Seminar history



2012-05-11	Fri	Andrew Gascoyne (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	PARTICLE TRAJECTORIES AND ACCELERATION DUE TO 3D MAGNETIC RECONNECTION

	Abstract: Magnetic reconnection is thought to be a primary mechanism in the acceleration of particles during flares in the solar corona. Particle acceleration by reconnection has been widely studied in 2D geometry, and thanks to recent work, particle acceleration in 3D is being investigated. We investigate the trajectories and acceleration of a particle injected into various 3D magnetic and electric field configurations by adopting a test particle approach. The electromagnetic fields studied here are solutions to the steady state, kinematic, resistive MHD equations (Wyper and Jain 2010). We numerically solve the equations that govern the motion of a charged particle in these electromagnetic fields and for various initial conditions, we analyse the kinetic energy of the particle and determine the regimes where efficient particle acceleration takes place.

2012-05-09	Wed	Dr Anantanarayanan Thyagaraja (Culham)
14:00	LT6

2012-05-09	Wed	Anantanarayanan Thyagaraja (Bristol)	Applied Maths Colloquium
14:00	LT6	A KdV-like advection-diffusion equation with remarkable properties

	Abstract: Nonlinear partial differential equations which arise naturally in the the- ory of wave propagation in many branches of physics have both a rich history and wealth of novel properties, not shared by their linearized equivalents. The Korteweg-de Vries Equation (KdVE), which is now more than 100 years old, occupies a special place in this class, along with the complex Nonlinear Schro ̈dinger Equation (NLSE), and forms the core of the modern theory of the Inverse-Scattering-Transform tech- nique of solving equations of this type. Some colleagues and I have recently encountered a close �cousin� of this equation [cf. Abhijit Sen et al, (2012), in press, Communications in Nonlinear Science and Numerical Simulations, also available as an ArXiv preprint] which has novel and interesting properties. It arose in a curious way during a �ge- netic programming� search looking for equations which share solutions in common with the KdVE. In this talk, I will outline some of the more in- teresting features of this equation which also serves as a counter-example to some commonly held views about recurrent solutions in certain con- servative nonlinear dispersive wave equations. The new equation also has some properties which are not shared by the KdVE and appears to define a new class of interesting nonlinear partial differential equations describing wave motions.

2012-05-04	Fri	Michael Bareford (University of St Andrews)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	The Energy Released from Relaxing Coronal Loops

	Abstract: Relaxation theory offers a straightforward method for determining the energy released from a magnetic field when it undergoes an instability. Thus, an upper limit to the heating caused by ensembles of coronal loops can be estimated and compared with the coronal heating requirement. This talk will discuss the results obtained from the nonlinear magnetohydrodynamic (MHD) simulations of a sample of idealised coronal loops that are known to be linearly kink unstable. The principle aim is to determine whether or not these results agree with helicity-conserving Taylor relaxation (Taylor 1986, 1974). A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of specific line-tied field configurations based on a cylindrical coronal loop model. Initially, all configurations carry zero net current and are in ideally unstable equilibrium. Helicity is conserved to an acceptable level for all numerically-stable simulations. In addition, the energy release and final field profiles produced by the numerical simulations are in agreement with the predictions of relaxation theory: the relaxed field approximates a linear force-free state. Magnetic energy dissipation predominantly occurs within thin currents sheets. These results support the use of relaxation theory for calculating the heating-event distributions produced by ensembles of marginally unstable loops (Bareford et al. 2011). Bareford, M. R., Browning, P. K.,			Van der Linden, R. A. M. 2011, Sol.Phys., 273, 93 Taylor, J. B. 1986, Rev. Mod. Phys., 58, 741 Taylor, J. B. 1974, Phys. Rev. Lett., 33, 1139

2012-04-27	Fri	Peter Whyper (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2012-04-25	Wed	Nick Monk (Sheffield)	Applied Maths Colloquium
14:00	LT6	Modelling decision making in multicellular tissues.

	Abstract: During the development of multicellular organisms, cells need to make decisions about their fate by integrating information from their neighbours, their surroundings, and their history. I will describe mathematical models of cellular decision making that reveal how cells can adopt different strategies depending on their setting, allowing them to make either rapid coordinated decisions or more measured decisions that provide more scope for the generation of cellular diversity.

2012-04-02	Mon	Dr Dipankar Banerjee (Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India)	SP2RC Friday Seminars
10:00	Lecture Theatre 9	Propagating Disturbances in open and closed magnetic structures of the Sun

	Abstract: Propagating disturbances are observed along open and closed magnetic structures of the sun. For characterizing the nature of the propagating disturbances a combination of spectroscopy and imaging is essential. In this talk I will show examples of such observations using SUMER/SoHO, EIS/Hinode with imaging sequences from AIA/SDO. We find two different groups of periodicities, short (<3 min) and long (>9 min) at different locations and circumstances. In the short range we find oscillations with periodicities as low as 50 s. Shorter periodicities show oscillations inall the three line parameters and the longer ones only show in intensity and Doppler shift butnot in line width. Often Line profiles at these locations do not show any visible blue-shiftedcomponent and can be fitted well with a single Gaussian. This allows us to conclude that the propagating disturbances represent waves and not flows. In the last part of my Talk I will also provide an update on the current status of the two large Indian solar observatory projects, namely the space coronagraph project called /Aditya/ and ground based facility from Himalayas called /NLST/.

2012-03-23	Fri	Nabil Freji (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	MHD Sausage Oscillations in Magnetic Wave guides in the lower Solar Atmosphere

	Abstract: The lower solar atmosphere is host to a wide range of magnetic wave guides. From sunspots to inter-granular bright points, they are constantly buffeted by the surrounding photosphere from granulation, p-modes or by coherent sub-photospheric drivers. Here, we present the results of an observational study of MHD sausage waves in magnetic wave guides (pores and sunspots). By studying the temporal variations in area and intensity of these magnetic wave guides, it allows the observation and identification of MHD sausage waves. Using series of high-resolution intensity images with a small cadence and employing wavelet analysis in conjunction with empirical mode decomposition allows us to have a robust method for searching for and identifying characteristic periods hidden in the area and intensity data series. We found that the magnetic pore in Active Region 10968 displays three strong periods, 2-3, 8 and 13-14 minutes. The most plausible conclusion is that both the 2-3 and 8 minute periods detected are a harmonic of the fundamental 13-14 minute period. Due to the sharp gradients in the background equilibrium plasma parameters that exist at the boundaries of the photosphere and the transition region sets up a cavity that can support standing waves. This is the first observation of concurrent higher harmonics in a solar magnetic wave-guide in the lower solar atmosphere while the third reported observation of sausage modes in solar pores.

2012-03-21	Wed	Alex Best (Sheffield)	Applied Maths Colloquium
14:00	LT6	Modelling the coevolution of parasites and their hosts

	Abstract: Understanding the dynamics of infectious diseases in human, animal and plant hosts is one of the biggest challenges for modern science, with considerable health, social and financial implications. Mathematical models of these host-parasite interactions can allow us to understand and predict the behaviour of many disease systems. Here I shall focus on the evolutionary dynamics of parasites and hosts, applying the evolutionary framework of adaptive dynamics to a classic model of host-parasite interactions. I shall show how parasite infectivity and host defence may be expected to evolve, both in isolation and when they coevolve with one another. Throughout I shall highlight the important role of the evolutionary trade-offs on the eventual outcome, particularly focussing on the potential for variation to arise through evolutionary branching.

2012-03-16	Fri	Khalil Al-Ghafri (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	The effect of variable background on oscillating hot coronal loop due to thermal conduction

	Abstract: We investigate the effect of a variable, i.e. time-dependent, background on the standing acoustic (i.e. longitudinal) modes generated in a hot coronal loop. A theoretical model of 1D geometry describing the coronal loop is applied. The background temperature is allowed to change as a function of time and undergoes an exponential decay with characteristic cooling times typical for coronal loops. The magnetic field is assumed to be uniform. Thermal conduction is the dominant mechanism of cooling the hot background plasma in the presence of an unspecified thermodynamic source that maintains the initial equilibrium. The influence of the rapidly cooling background plasma on the behaviour of standing acoustic (longitudinal) waves is investigated analytically. The temporally evolving dispersion relation and wave amplitude are derived by using the WKB theory. An analytic solution for the time-dependent amplitude that describes the influence of thermal conduction on the standing longitudinal (acoustic) wave is obtained by exploiting the properties of Sturm-Liouville problems. Next, numerical evaluations further illustrate the behaviour of the standing acoustic waves in a system with variable, time dependent background. The results are applied to a number of detected loop oscillations. We find a remarkable agreement between the theoretical predictions and the observations. The cooling of the background plasma due to thermal conduction is found to cause a strong damping for the slow standing magneto-acoustic waves in hot coronal loops in general. Further to this, the increase in the value of thermal conductivity leads to a strong decay in the amplitude of the longitudinal standing slow MHD waves.

2012-03-14	Wed	Joab Winkler (Sheffield)	Applied Maths Colloquium
14:00	LT6	The computation of multiple roots of polynomials whose coefficients are inexact

	Abstract: This lecture will show by example some of the problems that occur when the roots of a polynomial are computed using a standard polynomial root solver. In particular, polynomials of high degree with a large number of multiple roots will be considered, and it will be shown that even roundoff error due to floating point arithmetic, in the absence of data errors, is sufficient to cause totally incorrect results to be obtained. Since data errors are usually larger than roundoff errors (and fundamentally different in character), the errors encountered with real world data are significant and emphasise the need for a computationally robust polynomial root solver. The inability of commonly used polynomial root solvers to compute high degree multiple roots correctly requires investigation. A method developed by Gauss for computing the roots of a polynomial will be discussed, and it will be shown that it has an elegant geometric interpretation in terms of pejorative manifolds, which were introduced by William Kahan (Berkeley). Polynomials defined by points on these manifolds satisfy properties that are fundamentally different from the properties of polynomials defined by points that are not on these manifolds. The numerical interpretation of this difference provides the motivation for the method of Gauss, and the geometric properties of pejorative manifolds will therefore be emphasised and considered in detail. Furthermore, these properties explain why multiple roots are preserved in a floating point environment when the coefficients of the polynomial are corrupted by noise. This numerical interpretation leads naturally to a discussion of a structured condition number of a root of a polynomial, where structure refers to the form of the perturbations that are applied to the coefficients. It will be shown that this structured condition number, where the perturbations are such that the multi- plicities of the roots are preserved, differs significantly from the standard componentwise and normwise condition numbers, which refer to random (unstructured) perturbations of the coefficients. Several ex- amples will be given and it will be shown that the condition number of a multiple root of a polynomial due to a random perturbation in the coefficients is large, but the structured condition number of the same root is small. This large difference is typically several orders of magnitude. The computational implementation of the method of Gauss raises some non-trivial issues � the determi- nation of the rank of a matrix in a floating point environment and the quotient of two inexact polynomials � and they will be discussed because they are ill-posed operations. They must be implemented with care because simple methods will necessarily lead to incorrect results. Furthermore, problems occur when the coefficients of the polynomial span several orders of magnitude, in which case the polynomial must be processed before its roots are computed in order to guarantee computationally reliable arithmetic operations. I will finish the talk by demonstrating Matlab code that implements the method on several high degree polynomials whose coefficients have been corrupted by noise and whose theoretically exact forms have multiple roots of high degree.

2012-03-08	Thu	Ari Laptev (Imperial)	SoMaS Colloquium
17:30	LT7	Spectral Inequalities for Partial Differential Equations and their Applications

	Abstract: We shall discuss properties of the discrete and continuous spectrum of different classes of self-adjoint differential operators including Schr�dinger operators.

2012-03-07	Wed	John Hinch (Cambridge)	Applied Maths Colloquium
14:00		Large drops of a power-law fluid in a thin film on a vertical fibre

	Abstract: We study a thin liquid film on a vertical fibre. Without gravity, there is a Rayleigh-Plateau instability in which surface tension reduces the surface area of the initially cylindrical film. Spherical drops cannot form because of the fibre, and instead, the film forms bulges of roughly twice the initial thickness. Large bulges then grow very slowly through a ripening mechanism. A small non-dimensional gravity moves the bulges. They leave behind a thinner film than that in front of them, and so grow. As they grow into large drops, they move faster and grow faster. When gravity is stronger, the bulges grow only to finite amplitude solitary waves, with equal film thickness behind and in front. We study these solitary waves, and the effect of shear-thinning and shear-thickening of the fluid. In particular, we will be interested in solitary waves of large amplitudes, which occur near the boundary between large and small gravity. Frustratingly, the speed is only determined at the third term in an asymptotic expansion. The case of Newtonian fluids requires four term.

