with a non-local and non-equilibrium structure, such as impinging or convective flows, to be calculated more efficiently than by using large eddy simulation (LES), and more accurately than by using ‘engineering’ models for statistics at a single point. Generally it is shown that where the turbulence in a fluid volume is changing rapidly and is very inhomogeneous there are flows where even the most complex ‘engineering’ Reynolds stress transport models are only satisfactory with some special adaptation; this may entail the use of transport equations for the third moments or non-universal modelling methods designed explicitly for particular types of flow. LES methods may also need flow-specific corrections for accurate modelling of different types of very high Reynolds number turbulent flow including those near rigid surfaces.This paper is dedicated to the memory of George Batchelor who was the inspiration of so much research in turbulence and who died on 30th March 2000. These results were presented at the last fluid mechanics seminar in DAMTP Cambridge that he attended in November 1999.

scholarly journals Sir Michael Atiyah OM. 22 April 1929–11 January 2019

2020 ◽  
Author(s):  
Nigel Hitchin
Keyword(s):  
Differential Operators ◽  
Global Analysis ◽  
Index Theorem ◽  
Theoretical Physics ◽  
Yang Mills ◽  
Isaac Newton ◽  
Isaac Newton Institute ◽  
Fields Medal ◽  
Elliptic Differential Operators ◽  
Mathematical Sciences

Michael Atiyah was the dominant figure in UK mathematics in the latter half of the twentieth century. He made outstanding contributions to geometry, topology, global analysis and, particularly over the last 30 years, to theoretical physics. Not only was he held in high esteem at a worldwide level, winning a Fields Medal in 1966, the Abel Prize in 2004 and innumerable other international awards, but his irrepressible energy and broad interests led him to take on many national roles too, including the presidency of the Royal Society, the mastership of Trinity College, Cambridge, and the founding directorship of the Isaac Newton Institute for Mathematical Sciences. His most notable mathematical achievement, with Isadore Singer, is the index theorem, which occupied him for over 20 years, generating results in topology, geometry and number theory using the analysis of elliptic differential operators. Then, in mid life, he learned that theoretical physicists also needed the theorem and this opened the door to an interaction between the two disciplines that he pursued energetically until the end of his life. It led him not only to mathematical results on the Yang--Mills equations that the physicists were seeking, but also to encouraging the importation of concepts from quantum field theory into pure mathematics.

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