Eoin O’Colgain has been awarded a Marie Curie Fellowship, funded by the EU.  The project was proposed by Kostas Sfetsos along with Martin Rocek (Stonybrook).  The fellowship is expected to start in Autumn 2013.  Eoin is currently a research fellow at the Universidad de Oviedo, supported by a Juan de la Cierva Fellowship from the Spanish government.  His research interests are in the areas of supersymmetry and gravity.  Solutions to higher-dimensional supergravity correspond to string theory vacua, and it is of interest to combine supersymmetric geometries, consistent dimensional reductions and various dualities.  All three serve to generate higher-dimensional supergravity solutions that may offer some unifying description of our four-dimensional universe.  An interview with Eoin can be found here.

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Dr Alessio Camobreco (University of Parma) has been awarded a Della Riccia Fellowship.  The fellowship provides funds for a 6-9 month visit to the University of Surrey.  His visit, hosted by Alessandro Torrielli, will commence sometime in 2013. His PhD work (supervised by Prof Marisa Bonini) has been on the pure spinor formulation of the AdS string.

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The book “Invisible in the storm: the role of mathematics in understanding weather” is due to be published by Princeton University Press in February 2013.  The authors are John Norbury (Oxford) and Ian Roulstone. It is the first book to recount the history, personalities, and ideas behind one of the greatest scientific successes of modern times — the use of mathematics in weather prediction. Although humans have tried to forecast weather for millennia, mathematical principles were used in meteorology only after the turn of the twentieth century. From the first proposal for using mathematics to predict weather, to the supercomputers that now process meteorological information gathered from satellites and weather stations, Ian Roulstone and John Norbury narrate the groundbreaking evolution of modern forecasting.

The authors begin with Vilhelm Bjerknes, a Norwegian physicist and meteorologist who in 1904 came up with a method now known as numerical weather prediction. Although his proposed calculations could not be implemented without computers, his early attempts, along with those of Lewis Fry Richardson, marked a turning point in atmospheric science. Roulstone and Norbury describe the discovery of chaos theory’s butterfly effect, in which tiny variations in initial conditions produce large variations in the long-term behavior of a system–dashing the hopes of perfect predictability for weather patterns. They explore how weather forecasters today formulate their ideas through state-of-the-art mathematics, taking into account limitations to predictability. Millions of variables — known, unknown, and approximate — as well as billions of calculations, are involved in every forecast, producing informative and fascinating modern computer simulations of the Earth system.

The Princeton University Press website announcing the publication of the book is here.

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A paper of Michele Bartuccelli, Jonathan Deane and Guido Gentile appeared in the October issue of the Journal of Mathematical Physics.  The title of the paper is “Attractiveness of periodic orbits in parametrically-forced systems with time-increasing friction“.  The paper considers dissipative one-dimensional systems subject to a periodic force.  As a model system, particularly suited for numerical analysis, the driven cubic oscillator in the presence of friction is investigated, and the effect of time-varying friction is studied numerically.  The relevance of the results for the spin-orbit model in celestial mechanics is discussed in some detail.  The JMP webpage for the paper is here.

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Zbynek Urban from the Lepage Research Institute in the Czech Republic visited the department for the month of October.  During his visit he interacted with Peter Hydon, Cesare Tronci and Tom Bridges.  Zbynek works in differential geometry, specifically fibre bundles, variational principles, Grassmann fibrations, and variational sequences.

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Congratulations to Jessica Rowden on successfully passing her PhD confirmation examination. The examiner was Mark Roberts and the project is co-supervised by David Lloyd and Nigel Gilbert (Sociology). The project title is “Multi-level mathematical models of the real world“.  This project is part of the programme on Evolution and Resilience of Industrial Ecosystems (ERIE).

The aim of the project is to create multi-level mathematical models that use empirical data to simulate the real world. In this context the “real world” is a complex system or network which has been established over time by nature and/or human evolvement. This research combines ideas and techniques from disciplines like mathematics, social science, and political science, to create the models.

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The paper of Michele Bartuccelli, Jonathan Deane and Sergey Zelik, entitled “Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus” has been accepted for publication in the Proceedings of the Royal Society of Edinburgh.  The paper gives a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best constants, various remainder terms and so on.  Most attention is paid to the critical (logarithmic) Sobolev inequality in the two-dimensional case, although a number of results concerning the best constants in the algebraic case and different space dimensions are also obtained.  An electronic copy of the final-form preprint is available here.

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Gianne Derks, David Lloyd and Tom Bridges attended the SIAM Conference on Nonlinear Waves and Coherent Structures held at the University of Washington in Seattle in June 2012.  Gianne Derks gave an invited minisymposium talk on “Viscosity-induced instability for Euler and averaged Euler equations in a circular domain“.  David Lloyd gave an invited minisymposium talk on “Hamiltonian structure of the ferrofluid problem” and also presented a poster on “Localized patterns on the surface of a magnetic field“.  Tom Bridges co-organized a three-session mini-symposium with Frederic Chardard (ENS Lyon) and also gave a mini-symposium talk on “Emergence of unsteady dark solitary waves from large-amplitude periodic patterns“.  The website for the NW12 conference is here.

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Congratulations to Elisabet Herrera Sucarrat who passed her PhD viva on Thursday 22 November.  Her thesis title is “The full problem of two and three bodies: application to asteroids and binaries“.  The external examiner was Apostolos Christou (Armagh Observatory) and the internal examiner was Stephen Gourley.  The project is supervised by Mark Roberts and Phil Palmer (SSC).

An abstract of her thesis follows.  The smallest bodies of our Solar System, such as asteroids and comets, are characterized by very irregular sizes and shapes and therefore, very irregular gravitational fields. Moreover, asteroids are commonly found in binary or multiple systems, which allow for complicated dynamics with coupling between translational and rotational motion. Classical problems used to study astrodynamics such as Kepler’s problem, Hill’s equations or the Restricted Three Body Problem cannot describe the dynamics near asteroids and comets as they do not take into account the non-spherical shape of the bodies.

In this thesis, the non-linear dynamical environment around rotating non-spherical bodies or around binary systems when at least one of the bodies is not spherical has been studied. The study consists of the analysis of different mathematical models that can be used to describe the movement of massless particles, such as dust or a spacecraft, orbiting an elongated body, the dynamics between the components of a binary system, or a spacecraft orbiting the vicinity of a binary asteroid. In order to do this an analysis and development of gravitational potentials has been performed. A gravitational potential that takes the shape of the non-spherical bodies into account has allowed us to describe the movement of the dusty environment of an asteroid, to design trajectories to approach and observe an asteroid, and even land on it. Furthermore, the effect of the shape and rotation period of asteroids and binaries on the dynamics has been studied.

The fact that asteroids and comets are not point masses but elongated irregular bodies leads to a rich dynamics around them. Equilibrium points, periodic orbits and invariant manifolds exist in their vicinity. These are used in this thesis to design low cost landing missions to asteroids, understand the dynamics of binary systems or to explain a possible mechanism for the accretion of mass and formation of the Solar System.

 

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Peter Hydon has been appointed to the editorial board of the “LMS Journal of Computation and Mathematics“.  The aim of the LMS JCM is to publish internationally-leading papers addressing topics in computational pure and applied mathematics, including papers at the interface between mathematics and computer science.  The LMS JCM is an electronic-only open-access journal. The journal website is here.

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