2012-02-29	Wed	Ati Sharma (Sheffield)	Applied Maths Colloquium
14:00	LT6	Predicting structure in turbulence

	Abstract: How to find a simple model that predicts the important structural and statistical features of turbulence is a central unsolved problem in classical physics. Most commonly found flows are turbulent, for instance flow of air over an aeroplane wing or water past a ship's hull, flow of oil through an trans-continental pipeline, or the movement of the atmosphere. All these flows experience chaotic three-dimensional motion, but nonetheless show persistent, repeating structure. This talk will cover significant new advances, involving the application of systems-theoretic ideas to the equations governing turbulence, which predict these structures. The computationally cheap approach explains and predicts structures and velocity statistics that have previously been identified only in experiments or by direct numerical simulation. Short Biography After graduating as a physicist from UCL, Dr Sharma completed his doctoral thesis in control engineering at Imperial College, London on the modelling and control of tokamak nuclear fusion reactors. Following two years in industry, he returned to academia as a postdoc to work on fluid flow control, and was then awarded an Imperial College Junior Research Fellowship in that area. Dr Sharma joined ACSE as a lecturer in July.

2012-02-24	Fri	Richard Morton (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2012-02-10	Fri	Giuseppe Colantuono (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	A simple model to evaluate photovoltaics with energy storage: initial results and ideas

	Abstract: Energy storage can be a means of smoothing out the unpredictability of "green" energy sources and increase the availability of power at times of peak demand. Efforts for integrating photovoltaics (PV) with batteries are already going on, even if they still suffer from high costs. A possible metric to evaluate the impact of storage coupled to a PV array is "Loss Of Load Hours" (LOLH). LOLH represents the total amount of time, for a given period (e.g one month), during which the demand (e.g. the power usage of the home where the PV array is installed) cannot be satisfied and electricity must be drawn from the grid. An analogous measure is the total time during which the battery is fully charged, energy cannot be stored any longer and is therefore uploaded to the grid. A simple model for the computation of LOLH will be presented . The inputs of the model are given by the timeseries of the solar irradiance incident on the PV array and the timeseries of the power load. Some preliminary results and possible developments for both real-world and idealized loads will be discussed.

2012-02-08	Wed	Paul Linden (Cambridge)	Applied Maths Colloquium
14:20	LT6	Gravity-driven flows in stratified fluids

	Abstract: This talk will describe experiments on flows driven by horizontal density gradients in fluids which are stably stratified. Examples are intrusions on density interfaces or in stratified ambient fluids, and cases where the intruding fluid is also stably stratified. Traditional approaches that have been applied to unstratified fluids have been to use ideas of energy conversion from available potential energy to kinetic energy to predict the speeds of the gravity-driven flows, which in this simple case are gravity currents. I will explore how well these approaches work in systems which can support internal waves and discuss the resulting dynamics.

2011-12-14	Wed	Stephen Coombes (Nottingham)	Applied Maths Colloquium
14:00	LT10	Patterns and waves in cortical models

	Abstract: The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. Here I will present an overview of these techniques, and discuss the relevance of neural field models for describing the brain at the large scales necessary for interpreting EEG data. I will also discuss recent results on an interface approach for describing the evolution of intricate labyrinthine structures seen in planar neural field models.

2011-12-09	Fri	Adam Scaife (Met Office Hadley Centre)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Solar Variability Forcing of Regional Winter Climate in the Northern Hemisphere

	Abstract: An influence of solar irradiance variations on Earth�s surface climate has been repeatedly suggested, based on correlations between solar variability and meteorological variables. Specifically, weaker westerly winds have been observed in winters with a less active sun, for example at the minimum phase of the 11-year solar cycle. It has proved difficult for climate models to consistently reproduce this signal. However, recent Spectral Irradiance Monitor (SIM) satellite measurements indicate that variations in solar ultraviolet irradiance may be larger than previously thought. In this talk we will review some of the historical evidence for these links and then show what happens when we drive an ocean�atmosphere climate model with ultraviolet irradiance variations based on the SIM observations. We find that the model responds to the solar minimum with patterns in surface pressure and temperature that resemble the negative phase of the North Atlantic or Arctic Oscillation (a signature associated with cold conditions in northern Europe) and are of similar magnitude to observations. The signal descends through the depth of the extratropical winter atmosphere. If the updated measurements of solar ultraviolet irradiance are correct, low solar activity, as observed during recent years, drives cold winters in northern Europe and the United States, and mild winters over southern Europe and Canada. Note that there is little direct change in globally averaged temperature and therefore no impact on the anthropogenic interpretation of global warming. However, given the quasi-regularity of the 11-year solar cycle, our findings suggest a potentially important application in improving decadal climate predictions for highly populated extratropical regions in winter.

2011-12-02	Fri	Michael K Griffiths (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Computational Magnetohydrodynamics Using Graphical Processing Units

	Abstract: Parallel MHD algorithms are important for numerical modelling of astrophysical plasmas. Parallelisation techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPU's) possessing hundreds of processing units. The success has been recognised by the computational science and engineering commuinties who have harnessed the computational power of GPU's. In this seminar we describe the implementation of Magnetohydrodynamic codes for gravitationally stratified media on GPU's. We present the numerical methods used and the techniques for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the presentation of validation results and performance benchmarks.

2011-11-25	Fri	James McLaughlin (Northumbria University)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-11-23	Wed	Zhivko Stoyanov (Reading)	Applied Maths Colloquium
14:15	LT10	Communicability in the brain

	Abstract: Given a network of relationships between people, we naturally want to find the "big players" in the network. Furthermore, with the constant progress in technology, we are now able to capture the interactions between people in real time. We no longer have a static, but an evolving network of relationships. So we can now trace the flow of information on the network (passing of rumours, etc.). Therefore the term "big players" could have different meanings: it might mean people who are great broadcasters, but it could also mean people who are great receivers. Marketing companies, for example, might want to find the most influential people in the network, while the MoD could be interested in approaching the people with most information about the network. I will be interested in both: broadcasters and receivers, but instead of a social network, I shall be looking at the brain. In this talk I will suggest a simple way of using fMRI data to represent the brain as an evolving network. Then, using Network Theory and, in particular, a recently introduced notion of communicability, I will show a way to calculate the communicability score of each voxel (the 3D version of a pixel) in the brain. This score, which might be seen as a possible generalisation of PageRank, determines the extent to which a particular voxel is a broadcaster or a receiver. However, in our case there are around one million voxels in the brain. So there is little use in knowing the score for each voxel. Therefore, I shall discuss our attempt at summarising this information using the Discrete Fourier Transform. Furthermore, once we have "compressed" the communicability of the brain, I will try to discriminate between brains with a clinically diagnosed condition and healthy brains, using simple tools from Bayesian Statistics.

2011-11-18	Fri	Amy Scott (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-11-16	Wed	Chuong Van Tran (St Andrews)	Applied Maths Colloquium
14:00	LT10	A dynamical systems approach to fluid turbulence

	Abstract: This seminar presents an analytic approach to fluid turbulence as an alternative to Kolmogorov's phenomenology. The new approach uses basic elements and concepts in dynamical systems theory and applies to a variety of fluid models, allowing us to recover key predictions made by the classical method. These include the number of degrees of freedom, the dissipation wavenumber and the exponent of the power-law energy spectrum of the inertial range. The two-dimensional surface quasi-geostrophic and magnetohydrodynamic systems are used as illustrative examples, with the theoretical predictions corroborated by numerical results.

2011-11-09	Wed	Johan Anderson (Chalmers)	Applied Maths Colloquium
14:00	LT10

2011-11-04	Fri	Andrew Newton (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-11-02	Wed	William George (Chalmers)	Applied Maths Colloquium
14:00	LT10	Reconsidering Kolmogov for Non-stationary Turbulent Flows

	Abstract: One of the most important contributions to turbulence over the past century was the theory of Kolmogorov 1941. Since its introduction to the western world by Batchelor in 1946 it has dominated turbulence, both the interpretation of experiments and the development of turbulence models and scaling laws. It has been commonly assumed since the tidal channel measurements of Grant et al. 1961 that experiments have been uniformly supportive and that the coefficients are universal. Unfortunately the most important parameter, the turbulent dissipation, can almost never be measured directly and quite frequently is determined by `fitting' the measured data to the `established' results. Thus the `perfect' agreement is largely illusory, and in fact there is a considerable disagreement about what the `universal' constants are (or even if they are universal). Also it is seldom pointed out that almost all of the experiments cited are in statistical equilibrium, so that Kolmogorov's crucial first hypothesis of `local' equilibrium is statisfied identically. Thus none of these experiments can be regarded as a test of its generality. Worse, recent experiments and DNS in non-stationary turbulence show significant departures from Kolmolgorov behavior. These non-stationary homogeneous experiments are, however, consistent with the equilibrium similarity theory of George 1992 for these flows. So together the non-stationary theory and experiments together provide some confidence in these iconoclastic results. Therefore they present by counter-example a challenge to the Kolmogorov-based ideas for non-stationary flows, suggesting that we need to modify at least one of our fundamental beliefs.

2011-10-26	Wed	Rekha Jain (Sheffield)	Applied Maths Colloquium
14:00	LT10	Absorption and scattering of acoustic waves by thin magnetic flux tubes in a gravitationally stratified atmosphere

	Abstract: The sun's acoustic oscillations, p-modes, are observed to have more than half of their power absorbed by sunspots and almost 20-30 strong phase shifts but plages lack measurable phase shifts. The magnetic field within these structures is complex and highly structured which makes helioseismic observations troublesome to interpret and model. We study the propagation of acoustic waves through regions of plage, modeling the magnetic field therein as a collection of thin flux tubes. In this talk, I will present the background to this problem followed by the computation of the absorption and scattering coefficients arising from a single, axisymmetric magnetic tube. Implications for the measured absorption and phase shifts will also be discussed.

2011-10-24	Mon	Carsten van de Bruck (Sheffield)	CRAG
16:00	Hicks Seminar Room F41	Sections 3.1 - 3.6 of Zwiebach's string theory book

2011-10-21	Fri	Viktor Fedun (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-10-19	Wed	John Billingham (Nottingham)	Applied Maths Colloquium
14:00	LT10	How do droplets climb up a vibrating hill?

	Abstract: Recent experiments by Phillipe Brunet have shown that when a millimetric droplet of fluid is placed on a slope that strongly vibrates vertically it can climb up the slope. In this talk I will present some shallow water models for this phenomenon. I will begin with a model that includes just surface tension and the applied acceleration, but which can be solved numerically in its three-dimensional form. This model cannot capture the phenomenon. I will then include the effect of inertia in a two-dimensional model. The interaction of swaying and spreading modes of oscillation can cause the droplet to rise. However, we find that the behaviour of the moving contact lines is not realistic. Finally, we include the effect of viscosity, and model the moving contact lines more carefully.

2011-10-17	Mon	Carsten van de Bruck (Sheffield)	CRAG
16:00	Hicks Lecture Theatre 9	Chapter 2 of Zwiebach's string theory book

2011-10-12	Wed	Pieter Kok (Sheffield)	Applied Maths Colloquium
14:00	LT10	The ultimate limits to quantum measurements

	Abstract: Precision measurements are the cornerstone of the scientific enterprise, and whenever new measurement techniques have become available, new natural phenomena were discovered. One important question is therefore what the ultimate limits to precision measurements are. In particular, what is the best precision we can achieve with a particular quantum mechanical setup given a certain amount of resources? Traditionally, this question is answered in quantum mechanics by the so-called Heisenberg limit. However, there have been recent claims that this limit is broken. We demonstrate that the Heisenberg limit is in fact optimal for all parameter estimation procedures in quantum metrology, but it requires careful consideration as to which resource is appropriate for expressing the scaling behaviour of the precision.

2011-10-10	Mon	Brief research updates	CRAG
16:00	Hicks Seminar Room F41

2011-10-07	Fri	Richard Morton (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Solar jets and magneto-seismology

	Abstract: Solar jets are a common feature in the chromosphere, transition region and corona and are suspected to play a major role in determining the energy and mass balance in the upper atmosphere. Due to limitations on board the imaging satellites such as Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) and Hinode, determining the features of these jets geometry and plasma properties proves challenging. As demonstrated for coronal loops, magneto-seismology can play a role in helping to estimate otherwise unmeasurable plasma parameters. I present the observations of a UV/EUV 'blow-out' solar jet using SDO/AIA. In particular we focus on a thin dark thread seen to rise with jet. The thread supports a propagating kink wave, which we analyse and exploit with magneto-seismology. We are able to estimate the plasma temperature, density gradient, magnetic field gradient and sub-resolution expansion of the dark thread. The dark thread is found to be cool (3x10^4 K) with both strong density and magnetic field gradients. The expansion of the flux tube along its length is 300-400km.

2011-10-03	Mon	Brief research updates	CRAG
16:00	Hicks Lecture Theatre 9

2011-09-26	Mon	Susan Vu/Victor Ambrus (Sheffield)	CRAG
16:00	Hicks Seminar Room F30	Inflationary cosmology and string theory/Rotating fermions

2011-09-21	Wed	Sam Dolan (University of Southampton)	CRAG
14:30	See schedule	Self-force calculations for black hole inspirals

	Abstract: Advances in numerical relativity (NR) since 2005 have led to rapid progress in the modelling of black hole inspirals. Yet an important frontier awaits: the large mass-ratio regime. For example, in the final year before merger, an Extreme Mass-Ratio Inspiral (EMRI) will undergo 10^5 orbits in the strong-field regime. EMRIs may be analysed via black hole perturbation theory, by assuming the small body follows a trajectory on the background spacetime of the large black hole, and that the trajectory is perturbed away from a geodesic of the background by a `self-force'. Practical methods for computing self-force effects at first order in the mass ratio are now well-established. In this short review, I will focus on four emerging themes in the self-force programme: (i) comparison of gauge-invariant results from gravitational self-force (GSF) calculations with other methodologies (e.g. Post-Newtonian, EOB and NR); (ii) ongoing development of numerical schemes for highly accurate calculations of GSF on Kerr spacetime; (iii) aspirations to achieve accurate, self-consistent long-term orbital evolutions of EMRIs using GSF calculations; (iv) understanding of qualitatively new phenomena, such as resonances [arXiv:1009.4923], which have practical implications for data analysis strategies.

2011-06-27	Mon	Elizabeth Winstanley (Sheffield)	CRAG
16:00	See schedule	Asymptotically Lifshitz space-times

2011-06-20	Mon	Elizabeth Winstanley (Sheffield)	CRAG
16:00	See schedule	Kerr black holes

2011-06-13	Mon	Ben Shepherd	CRAG
16:00	See schedule	AdS/CFT correspondence

2011-06-08	Wed	Georg Struth (Sheffield)	Applied Maths Colloquium
14:00	LT A	Algebraic Methods for Developing and Analysing Computing Systems

	Abstract: Programs without bugs is one of the grand ideals of computer science. It has stimulated decades of research, resulted in a number of Turing Awards, and has significant, and increasing, societal and economic relevance. It is widely accepted that mathematical methods are essential for analysing computing systems, and that new methods need to be developed to deal with their discrete, often nondeterministic nature. In turn, it has been claimed that these methods are increasingly relevant to other disciplines, such as physics, biology or economics. In this talk I will introduce variants of semirings, iteration algebras and relation algebras as fundamental structures of computing which are applicable to a variety of program analysis tasks. I will show how such algebraic methods can be used for proving theorems about programs that appear, for instance, in compiler optimisation, and how they provide frameworks in which the correctness of programs can be analysed. I will demonstrate that automated theorem provers and counterexample generators are instrumental both for program analysis and the development of algebraic methods. I will show how decision procedures and representation theorems for (fragments) of these algebras further support program analysis tasks. If time permits I will report on ongoing work on algebraic methods for concurrent and probabilistic systems, and mention some mathematically interesting open questions in these areas.

2011-06-06	Mon	Joel Weller (Sheffield)	CRAG
16:00	See schedule	MOND

2011-06-02	Thu	Professor Chris Budd (Bath)	SoMaS Colloquium
17:30

2011-05-27	Fri	Rosa Diaz-Sandoval (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-05-23	Mon	Greg Sculthorpe/Joel Weller/Susan Vu/Elizabeth Winstanley	CRAG
16:00	See schedule	Report back from UKCOSMO meeting and BHVIII conference

2011-05-20	Fri	Pedro Gonzales-Morales (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-05-18	Wed	Ben Shepherd (Sheffield)	Applied Maths Colloquium
14:00	LT A	Holographic Superconductivity

	Abstract: Superconductors are materials which have zero electrical resistance below a certain critical temperature. However, there is no theory in condensed matter physics to describe the best superconductors, i.e. those with the highest critical temperature. The AdS/CFT correspondence provides a way to investigate these high temperature superconductors, in which we consider a higher dimensional gravitational theory with a black hole in anti de Sitter (AdS) space. The theory describing our superconductor is then given by the boundary of AdS. After introducing superconductivity and the AdS/CFT correspondence, we will show that a planar black hole with an SU(N) gauge field gives the correct properties associated with high temperature superconductors.

2011-05-16	Mon	Victor Ambrus (Sheffield)	CRAG
16:00	See schedule	Spinors in curved space

2011-05-12	Thu	Inigo Arregui (Departament de F�sica, Universitat de les Illes Balears, Palma de Mallorca, Spain)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Bayesian magnetohydrodynamic seismology of coronal loops

	Abstract: Current magnetohydrodynamic seismology inversion techniques using both theoretical and observed wave properties in coronal structures show a number of limitations, such as the obtention of infinite number of solutions that equally well reproduce observed wave properties. We perform a bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations that aims to overcome these limitations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube and thin boundary approximations. This reduces the problem to solving two analytic algebraic equations for the period and damping of kink oscillations. For the inverse problem, we adopt a bayesian approach to infer the most probable values of the relevant parameters, for given observed periods and damping times, and to extract their confidence levels. The posterior probability distribution functions are obtained by means of Markov Chain Montecarlo simulations, incorporating observed uncertainties in a consistent manner. We find well localized solutions in the posterior probability distribution functions for two of the three parameters of interest, namely the Alfvén travel time and the transverse inhomogeneity length-scale. The obtained estimates are consistent with previous classic inversion results, but the method enables us to additionally constrain the transverse inhomogeneity length-scale and to estimate real error bars for each parameter. These results can serve to improve our current estimates of unknown physical parameters in coronal structures and to test the assumed theoretical model(s).

2011-05-11	Wed	Iñigo Arregui (Universitat de les Illes Balears, Palma de Mallorca)
14:00	LT A	Prominence thread oscillations: seismology and dynamics of transverse kink waves

	Abstract: Quiescent prominences are large clouds of plasma suspended against gravity in the solar atmosphere, by forces thought to be of magnetic origin. High resolution observations show that prominences consist of fine threads. Transverse oscillations in prominence �threads and their temporal damping are a common feature in a number of recent observations obtained by, e.g., the Swedish Solar Telescope (SST) in La Palma. Consider cylindrically symmetric magnetic flux tubes in the zero plasma beta approximation. Physical models for prominence threads can then be constructed by specifying particular density distributions. By analyzing the oscillatory properties of transverse kink waves in rather general two-dimensional density models, we provide insight to both seismology of transversely oscillating structures and to the physics of resonantly damped kink modes. Concerning the inversion of physical parameters using transverse kink waves, we find that the details of longitudinal density structuring have a significant impact on the inferred values of the Alfvén speed in those structures, while they are almost irrelevant when determining their transverse density structuring. On the subject of the physics of resonantly damped kink modes, we show the potential of combining the information from the spatial distribution of eigenfunctions together with energy arguments to better understand the energy transfer between kink waves of global character and oscillations at small spatial scales around the resonance. A detailed examination of the time-averaged Poynting flux in a two-dimensional region around the resonance shows how and where energy is fed into the resonance and the way it is thereafter distributed along the magnetic field lines. The use of the governing equations in the form of energy conservation laws and the computation of the different terms informs us about the spatial distribution of relevant quantities, such as the kinetic and magnetic energies, the generated current densities, and the associated resistive heating. The method and results here reported are also applicable to coronal loops and their transverse oscillations.

2011-05-11	Wed	Inigo Arregui (Universitat de les Illes Balears, Palma de Mallorca, Spain)	Applied Maths Colloquium
14:00	LT A	Prominence thread oscillations: seismology and dynamics of transverse kink waves

	Abstract: Quiescent prominences are large clouds of plasma suspended against gravity in the solar atmosphere, by forces thought to be of magnetic origin. High resolution observations show that prominences consist of fine threads. Transverse oscillations in prominence �threads and their temporal damping are a common feature in a number of recent observations obtained by, e.g., the Swedish Solar Telescope (SST) in La Palma. Consider cylindrically symmetric magnetic flux tubes in the zero plasma beta approximation. Physical models for prominence threads can then be constructed by specifying particular density distributions. By analyzing the oscillatory properties of transverse kink waves in rather general two-dimensional density models, we provide insight to both seismology of transversely oscillating structures and to the physics of resonantly damped kink modes. Concerning the inversion of physical parameters using transverse kink waves, we find that the details of longitudinal density structuring have a significant impact on the inferred values of the Alfvén speed in those structures, while they are almost irrelevant when determining their transverse density structuring. On the subject of the physics of resonantly damped kink modes, we show the potential of combining the information from the spatial distribution of eigenfunctions together with energy arguments to better understand the energy transfer between kink waves of global character and oscillations at small spatial scales around the resonance. A detailed examination of the time-averaged Poynting flux in a two-dimensional region around the resonance shows how and where energy is fed into the resonance and the way it is thereafter distributed along the magnetic field lines. The use of the governing equations in the form of energy conservation laws and the computation of the different terms informs us about the spatial distribution of relevant quantities, such as the kinetic and magnetic energies, the generated current densities, and the associated resistive heating. The method and results here reported are also applicable to coronal loops and their transverse oscillations.

2011-05-10	Tue	David Spiegelhalter (Cambridge)	SoMaS Colloquium
17:00		Living with risk and uncertainty - we're all going to die (sometime)

2011-05-09	Mon	Carsten van de Bruck (Sheffield)	CRAG
16:00	See schedule	Chameleons in cosmology

2011-05-06	Fri	JingSong He (Department of Mathematics, Ningbo University, P.R. China)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Rogue wave solution for the NLS and DNLS type equations

	Abstract: In this talk, the variable coefficient nonlinear Schrodinger equation(VCNLSE), deriva- tive nonlinear Schrodinger equation(DNLSE) and variable coefficient derivative non- linear Schrodinger equation(VCDNLSE) are discussed. The rogue wave solution of VCNLSE, DNLSE and VCDNLSE are given. The DNLSE is solved by Darboux transformation. The solutions of VCNLSE (VCDNLSE) are given from known solutions of NLSE(DNLSE) by a transformation developed by us recently. Several figures for these solutions are plotted to understand intuitionally its dynamical evolution. This is a joint work with Prof. Yishen Li, Lihong Wang and my students (Youying Wang and Shuwei Xu).

2011-05-04	Wed	James Douglas (Sheffield)	Applied Maths Colloquium
14:00	LT A	Linear stability analysis of non ideal tokamak plasma fluid models

	Abstract: As the price of energy increases in an age of austerity, it is proper to invest in alternate energy sources. A tokamak is a magnetic confinement fusion device which seeks to maintain a burning plasma at temperatures comparable to the core of the Sun, thus harnessing the energy released during fusion reactions. Although many of the applied mathematical and theoretical physics aspects of maintaining a fusion plasma are well understood, some aspects of linear theory remain unexplored. Using the CUTIE tokamak fusion plasma simulation code developed at the Culham Science Centre, which has successfully reproduced many nonlinear features of tokamak plasmas, a thorough investigation of the linear properties of these plasmas is presented. This investigation includes reduced models, such as RMHD, and pertinent extensions covering the role of advective flows and toroidal curvature on linear stability. An introduction to nuclear fusion, tokamak reactors and the CUTIE code is discussed, before outlining some of the linear modes we have investigated using a linear version of the CUTIE code. This linear code employs two powerful new techniques for finding linear modes: the resolvent eigenvalue technique which reveals the entire linear spectrum; and the nonlinearisation technique for finding the dominant linear mode.

2011-04-18	Mon	Elizabeth Winstanley (Sheffield)	CRAG
16:00	G08	Report back from Bologna meeting

2011-04-11	Mon	Ben Shepherd and Matt Hewitt	CRAG
16:00	See schedule	Report back from NPPD 2011 conference in Glasgow

2011-04-08	Fri	Abhi Srivastava (Aryabhatta Research Institute of Observational Sciences (ARIES), Manora Peak, Nainital, India)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-04-04	Mon	Carl Kent (Sheffield)	CRAG
16:00	G08	Petrov classification of spacetimes

2011-04-01	Fri	Beniamin Orza (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-03-28	Mon	Sming Tsai	CRAG
16:00	Hicks LT9	Observational signatures of SUSY dark matter

2011-03-25	Fri	Balazs Pinter (University of Aberystwyth)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-03-24	Thu	Professor Sir Roger Penrose OM FRS (Oxford)	SoMaS Colloquium
17:30	Richard Roberts Auditorium	Are we able to see through the Big Bang, into another World?

	Abstract: The proposal of Conformal Cyclic Cosmology (abbreviated CCC) asserts that what we presently regard as the entire history of our universe, from its Big-Bang origin to its indefinitely expanding future (but without inflation), is but one aeon in an unending succession of similar such aeons, where the infinite future of each matches to the big bang of the next via an infinite change of scale. CCC predicts that supermassive black-hole encounters in the aeon prior to ours would be observable to us as families of concentric rings of unusual temperature structure in the cosmic microwave background. Recent analysis of data from the WMAP satellite has been argued to provide confirmation of this signal, allowing us to ßee through" our Big Bang to such events occuring in the aeon prior to ours. The present status of this controversial proposal will be discussed.

2011-03-23	Wed	Christian Beck (Queen Mary, UL)	Applied Maths Colloquium
14:00	tbd	Superstatistical techniques for complex systems with time scale separation

	Abstract: Many complex driven nonequilibrium systems are effectively described by a superposition of several statistics on different time scales, in short a `superstatistics'. Superstatistical techniques have recently been successfully applied to a variety of complex systems, for example turbulence (Lagrangian, Eulerian, environmental), hydroclimatic fluctuations, pattern formation, mathematical finance, traffic delay statistics, random matrix theory, networks, scattering processes in high energy physics, as well as medical and biological applications. In this talk I will first give a general overview of this concept and its recent applications, and then discuss three examples is somewhat more detail: Train delay statistics on the British railway network, accelerations of tracer particles in turbulent flows, and cancer survival statistics.

2011-03-18	Fri	Andrew Gascoyne (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-03-17	Thu	Malwina Luczak (LSE)	SoMaS Colloquium
17:00	Hicks LT 3	Markov chain models of complex systems

	Abstract: Markov chains provide a useful paradigm for modelling complex systems from various application areas. Rigorous analysis of their evolution can provide insights into the real situations they model. In this lecture, I will describe one Markov chain model from each of the following fields: computer science, statistical mechanics and mathematical biology. In each case, I will give some details of what is known about the model's behaviour.

2011-03-16	Wed	Ineke de Moortel (St Andrews)	Applied Maths Colloquium
14:00	LTA	Coupled Kink and Alfv�n Mode Propagation in the Solar Corona

	Abstract: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform 3D numerical simulations of broadband footpoint-driven transverse waves propagating in a low β plasma. When density structuring is present, mode coupling in inhomogeneous regions leads to very efficient coupling of the kink mode to the Alfv�n mode. The frequency-dependent decay of the propagating kink wave is observed as energy is transferred to the local Alfv�n mode. For all density structures considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localised Alfv�n modes. Hence, transverse footpoint motions at the base of the corona will transfer energy to Alfv�n modes in the corona.

2011-03-11	Fri	Peter Whyper (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2011-03-04	Fri	Khalil Alghafri (Sheffield)	SP2RC Friday Seminars
13:05	F20

2011-03-02	Wed	Erwin Verwichte (Warwick)	Applied Maths Colloquium
14:00	LTA	Observations of MHD wave activity in the solar corona

	Abstract: The advent of extreme-ultraviolet and x-ray imagers and spectrometers in the last decade has brought overwhelming observational evidence of magnetohydrodynamic wave activity in the solar corona. Such waves carry in their signatures valuable information about the structures along which they travel and has given birth to the field of coronal seismology that aims to extract this information. In this seminar I will highlight some of the key discoveries and discuss the nature of these waves, taking examples from established and new instruments such as TRACE, Hinode and SDO.

2011-02-25	Fri	James McLaughlin (School of Computing, Engineering and Information Sciences, Northumbria University,)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection

	Abstract: he work of McLaughlin et al. (2009) provides a link between two traditionally separate areas of solar physics: MHD wave theory and reconnection, and is one of the first demonstrations of reconnection naturally driven by MHD wave propagation. I shall introduce the topic, discuss the results of McLaughlin et al. (2009) and set the work in the larger context and general interest of wave-driven reconnection and reconnection generating wave-motions.

2011-02-16	Wed	Eduard Kontar (Glasgow)	Applied Maths Colloquium
14:00	LTA

2011-02-09	Wed	Jesse Andries (Monash)	Applied Maths Colloquium
14:00	LT A	Some theoretical considerations on magnetohydrodynamical waves in shear flows

	Abstract: The theoretical foundation of the study of linear MHD waves and instabilities in stationary equilibria, is much less developed than its counterpart in static equilibria. For static equilibria a sound theory is based on the eigenmodes of a self-adjoint force operator, which can be equivalently expressed by a variational principle (Rayleigh-Ritz) for the quadratic potential energy functional. Such an approach seems impossible for stationary equilibria. While some relations between the eigenfrequencies and a number of quadratic functionals have long been known (Frieman and Rotenberg, 1960), those do not straightforwardly allow to construct a corresponding variational principle. Attempts so far involved the generalisation to a bilinear functional (where the energy interpretation is absent), and the associated doubling of the dimensionality of the variational space, or the assumption of some symmetry in the equilibrium. We will discuss the central problem and show that, contrary to what is often believed and claimed, many results do generalise to stationary media (shear flows). In particular, we focus on the clear interpretation of the energy functionals as they appear in a generalised variation principle that we formulated recently (Andries 2010, Physics of Plasmas, 17, 2106).

2011-02-02	Wed	Sandra Chapman (Warwick)	Applied Maths Colloquium
14:00	LTA	Quantifying and understanding the statistical properties of turbulence - what we have learned from the solar wind

	Abstract: The solar wind exhibits fluctuations over a broad range of timescales characteristic of magnetohydrodynamic (MHD) turbulence evolving in the presence of structures of coronal origin. In- situ spacecraft observations of plasma parameters are at minute (or below) resolution for intervals spanning the solar cycle and provide a large number of samples for statistical studies. The magnetic field power spectrum typically has an inertial range of turbulence over several orders of magnitude with approximately Kolmogorov power law and at lower frequencies, an approximately �1/f� energy containing range believed to be of direct coronal origin and at higher frequencies, a kinetic range of turbulence. With a magnetic Reynolds number estimated to be of order 10^5 the solar wind provides a unique �laboratory� for the study of MHD turbulence, and dissipation processes. Recent results however also suggest that in the ecliptic, signatures of scaling which are of direct coronal origin are embedded in the inertial range of turbulence of the solar wind, and as a consequence these show solar cycle and latitudinal dependence. At high latitudes, in uninterrupted streams of fast solar wind flow, and with recent high cadence observations of coronal structures there is the opportunity to study evolving finite range turbulence which can also inform our understanding of turbulence in boundary layers. This talk will survey quantitative statistical methods that can be used to distinguish these distinct physical processes in the solar wind and offer connections to a wider class of nonlinear systems approaches.

2011-01-26	Wed	Phil Livermore (Leeds)	Applied Maths Colloquium
14:00	LT A	Inviscid dynamos: evolving a magnetic field subject to a continuum of constraints

	Abstract: The geomagnetic field is generated in Earth's liquid core by a dynamo process, a complex nonlinear system described by a collection of partial differential equations. In the last few decades, running numerical models of the geodynamo has become fairly widespread, although these are so complex and run with parameters so many orders of magnitude different from Earth's core that there remains large gap between the current state of the art and models that are defensibly realistic. Since 1963 it has been known how to model the slow time evolution of the geodynamo system with zero viscosity, arguably one of the the simplest realistic descriptions of the system. However, this limit has associated a continuum of constraints that the magnetic field must satisfy, a stumbling block that has hindered progress on this front for 48 years. In this talk, I shall summarise recent work that allows, on the adoption of a suitable numerical method, this continuum of constraints to collapse to a finite number and therefore admits the possibility of numerical models that evolve whilst simultaneously satisfying these constraints. I will describe some basic time evolution models that exploit these developments.

2010-12-15	Wed	Ian Craig (Waikoto, New Zealand)
14:05	LT A	Exact models for magnetic reconnection in coronal plasmas

	Abstract: An introduction to magnetic reconnection in coronal plasmas is given. Some exact analytic solutions are presented that describe recent 'fan' and 'spine' reconnection models.

2010-12-10	Fri	David Robertson (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2010-12-03	Fri	Ashley Willis (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2010-11-26	Fri	Richard Morton (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Sausage Oscillations in Magnetic Pores

	Abstract: A large number of waves and oscillations observed throughout the solar atmosphere are thought to occur due to driving mechanisms in the solar interior and solar photosphere, e.g. p-modes, granular buffeting. It is important to assess how the wave energy generated in the solar interior/photosphere is transported and dissipated in the higher layers of the solar atmosphere, as the wave energy is thought to be one of the main mechanisms responsible for the heating and the dynamics observed in the transition region and corona. Recent advances in ground-based instruments and analysis techniques has paved the way for high spatial resolution and high cadence observations of the lower solar atmosphere. It is now possible to study wave phenomena occurring in some of the smallest known magnetic features, e.g. magnetic bright points. We present here high cadence observations of the sausage oscillations occurring in magnetic pores. We are able to identify the oscillations using a relatively new analysis technique (with respect to solar applications) known as Empirical Mode Decomposition (EMD).

2010-11-24	Wed	Nils Mole (Sheffield)	Applied Maths Colloquium
14:00	LTA	Modelling the moments of the expected mass fraction for a line source in decaying grid turbulence

	Abstract: To assess hazards resulting from dispersing clouds or plumes of toxic or flammable gases, one would like to know the probability density function (pdf) of concentration, including its dependence on space and time. The expected mass fraction (EMF) provides a space-integrated equivalent of the pdf. Here I develop a model for the moments of the EMF, which I apply to the particular case of a plume dispersing from a steady line source in decaying grid turbulence. The results will be compared with measurements from some laboratory experiments in wind and water tunnels.

2010-11-19	Fri	Andrew Gascoyne (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2010-11-17	Wed	Edmund Ryan (Sheffield)	Applied Maths Colloquium
14:00	LTA	Improving estimates of atmosphere-land carbon flux by assimilating satellite observations of biomass

	Abstract: There are large uncertainties in estimates of the atmosphere-land exchange of carbon by natural processes (photosynthesis and respiration). Accurate estimates are crucial for better understanding of the global carbon cycle and climate modelling. Traditonally the models we use to get these estimates are tested for their ability to reproduce real-life processes by comparing model output with observations. However, a more useful way of using the observations, which takes into account the observational error, is to assimilate the observations into the model. This is called Data Assimilation or DA. We can use DA to estimate the states of the system or to estimate some or all of the parameters to the model. While DA has been generally performed on small models, some recent work is using it on the larger ones for example JULES (Joint Uk Land Surface Simulator) which is the land part to the climate model used by the met office. However, up till now, DA has been mainly carried out using ground observations. In this PhD, I am exploring the value of using satellite observations instead, due to the major advantages such observations have over ground based ones (ie more frequent observations and more observations on the spatial scale).

2010-11-12	Fri	Michael Balikhin (m.balikhin@googlemail.com)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2010-11-10	Wed	Ashley Willis (Sheffield)	Applied Maths Colloquium
14:00	LTA	Charting the phase-space of transitional fluid flow

	Abstract: In 1883, Reynolds observed a transition from laminar to turbulent flow in a pipe. Although more than 125 years have passed, fundamental questions on the nature of this transition remain. All evidence to date suggests that laminar pipe flow (Hagen Poiseuille flow) is linearly stable, but it has only been proved rigorously for special cases. At the modest flow rates examined by Reynolds, it is now clear the finite amplitude disturbances to the laminar are required to trigger the transition to turbulence. Recently, a host of finite-amplitude solutions for pipe flow has been discovered (Faisst			Eckhart 2004; Pringle, Duguet	Kerswell 2008). While a few have been shown to be embedded within the 'laminar-turbulent boundary', the role of the vast majority of solutions is yet to be determined. In this talk, evidence for the appearance of travelling waves during transition is presented, plus a method for projection of the underlying dynamics.

2010-11-05	Fri	Viktor Fedun (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2010-11-03	Wed	Joel Weller (Sheffield)	Applied Maths Colloquium
14:00	LTA	Cosmological inflation with a Dirac-Born-Infeld field

	Abstract: Our understanding of the cosmos is underpinned by precision observations on very large and very small scales, and theoretical models must not only be well-motivated but also consistent with the wealth of data available. The inflationary paradigm, in which the universe experiences a period of rapid expansion early in its history, stands as a crowning example of this principle, in that it leaves observable traces in the distribution of structure on large scales and the cosmic microwave background (CMB) radiation that can be explained in terms of the microscopic quantum fluctuations of the field(s) driving inflation. The availability of high precision observational data in cosmology means that it is possible to go beyond the simple descriptions of cosmic inflation in which the expansion is driven by a single scalar field. One set of models of particular interest involve the Dirac-Born-Infeld (DBI) action, arising in string cosmology, in which the dynamics of the field are affected by a speed limit in a manner akin to special relativity. In this talk, I will discuss how the problems faced by the standard hot big bang model are resolved by introducing an inflationary period, and describe the mathematical treatment of the standard and DBI scenarios.

2010-10-29	Fri	Jamie Douglas (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Linear eigenspectra in tokamak plasmas: advanced theory

	Abstract: Following from the recent Applied Maths seminar on the same topic, we delve deeper into the theory of the underlying plasma physics and numerical methods used in solving the linear systems governing tokamak plasmas. Under investigation are: the presence of Alfven waves and tearing modes in resistive MHD systems; the introduction of nontrivial mean density gradients leading to drift waves and drift instabilities; ion sounds waves in the four field model of Hazeltine [Phys. Fluids 28, 1985]; and extensions including the effects of ion temperature and toroidal curvature. The resolvent eigenvalue method for revealing linear spectra and the nonlinearisation method for finding the dominant mode are expounded in more detail.

2010-10-22	Fri	Giuseppe Colantuono (Italy)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Effect of stratification and background flow on the frequency of bounded Rossby modes with topography

2010-10-20	Wed	Peter Haynes (Cambridge)	Applied Maths Colloquium
14:00	LTA	What controls the rate of mixing of passive scalars in smooth flows?

	Abstract: Stirring and mixing of chemical and biological species is an important in atmospheric and oceanic flows and in many other contexts. Some aspects of stirring and mixing can be captured by 'Lagrangian stretching theories' which essentially consider evolution in small fluid elements in which the flow may be approximated as a linear function of space coordinates, but time varying. This is a great simplification to solving the full advection-diffusion equation and potentially gives a practical approach to calculation. It also motivates an examination of whether 'Lagrangian stretching theories' are always correct. Solution of a suitable idealised problem shows that Lagrangian stretching theories make correct predictions (for an initial value problem) if the advection diffusion operator, which always has a continuous spectrum in the limit of vanishing diffusivity, has no discrete eigenvalues.

2010-10-15	Fri	Rekha Jain (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Axisymmetric Scattering (and Absorption) of p Modes by a Thin Magnetic Flux Tube

	Abstract: The buffeting action of the solar acoustic waves (p-modes) excites MHD tube waves. The propagation of these tube waves along the length of the tube creates a back reaction on the field-free fluid surrounding the tube, generating outgoing scattered wave field. I will present a calculation of the far-field scattering matrix for the special case of axisymmetric, vertically oriented, thin, magnetic flux tube. Our ultimate goal is to model the absorption and scattering of acoustic waves by magnetic plages. However, the first step in this future line of inquiry is the calculation of the scattering matrices (both near- and far-field) for a stratified single magnetic flux tube. The work presented will be one piece of many required to accomplish this goal.

2010-10-13	Wed	Jamie Douglas (Sheffield)	Applied Maths Colloquium
14:00	tbd	Linear eigenspectra in tokamak fusion plasmas

	Abstract: Nuclear fusion has become one of the "hot" topics in recent years, with the likes of Prof. Stephen Hawking and Prof. Brian Cox offering their own perspective on the issue (see below). Although many of the applied mathematical and theoretical physics aspects of maintaining a fusion plasma are well understood, some aspects of linear theory remain unexplored. Using the CUTIE tokamak fusion plasma simulation code developed at the Culham Science Centre, which has successfully reproduced many nonlinear features of tokamak plasmas, we are now investigating the linear properties of these plasmas. This seminar will cover an introduction to nuclear fusion, tokamak reactors and the CUTIE code, before outlining some of the linear modes we have investigated using a linear version of the CUTIE code which employs two new techniques for finding linear modes: the resolvent eigenvalue technique which reveals the entire linear spectrum; and the nonlinearisation technique for finding the dominant linear mode. Prof. Stephen Hawking, quoted in the Guardian newspaper 11th September 2010: "Nuclear fusion...would provide an inexhaustible supply of energy without pollution or global warming. Many badly needed goals, like fusion and cancer cures, would be achieved much sooner if we invested more." Prof. Brian Cox quoted in the same article: "The provision of clean energy is of overwhelming importance. What frustrates me is that we know how to do [fusion] as physicists, and how it works. It is an engineering solution that is within our grasp. I think the most important practical problem, which may be more of an engineering challenge than a scientific one, is to build economically viable nuclear fusion power stations. If we haven't dealt with our world's increasing appetite for energy by the end of this century, I think we will be in very deep trouble indeed."

2010-10-08	Fri	Brad Hindman (JILA, University of Colorado, Boulder, CO 80309-0440, USA)	SP2RC Friday Seminars
13:05	Lecture Theatre 5	Using eigenfunction phases to measure deep meridional circulation

	Abstract: A steady meridional flow makes only a second-order shift to the Sun's p-mode frequencies while producing a first-order distortion in the p-mode eigenfunctions. In particular, the flow induces latitudinal variation in the eigenfunction's phase. We suggest a technique to extract the meridional flow by detailed measurement of this phase variation. Using a simple toy model we estimate and illustrate the viability of detecting and measuring meridional flow deep in the convection zone using the suggested procedure.

2010-06-22	Tue	Iakovos Androulidakis (Gottingen)	Quantisation
16:00	LT 6	Pseudodifferential calculus for singular foliations

	Abstract: Regular foliations have been studied for many decades but their leaf spaces are in general very pathological topological spaces. One of the aims of Connes' noncommutative geometry has been to study such leaf spaces in terms of their holonomy groupoids. In joint work with G. Skandalis (Paris 7) we have begun to extend these methods to singular foliations. These are widespread: group actions and Poisson manifolds, for example, give rise to singular foliations. The holonomy groupoid of a singular foliation (M,F) is an even more ill-behaved object, nevertheless in earlier work we showed how to construct the associated C*-algebra. In this lecture, we will give an overview of this construction, and discuss how it can be used to give a longitudinal pseudodifferential calculus for such leaf spaces and develop an index theory.

2010-06-02	Wed	Misha Ruderman (Sheffield)	SoMaS Colloquium
14:00	LTA	Transverse oscillations of coronal loops

	Abstract: On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this talk we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the talk we summarize the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.

2010-05-12	Wed	Vladimir Vladimirov (York)	Applied Maths Colloquium
14:00	LT A

2010-05-07	Fri	Amy Scott (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-05-05	Wed	Richard Morton (Sheffield)	Applied Maths Colloquium
14:00	LT A	Oscillations in solar plasma with variable background

	Abstract: The solar atmospheric plasma is an extremely dynamic medium threaded by a complex magnetic field that is constantly subject to heating and cooling processes. The magnetic field provides the foundations for a wide variety of plasma fine structure in the solar atmosphere, e.g. coronal loops, coronal holes, prominences. Each of these features in the solar atmosphere can support an array of magneto-hydrodynamic (MHD) oscillatory modes. We present here a first study of the propagation of MHD waves in a magnetised plasma environment that is cooling due to radiation. Previous investigations have concentrated on the affect of radiation on the perturbations only. An approximate radiation function that has the form of Newtonian cooling is used for the sake of simplicity. We find that the cooling of the plasma leads to a time dependent frequency of MHD waves (or oscillations) and causes both damping and amplification of these periodic phenomena. This result could have important implications for various aspects of magneto-seismology in the solar atmosphere.

2010-05-04	Tue	Martin Lindsay (Lancaster)	Quantisation
16:00	Lecture Theatre 6	Quantum Stochastic Integrals and Semimartingales (Yorkshire Functional Analysis Group meeting)

2010-04-30	Fri	Xenophon Moussas (Faculty of Physics, National and Kapodistrian University of Athens)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-04-28	Wed	Francesca Ticconi (DLR - German Aerospace Center)	Applied Maths Colloquium
14:00	LT A	SAR Polarimetry

	Abstract: The direction of the electric field vector, describing an ellipse in a plane transverse to propagation, plays an essential role in the interaction of electromagnetic waves with material bodies and the propagation medium. This polarisation transformation behaviour is denoted as "Polarimetry" in radar and synthetic aperture radar (SAR) sensing and imaging. A fully polarimetric radar transmits two orthogonal polarisations and receives the backscattered wave on the same two polarisations. This results in four received channels where both the amplitude and relative phase are measured. The measured signals in these four channels represent all the information needed to measure the polarimetric scattering properties of the target. Such information is necessary for the estimation of soil moisture and surface roughness parameters, since a major problem in this estimation is the separation of soil moisture and surface roughness contributions to the backscattered radar signal. A set of methods known as target decomposition theorems have been developed for the interpretation of polarimetric SAR data and two different approaches will be shown based respectively on a physical-based model decomposition and on the eigenvector-based target decomposition. For the soil moisture content retrieval, an inversion model, based on this latter decomposition, has been applied on L-band airborne SAR data and the result of the inversion will be shown.

2010-04-23	Fri	Abhishek Srivastava (Aryabhatta Research Institute of Observational Sciences (ARIES), Manora Peak, Nainital, India.)	SP2RC Friday Seminars
13:05	Lecture Theatre 10	On Probing the Solar Atmosphere by Observed MHD Waves

	Abstract: The observed MHD wave harmonics in a large-scale (e.g., loops) and small-scale (e.g., bright points, network cavities) magnetic structures of the solar atmosphere, are being very important recent days to probe the crucial plasma conditions of these solar structures to understand their dynamics and heating. While, the observations of propagating MHD waves in various solar structures are also significant to probe their medium in which these waves propagate. Under the new light of my recent observational findings, I present some trends of the local plasma diagnostics based on the observed MHD waves in various solar structures, and also discuss their implications and future aspects.

2010-04-21	Wed	Tatiana Talipova (Nizhny Novgorod, Russia )	Applied Maths Colloquium
14:00	LT A	Avalanche and Landslide Dynamics

	Abstract: The Savage-Hutter model is applied to describe the gravity driven shallow-water flows in inclined channels of parabolic-like shapes modeling the avalanches moved in the mountain valleys or the landslide motions in underwater canyons. The Coulomb (sliding) friction term is included in model. The Riemann invariants are found for this hyperbolic system. Several analytical solutions described the nonlinear dynamics of avalanche are obtained: Riemann wave, dam-break problem, self-similar solutions and the Carrier-Greenspan-like solutions. Some of them extend the known solution for inclined plate (1D geometry). They can be used to test the 2D numerical models of debris volcano avalanches, mountain flanks and landslides in submarine continental slopes.

2010-04-16	Fri	Richard Morton (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-04-14	Wed	Reidun Twarock (York)	SoMaS Colloquium
14:00	Lecture Theatre A	Viruses and geometry : New insights into virus architecture and function via affine extended symmetry groups

	Abstract: Simple viruses consist of a genome (RNA or DNA) surrounded by a protective protein container. For a significant number of viruses, these containers exhibit icosahedral symmetry. The locations of the proteins in these containers can therefore be predicted in terms of surface lattices that are invariant under icosahedral symmetry as shown in Caspar and Klug�s seminal work on virus architecture from the 1960s. In this talk I will show that there exists a deeper level of geometric organisation that orchestrates the full three-dimensional structures of simple virus particles, providing for the first time predictive information on shapes and dimensions of the individual viral components. The principle of this organisation is encoded in a finite library of three-dimensional point arrays that are a consequence of our recent classification of affine extensions of the icosahedral symmetry group. I will demonstrate with a range of viruses that our theory is capable of predicting a wide spectrum of distinct viral features and their relative sizes in striking detail. These include the edges of protein subunits, the double-shelled genomic RNA structure in MS2, and the dodecahedral RNA cage in Pariacoto virus. Several applications of this fundamental geometric principle of virus architecture are discussed, including virus assembly, viral evolutions and the prediction of structural transitions important for infection.

2010-03-19	Fri	Andrew Gascoyne (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-03-17	Wed	Michael Proctor	Applied Maths Colloquium
14:00	tbd	Fully consistent mean field MHD

	Abstract: We consider the linear stability of two-dimensional nonlinear magnetohydrodynamic basic states to long-wavelength three-dimensional perturbations. Following the work of Hughes and Proctor the 2D basic states are obtained from a specific forcing function in the presence of an initially uniform mean field of strength B. By extending to the nonlinear regime the kinematic analysis of Roberts, we show that it is possible to predict the growth rate of these perturbations by applying mean field theory to both the momentum and the induction equations. If B = 0, these equations decouple and large-scale magnetic and velocity perturbations may grow via the kinematic effect and the AKA instability respectively. However, if the imposed field is non-zero, the momentum and induction equations are coupled by the Lorentz force; in this case, we show that four transport tensors are now necessary to determine the growth rate of the perturbations. We illustrate these situations by numerical examples; in particular, we show that a mean field description of the nonlinear regime based solely on a quenched coefficient is incorrect.

2010-03-12	Fri	Carlos Jaimes (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-03-05	Fri	Andrew Newton (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-03-03	Wed	Marina Skender (Leuven)	Applied Maths Colloquium
14:00	LT A	Quasi-equlibrium current sheet and the onset of impulsive bursty reconnection

	Abstract: A two-dimensional reconnecting current sheet is studied numerically in the MHD approach. Different simulation setups are employed in order to follow the evolution of the formed current sheet in diverse configurations: Two types of initial equilibria, Harris and force-free, two types of boundary conditions, periodic and open, with uniform and non-uniform grid set, respectively. All the simulated cases are found to exhibit qualitatively the same behavior in which a current sheet evolves slowly through a series of quasi-equilibria; eventually it fragments and enters a phase of fast impulsive bursty reconnection. In order to gain more insight on the nature and characteristics of the instability taking place, physical characteristics of the simulated current sheet are related to its geometrical properties. The aspect ratio of the current sheet is observed to increase slowly in time up to a maximum value at which it fragments. Additional turbulence introduced to the system is shown to exhibit the same qualitative steps, but with the sooner onset of the fragmentation and at smaller aspect ratio.

2010-02-26	Fri	Marialejandra Luna-Cardozo (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-02-22	Mon	Tom Sutherland (Sheffield)	Quantisation
16:10	J11	Deformation quantisation

	Abstract: Deformation quantisation (or phase-space quantisation) comes from the idea of constructing a representation of quantum mechanics by deforming the commutative product in the algebra of functions on a Poisson manifold to a non-commutative so-called star-product. It first appeared in the work of Dirac, and over the years many different authors have proved that deformation quantisations exist for successively broader classes of manifolds. The case of a general Poisson manifold was finally proved by Kontsevich who showed that it was implied by his Formality Conjecture. This talk will focus on giving an outline of his proof.

2010-02-19	Fri	Jamie Douglas (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2010-02-17	Wed	Martin Whittle (SheffieldSheffield)	Applied Maths Colloquium
14:00	LTA	Dissipative Particle Dynamics Simulation of Colloids

	Abstract: Clearing legacy radioactive sludge from cooling ponds is a priority for the nuclear industry in its current renaissance. To develop and optimise the necessary machinery it is relying heavily on simulation to model flow and part of this programme involves the incorporation of mesoscopic simulations directed at the rheology of colloids. Here we look at one such approach using Dissipative Particle Dynamics (DPD). DPD was developed in the 1990's and is one of a steadily increasing number of mesoscopic simulation techniques that has been used to model complex fluids and flows in microchannels. Here we discuss methods of modelling colloids using DPD and compare the results of simulations with some other approaches. Although DPD has an inbuilt thermostat this becomes ineffective at high shear rates and we will explore some methods of applying auxiliary thermostatting for non-equilibrium simulations. The results display several classic features of colloidal rheology including evidence of pseudo-plasticity at high volume fraction. Nevertheless, despite the advantages of simplicity, the model still presents a number of challenges that will be discussed.

2010-02-12	Fri	Viktor Fedun (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10	3D numerical simulations of a MHD waves in solar atmosphere

2010-02-10	Wed	Mitchell Berger (Exeter)	Applied Maths Colloquium
14:00	LTA	Applications of Braid Theory

	Abstract: Two great puzzles in solar astrophysics concern the source of coronal heating and the distribution of solar flares. The atmosphere of the sun is heated to one million degrees or more, possibly by swarms of tiny flares. These tiny flares could be consequences of the braiding of magnetic field lines. Reconnection between braided threads of magnetic flux can release energy stored in the braid. The larger flares exhibit a power law energy distribution. Several authors have suggested that a self-organization process in the solar magnetic field could lead to such a distribution. Here we show how reconnection of braided lines can organize the small scale structure of the field, leading to power law energy release. An application of braids to mixing theory will also be discussed.

2009-12-16	Wed	Yi Li (Sheffield)	Applied Maths Colloquium
14:00	LT A	tbd

2009-12-11	Fri	Adam Scaife (MetOffice)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Gravity waves in the Earth's atmosphere: propagation, dissipation and global scale effects

	Abstract: Starting from linear theory, we will discuss the propagation of small scale gravity waves from their source in the lower, convective layer of the Earth's atmosphere, to their dissipation in the stratosphere and mesosphere above. The role of critical lines and density stratification in wave dissipation will be introduced. These ideas will be used to interpret experiments with global models of the Earth's atmosphere on how gravity waves drive mean circulation and mean temperature structures in the stratosphere and mesosphere. We will also show how gravity waves conspire to drive remarkable low frequency oscillations in the tropical atmosphere.

2009-12-09	Wed	David Pontin (Dundee)	Applied Maths Colloquium
14:00	LT A	Magnetic reconnection in three dimensions

	Abstract: Magnetic reconnection is of fundamental importance in many plasmas, for example the Solar corona. It plays a role in heating the corona and is thought to be responsible for many dynamic phenomena observed there. The magnetic field in the corona has a highly complex structure that is clearly three-dimensional. Furthermore, recent advances in theory and computational experiments have shown that the nature of reconnection in 3D is fundamentally different from 2D models. Here we discuss the underlying theory of three-dimensional magnetic reconnection. We also review a selection of new 3D reconnection models that illustrate the current state of the art, as well as highlighting the complexity of the process in complicated 3D magnetic fields.

2009-12-07	Mon	Elizabeth Winstanley (Sheffield)	Quantisation
16:10	J11	Quantisation and Physics

2009-12-04	Fri	Rosa Diaz-Sandoval (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2009-11-30	Mon	Dave Applebaum (Sheffield)	Quantisation
16:10	J11	Mysteries and functors (part 2)

2009-11-27	Fri	Nicolas Leprovost (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2009-11-25	Wed	Alan Zinober (Sheffield)	Applied Maths Colloquium
14:00	LT A	A New Non-Classical Class of Optimal Variational Problems

	Abstract: The Calculus of Variations was developed in the 18th Century and forms a basic foundation of modern optimal (maximising or minimising) variational problems, nowadays often called optimal control. An introduction to the Calculus of Variations with some sample examples will be presented. This will include the Euler-Lagrange and Hamiltonian formulation together with the associated final boundary value conditions. Maple or the numerical shooting method can be used to solve the resulting Two Point Boundary Value Problem (TPBVP), a set of differential equations. A new non-classical class of variational problems has been motivated by recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the Calculus of Variations (CoV) or Optimal Control. However, the state value at the final fixed time, y(T), is a priori unknown and the integrand to be maximised is also a function of the unknown y(T). This is a non-standard CoV problem that has not been studied before. New final value costate boundary conditions will be presented for this CoV problem and some results will be shown.

2009-11-25	Wed	Kostas Triantafyllopoulos (Sheffield)	AM/P+S Colloquium
16:00	LT A	Bayesian methods for flexible manoeuvring systems in control

	Abstract: This talk serves as an Interim Report of the BtG grant on a Flagship project between the Departments of Probability and Statistics, Applied Mathematics and Automatic Control and Systems Engineering. This project investigates the application of Bayesian statistical modelling to a class of problems in control, and in particular to the system modelling and tracking control of a twin rotor multi-input multi-output system (TRMS) in hovering mode. Systematic stochastic modelling of the hovering property of the helicopter/TRMS is vital for a variety of flight missions including load delivery and air-sea rescue. We describe parametric and non-parametric models (forward and inverse), with the aid of which we empirically explore the non-minimum phase phenomenon of the non-linear system. The parametric model is a linear Bayesian time series model which shares some resemblance to the celebrated Kalman filter, and the non-parametric model is a Neural Network (NN) model. We discuss in detail the Bayesian model and provide a comparative analysis with the NN model, in relation to non-minimum phase behaviour. We provide some discussion on future directions of modelling, in particular in the view of (a) establishing non-minimum phase behaviour of the models theoretically and (b) proposing other non-parametric statistical modelling approaches. Finally, we showcase the application of Bayesian statistics in signal processing and in control, something that has not been explored / developed in the literature.

2009-11-23	Mon	Dave Applebaum (Sheffield)	Quantisation
16:10	J11	On mysteries and functors (part 1)

	Abstract: Don't expect much category theory (even lower order). The title is based on a quote from Ed Nelson: "First quantisation is a mystery, second quantisation is a functor,"

2009-11-20	Fri	Christopher Clack (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2009-11-18	Wed	Colin Steele (Manchester)	Applied Maths Colloquium
14:00	LT A	Tadpoles, Horseshoes and the Trojan Wars: the restricted 3-body problem in the Solar System

	Abstract: The two-body problem in Celestial Mechanics has been solved to give orbits in the form of conic sections (ellipses etc.). The introduction of a third body, however, disallows any algebraic solutions and numerical work is required in order to follow the motion of the objects. The restricted three body problem assumes that one of the three objects is of negligible mass i.e. the third body responds to the gravitational attraction of the first two bodies but does not itself influence the motion of these first two bodies. In the solar system, with there being a wide range of masses of Sun, planets, satellites, minor planets, comets etc, this restricted three-body problem is certainly relevant. Under the restricted three-body problem, the third (light) body can be followed through a wide variety of situations. Without retracting from dynamical solutions, this talk will concentrate on cases close to equilibria and/or involving cycles. Such cases will be modelled including an analysis of the linear stability and a numerical simulation. Particular real cases in the solar system involve minor planets with orbits affected by Jupiter and the motions of some of the inner satellites of Saturn.

2009-11-17	Tue	Eugenia Cheng (Sheffield)	SoMaS Colloquium
17:00	tbd	2-vector spaces: an introduction to higher-dimensional category theory

	Abstract: What is a 2-vector space, and how is it different from a 2-dimensional vector space? Why would anyone want to come up with such a notion? And once we have come up with such a notion, how do we know it deserves to be called a"2-vector space"? In this talk we will show how to answer all these questions using category theory. This example highlights one of the ways that category theory can help in mathematics: it helps us give good generalisations of structures that appear in various branches of mathematics including homotopy theory, stacks, topological quantum field theory, type theory, representation theory and concurrency theory. This talk will be introductory; in particular it should not be necessary to be familiar with any category theory, and I will encourage Level 4 undergraduate students to attend. It will help to know what an ordinary vector space is.

2009-11-16	Mon	David Jordan (Sheffield)	Quantisation
16:10	J11	Poisson Algebras

2009-11-11	Wed	Judith Wolf (POL)	Applied Maths Colloquium
14:00	tbd	Wave-Current Interaction in Liverpool Bay

	Abstract: Waves in shallow water are strongly controlled by the water level as well as the wind forcing and can be refracted by strong current shear. Theory suggests that the mechanisms by which waves and the wind-driven mean flow are generated are closely interconnected in the surface layer through the wind-stress. Also there is evidence that the bottom friction experienced by waves and near-bed currents are mutually enhanced. New theoretical work has been implemented in the POLCOMS-WAM coupled hydrodynamic and wave model system to include the effect of 3D currents, allowing the vertical current shear to affect wave propagation and accounting for 3D radiation stress and Stokes' drift. We investigate the occurrence of typical and extreme wave conditions in Liverpool Bay and the adjacent estuaries and assess which areas may be prone to flooding and erosion due to waves in combination with high water levels. This is a macro-tidal environment prone to storm surges and moderate storm waves with occasional flooding in low-lying areas. Data from the POL Coastal Observatory, including the HF radar system which simultaneously measures waves and currents, have been employed to validate wave, tide and surge models for this area. We have also used the SWAN model in one-way coupled mode in comparison with the POLCOMS-WAM model to investigate the magnitude of interactions between waves, tides and surges. Here we review the physical mechanisms, their effects, and the implications for our understanding of coastal processes, and discuss where further development is still needed in shallow water wave models.

2009-11-09	Mon	Paul Mitchener (Sheffield)	Quantisation
16:10	J11	C*-algebraic deformation quantisation.

2009-11-06	Fri	Viktor Fedun (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2009-11-02	Mon	Paul Mitchener (Sheffield)	Quantisation
16:10	J11	C-algebras, states, and first steps towards C-algebraic quantisation

2009-10-30	Fri	Jaume Terradas (Centre Plasma Astrophysics and Leuven Mathematical Modeling and Computational Science Center, Katholieke Universiteit Leuven)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Nonlinear instability of kink oscillations due to shear motions

2009-10-28	Wed	Elizabeth Winstanley (Sheffield)	Applied Maths Colloquium
14:00	LT A	Black holes at the LHC

	Abstract: Brane world models in string theory suggest that our universe is a slice, or �brane�, of a higher-dimensional space-time. In this talk we will discuss why one consequence of these models is that copious numbers of mini black holes may be formed by collisions at the Large Hadron Collider (LHC) at CERN. We will describe how these mini black holes are created, and what happens to them once they have been produced. In particular, we discuss why these black holes will not swallow up the entire Earth.

2009-10-26	Mon	Kirill Mackenzie (Sheffield)	Quantisation
16:00	J11	Poisson Manifolds (part 2)

2009-10-23	Fri	Daniel Reese (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2009-10-21	Wed	Chutiphon Pukdeboon	Applied Maths Colloquium
14:00	LT A	Optimal Sliding Mode Controllers for Attitude Tracking of Spacecraft

	Abstract: This research studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternion-based spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinite-time nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers.

2009-10-21	Wed	Lawrence Chan (Sheffield)	Applied Maths Colloquium
14:30	LTA	The relationship between concentration and its dissipation rate in turbulent dispersion

	Abstract: To model the probability distribution of concentration in turbulent dispersion it is necessary to make closure assumptions. One aspect of interest in looking for reasonable closure assumptions is the relationship between concentration and its dissipation rate. Here it is assumed that Taylor's frozen turbulence hypothesis can be used to approximate the dissipation rate of concentration using the time derivative of concentration at a fixed point in space. I then use measurements of concentration from line source experiments in wind tunnel grid-turbulence to examine the behaviour of the joint and marginal distributions of concentration and its dissipation rate. A simple stochastic process model is constructed for the concentration time series, from which these distributions are also derived , and then compared with those from the experiments.

2009-10-19	Mon	Kirill Mackenzie (Sheffield)	Quantisation
16:00	J11	Poisson Manifolds (part 1)

	Abstract: Here is a sketch of what I propose for the lectures on Poisson manifolds. + Linear Poisson structures from Lie algebras + Tangent bundles are like Lie algebras ... + Symplectic structures and the Poisson bracket + Reduction of a Hamiltonian action leads to a Poisson manifold + Formalisms for working with Poisson structures: bracket of functions, bracket of 1-forms, Schouten bracket. + The symplectic leaves of a Poisson manifold + The `pre-Kontsevich approach' to quantization: Symplectic realizations. Sketch of integrability. I'm assuming familiarity with manifolds and tangent and cotangent bundles, and differential forms. For Lie algebras and Lie groups nothing at a deep level is required.

2009-10-16	Fri	Youra Taroyan (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2009-10-14	Wed	Edmund Chadwick (Salford)	Applied Maths Colloquium
14:00	LT A	Oscillatory oseenlets

	Abstract: Consider uniform flow past an oscillating body. Assume that the resulting far-field flow consists of both steady and time periodic components. The time periodic components can be decomposed into a Fourier expansion series of time harmonic components. The form of the steady component in terms of the steady oseenlet is well-known. However, the time-harmonic components in terms of oscillatory oseenlet does not yet appear to be in the literature.

2009-10-12	Mon	Paul Mitchener (Sheffield)	Quantisation
16:00	J11	Introduction to C^∗-algebras

	Abstract: This talk is intended to be extremely elementary, introducing C^∗-algebras and looking at some fundamental properties. We assume no know knowledge of analysis beyond the definitions of a normed vector space and completeness.

2009-10-09	Fri	Istvan Ballai (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Introduction into the theory of nonlinear waves

2009-10-07	Wed	Prof Michael Berry FRS (Bristol)
16:00	J11	Two by two

	Abstract: A tutorial account of families of 2x2 matrices labelled by several parameters will concentrate on the neighbourhood of degeneracies. The emphasis will be on the differences between hermitian and nonhermitian matrices, considered geometric. Physical phenomena in optics and atomic physics where such degeneracies play a crucial role will be described. This introductory talk by Prof Berry will serves to launch the MAGIC courses for 2009/10.

2009-10-02	Fri	Inigo Aregui (Departament de F�sica, Universitat de les Illes Balears, Palma de Mallorca, Spain)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Magnetohydrodynamic seismology of coronal loops and prominence fine structures

	Abstract: In this talk I will present some recent results from the application of MHD wave seismology inversion techniques to transverse oscillations observed in coronal loops and prominence fine structures. In coronal loops, damping by resonant absorption is considered. First, we will briefly demonstrate how the use of scaling laws is of no use at all for the discrimination between different damping mechanisms. In a seismological context, the combination of observed periods and damping rates with analytical and numerical results for resonantly damped kink waves in non-uniform flux tubes allows us to obtain a restricted 1D solution space that links the internal Alfven speed, the density contrast, and the transverse density structuring, in a fully consistent manner. The resulting Alfven speed is well constrained to a narrow range of values. Similar inversion techniques have recently been applied to oscillating quiescent and active region prominence threads. In quiescent filament threads resonant damping becomes independent of density contrast, for the typical large filament-to-coronal values of this parameter. This allows us to obtain precise estimates for the internal Alfven speed and the transverse inhomogeneity length-scale. Recent results from two-dimensional non-uniform thread models are also presented. They display significantly different results when compared to 1D model results. In an active region prominence, a seismological analysis of oscillating threads observed with Hinode SOT shows that, even if the available data are insufficient to derive well constrained values of the physical variables, a lower limit for the Alfven speed in each of the threads can be established.

2009-09-30	Wed	Dave Roscoe (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	The conflict between realism and the scalar potential in electrodynamics

2009-09-25	Fri	Gary Verth (K.U. Leuven (Belgium))	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Plasma diagnostics with torsional Alfven waves

2009-09-17	Thu	David Southwood (European Space Agency)	Applied Maths Colloquium
14:00	LT7	Magnetism and Rotation at Saturn: the puzzles produced by the Cassini space mission

	Abstract: The planet Saturn has for long had properties that defied expectations concerning planetary magnetism. A fast rotating gas giant, it was hardly surprising it had a dipolar magnetic field but it was surprising when early spacecraft flybys revealed that the dipole seemed almost perfectly aligned with the rotation axis. More surprises were to come. In the early nineties, measurements of the radio signals with the sensitive Ulysses spacecraft antenna revealed the Saturn kilometric radio signal was pulsing with a rate that varied slowly with time ( few times 0.1

2009-09-03	Thu	Tom Leinster (Glasgow (visiting Sheffield))
15:00	J11	Quantifying Biodiversity III

	Abstract: There is a lively and chaotic literature on how to quantify the diversity of a biological community. The challenge is to take a big mass of data about a community and distill it down to a single number, measuring its `diversity'. People have been arguing about how to do it for decades. In my talks I hope to shed some light on the matter. This involves various new pieces of mathematics: some newish category theory, a new invariant of metric spaces, and some new aspects of the notion of entropy. The emphasis these get in the talks will depend entirely on the audience; rest assured that I'll explain whatever's necessary. For better or worse, I'll entirely ignore the statistical side. [Some people might feel that one talk is all the appreciation they can handle. For their sake, I'll try to put the material of broadest appeal into the first one.]

2009-09-02	Wed	Tom Leinster (Glasgow (visiting Sheffield))
15:00	J11	Quantifying Biodiversity II

	Abstract: There is a lively and chaotic literature on how to quantify the diversity of a biological community. The challenge is to take a big mass of data about a community and distill it down to a single number, measuring its `diversity'. People have been arguing about how to do it for decades. In my talks I hope to shed some light on the matter. This involves various new pieces of mathematics: some newish category theory, a new invariant of metric spaces, and some new aspects of the notion of entropy. The emphasis these get in the talks will depend entirely on the audience; rest assured that I'll explain whatever's necessary. For better or worse, I'll entirely ignore the statistical side. [Some people might feel that one talk is all the appreciation they can handle. For their sake, I'll try to put the material of broadest appeal into the first one.]

2009-09-01	Tue	Tom Leinster (Glasgow (visiting Sheffield))
15:00	J11	Quantifying Biodiversity I

	Abstract: There is a lively and chaotic literature on how to quantify the diversity of a biological community. The challenge is to take a big mass of data about a community and distill it down to a single number, measuring its `diversity'. People have been arguing about how to do it for decades. In my talks I hope to shed some light on the matter. This involves various new pieces of mathematics: some newish category theory, a new invariant of metric spaces, and some new aspects of the notion of entropy. The emphasis these get in the talks will depend entirely on the audience; rest assured that I'll explain whatever's necessary. For better or worse, I'll entirely ignore the statistical side. [Some people might feel that one talk is all the appreciation they can handle. For their sake, I'll try to put the material of broadest appeal into the first one.]

2009-06-10	Wed	Christoffer Karoff (Birmingham)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Flares, oscillations and cycles in the Sun and other stars

	Abstract: We recently presented evidence of a strong correlation between the energy in the high-frequency part of the acoustic spectrum of the Sun and the solar X-ray flux (Karoff and Kjeldsen, 2008). The discovery indicates that flares drive global oscillations in the Sun. If this indication turns out to be true we might be able to use the relation between flares and the energy in the high-frequency part of the acoustic spectrum to detect e.g. flares on the far side of the Sun and flares on other solar-like stars. The last possibility will be tested with observations from the nearly launched Kepler satellite as part of a larger project of sounding stellar cycles with asteroseismology. Asteroseismology can sound stellar cycles by studying periodic changes, in the amplitudes and frequencies of the oscillation modes in the stars, that follow the stellar cycles. By comparing these measurements with conventional ground-based chromospheric activity measurements we might be able to increase our understanding of the relation between the chromospheric changes and the changes in the oscillation modes. Also, asteroseismic measurements of e.g. the depth of the convection zone and internal differential rotation could enable us to answer the question: Are the stellar cycles driven at the top or the base of the convection zone?

2009-05-29	Fri	David Robertson (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-05-27	Wed	Alice Robinson (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	HF Radar and Wind turbine interaction in Liverpool Bay

	Abstract: HF radar has become accepted over the last 50 years as a key tool in remote sensing of ocean currents and waves. It is favoured for excellent spatial and temporal coverage, and ease of access compared to more traditional buoy's and ADCP's. Data is available in near to real time and is well used by the maritime industry. The Proudman Oceanographic Laboratory operates a 13MHz HF WERA radar in Liverpool Bay. It is by nature sensitive to RFI and clutter which can degrade the accuracy and availability of the current and wave measurements. Liverpool Bay is undergoing extensive wind farm development which will present problems for any radar system due to their large radar cross sections. It is important to understand and mitigate any effects of the wind turbines on data accuracy and availability to achieve maximum performance from the HF radar.

2009-05-27	Wed	Andrew Newton (Sheffield)	Applied Maths Colloquium
14:30	Hicks Lecture Theatre A	Numerical Investigation into sheared MHD turbulence

	Abstract: Shear flows and magnetic fields are ubiquitous in astrophysical plasmas, playing a crucial role in turbulent transport. Here, we present the first numerical results of the suppression of magnetic diffusion by a shear flow in 2D MHD turbulence. For a very strong magnetic field, a new scaling regime of magnetic diffusion quenching by magnetic fields is found, with a stronger dependence on magnetic field strength compared to the previous result [1]. Furthermore, we show the first numerical evidence of enhanced transport due to the interaction between shear flow and magnetic field via resonances,which weakens the magnetic diffusion quenching. Similar results are also presented for momentum transport. These results highlight the importance of shear flows, (Alfven) waves, and resonances in understanding turbulent dissipation of magnetic fields. We discuss important implications of these results in turbulent magnetic reconnection and dynamos. [1] F. Cattaneo and S.I. Vainshtein, Astrophys. J. Lett. 376. L21 (1991)

2009-05-22	Fri	Andrew Gascoyne (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-05-20	Wed	Carsten van de Bruck (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Dark Energy in the Cosmos and the Laboratory

	Abstract: According to observations the expansion of the universe seems to be speeding up, instead of slowing down. To explain this observation, one is either forced to introduce a new energy component (dark energy) with strange properties (such as negative pressure) or to change the laws of gravity. In this talk I will focus on the former possibility and describe theoretical models for dark energy and how to test these with cosmological observations or even in the laboratory.

2009-05-19	Tue	John Biggins (Sheffield)	SoMaS Colloquium
17:05	LT 6 Hicks	Branching Out

	Abstract: I aim to give an overview of the synthesis of two classical probability models (branching processes and random walk) and to indicate connections with several other parts of mathematics.

2009-05-15	Fri	Carlos Jaimes (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-05-13	Wed	Jamie Douglas (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	An examination of the linear structure of the CUTIE plasma turbulence code

2009-05-08	Fri	Andrew Newton (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-05-06	Wed	D Kurtz (Central Lancashire)	Applied Maths Colloquium
14:00	Student Union Auditorium	Songs of the Stars

2009-05-06	Wed	Mike Thompson (Sheffield)	Applied Maths Colloquium
15:30	Student Union Auditorium	Helioseismology

2009-05-06	Wed	Roger Webster (Sheffield)	Applied Maths Colloquium
16:30	Student Union Auditorium	The tail of Pi

2009-05-01	Fri	Marialejandra Luna (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-04-03	Fri	Jamie Douglas (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-04-01	Wed	Steve Cowley (Director of the UKAEA, Culham Laboratory)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Fusion - the Theoretical Challenge

	Abstract: The international fusion experiment ITER will start operating in the south of France late in the next decade. This historic experiment will generate up to 500 megawatts of fusion power and provide a proof of principle for fusion energy. The theoretical description of fusion plasmas is very challenging and there are many unanswered questions. For example, the plasma is permeated with small scale turbulence that determines the confinement and the evolution. But, a full predictive model of the turbulence is still unavailable. I will outline the challenges and the progress that has been made.

2009-03-27	Fri	Christopher Clack (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-03-25	Wed	Alan Hood (St Andrews)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Heating the solar corona by nanoflares triggered by a kink instability

	Abstract: The heating of solar coronal plasma to millions of degrees may be due to the superposition of many small energy-releasing events, known as nanoflares. Nanoflares dissipate magnetic energy through magnetic reconnection. It is proposed that heating is triggered by the onset of an ideal MHD instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. Numerical simulations are used to investigate the energy release and the heating process.

2009-03-20	Fri	Sergey Zharkov (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-03-17	Tue	Simon Willerton (Sheffield)	SoMaS Colloquium
17:10	LT6	Measuring metric spaces: short-sightedness and population diversity

	Abstract: Metric spaces can be used to represent many disparate things including shapes in space and the differences between species in a population. I will describe one way to measure the size of a metric space arrived at from pure mathematical considerations but discovered independently by ecologists. I will discuss connections with diversity measures and geometry. This is intended to be accessible to all in the School.

2009-03-11	Wed	Youra Taroyan (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Alfven instability in a compressible flow

	Abstract: Abstract: Macroscopic instabilities have important energetic and dynamic consequences in space plasmas and laboratory devices. Well known examples include the current pinch, Rayleigh-Taylor and shear flow instabilies which can be studied using the magnetohydrodynamic approach. A brief introduction will be followed by a presentation of a new magnetohydrodynamic instability. It will be demonstrated that linear incompressible Alfvenic disturbances can become exponentially amplified in compressible plasma flows. The instability does not require high flow speeds or shear. The amplification process is based on the mechanism of over-reflection well-known from previous studies of shear flows. A transparent stability criterion can be derived for a simple two-layer model. The instability may arise in both open and closed magnetic structures. An application to a solar coronal loop model with a siphon flow will be presented. Theoretical and observational implications of the Alfven instability will be discussed.

2009-03-06	Fri	Youra Taroyan (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-03-04	Wed	Dr Takashi Sakajo (Hokkaido)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Dynamics of point-vortices in multiply connected domains

	Abstract: The motion of incompressible and inviscid flow is described by the two-dimensional Euler equations. According to Kelvin's theorem, the circulation is conserved along the path of a fluid particle and thus the vorticity neither generates nor disappears during its evolution. Hence in order to solve the Euler equations, we have only to investigate the evolution of the non-zero vorticity domain at the initial moment. Based on this observation, we discretize the initial non-zero vorticity domain with a set of N points, called point vortices, whose strengths are determined by the circulation around these points. Then we track the evolutions of the N point vortices. This discretization method for the Euler equations is known as the vortex method, which reduces the Euler equations to a system of ordinary differential equations for the N point vortices. The present talk gives the equation of motion for N point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles. The equation not only describes fundamental interactions between solid obstacles and fluids, but also contributes toward understanding of geophysical flows with many islands and artificial obstacles such as lakes, inland seas and coastal region. As an example, we consider the motion of a vortex dipole that consists of two point vortices with the unit strength of the opposite signs. When the multiply connected domain is symmetric with respect to the real axis, the motion of the vortex dipole is integrable for the initial configuration with the same symmetry. We investigate the integrable system in detail and discuss a non-integrable motion of the vortex dipole without the reflectional symmetry.

2009-02-27	Fri	Toshi Ogawa (Engineering Science, Osaka University, Japan)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-02-20	Fri	Philippe Caillol (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-02-18	Wed	Alice Courvoisier (Leeds)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	The Mean Field Approach to the Transport of Magnetic Fields

	Abstract: The Sun's global magnetic field is believed to be the result of a `large-scale dynamo', whereby inductive motions within the solar convection zone are able to generate and sustain a magnetic field on scales larger than their own. Mathematically, the evolution of the Sun's large-scale magnetic field is conveniently described using mean field electrodynamics, a turbulence closure theory that relies on the parametrisation of small-scale effects by transport coefficients. Among these, the so-called `alpha-effect' is responsible for the growth of the mean magnetic field and will be the focus of my talk. Trying to understand how this coefficient depends on the turbulent motions within the solar plasma is tricky. Instead, we construct simpler models based on 2D motions for which the alpha-effect can be unambiguously determined and we study systematically how the spatial and temporal coherence of the flows influence it. I will start by introducing the alpha-effect from a phenomenological and mathematical point of view before presenting the results of our calculations and discussing their implications.

2009-02-13	Fri	Eamon Scullion (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2009-02-11	Wed	Philippa Browning (Manchester)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Magnetic reconnection and the active solar corona

	Abstract: Magnetic reconnection is a process by which the topology of magnetic fields can change, even in a highly conducting plasma, and which allows efficient dissipation of magnetic energy. One of the major outstanding problems in solar physics is to explain the high temperature of coronal plasma, and a strong candidate is the dissipation of free magnetic energy by magnetic reconnection. The physical process is then essentially the same as in solar flares - dramatic energy-releasing events in the solar atmosphere - and coronal heating can be viewed as a superposition of many small flare-like events. A key feature of solar flares is the presence of non-thermal high energy charged particles, and understanding the origin of these is a challenge for theorists. These high energy particles provide an important diagnostic of the magnetic reconnection process. After an introduction to coronal heating and solar flares, some recent work concerning acceleration of high energy particles by magnetic reconnection in solar flares will be presented. Also, a new model of coronal heating by reconnection, occurring during the nonlinear phase of kink instability of coronal loops, will be described. A theoretical model based on a minimum energy principle will be described, complemented by numerical simulations.

2008-12-19	Fri	Daniel Reese (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-12-17	Wed	Dr Dave Roscoe (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Via Aristotle, Leibniz, Berkeley and Mach to necessarily large-scale fractal structure in the Universe

	Abstract: Abstract The claim that the large scale structure of the Universe is heirarchical has a very long history going back at least to Charlier's papers of the early 20th century. In recent years, the debate has centered largely on the works of Sylos Labini, Joyce, Pietronero and others, who have made the quantative claim that the large scale structure of the Universe is quasi-fractal with fractal dimension D=2. There is now a concensus that this is the case on medium scales, with the main debate revolving around what happens on the scales of the largest available modern surveys. Apart from the (essentially sociological) problem that their thesis is in absolute conflict with any concept of a Universe with an age of 14 billion years or, indeed, of any finite age, the major generic difficulty faced by the proponents of the heirarchical hypothesis is that, beyond hypothesizing the case (eg: Nottale's Scale Gravity), there is no obvious mechanism which would lead to large scale structure being non-trivially fractal. This talk describes a surprising resolution to this problem: in effect, the conflict between a homogeneous vs fractal universe is shown, at root, to be a conflict between two opposing views of ßpace". One has its roots in ideas which can be traced from Democritus, through Newton to Einstein whilst the other has its roots in ideas which can be traced from Aristotle through Leibniz, and Berkeley to Mach.

2008-12-12	Fri	Youra Taroyan (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-12-10	Wed	Dr Anne Juel (Manchester)	Applied Maths Colloquium
14:00	LTA	Steep capillary-gravity waves in oscillatory shear flows

	Abstract: Nonlinear waves in uids are associated with a rich variety of dynamics that often underpin important natural phenomena. Examples range from internal solitary-like waves that are ubiquitous features of coastal oceans to the surface ocean spectra, whose interpretation relies on the nonlinear interaction between surface water waves and wind. We study steep capillary-gravity waves that form at the interface between two stably stratied layers of immiscible liquids in a horizontally oscillating vessel, and are commonly referred to as frozen waves. The oscillatory nature of the external forcing prevents the waves from over- turning, and thus enables the development of steep shear-driven waves at large forcing. The onset of `frozen waves' occurs through a supercritical pitchfork bi- furcation, with a non-monotonic dependence on the viscosity ratio between the layers. Thus, increasing the viscosity of one of the uids often results in a more unstable interface. For larger values of the forcing parameters, a qualitative change in the wave growth takes place. Beyond a critical value of Wc (ratio of vibrational to gravity forces, proportional to the square of the forcing velocity), the experimental data collapses onto a single curve that exibits a linear depen- dence on W. The evolution of the interface shape suggests a transition from gravity to capillary dominated waves, which is consistent with the wavelength reaching a minimum for W = Wc. For larger values of the forcing parameter, the two-dimensional array of waves becomes unstable to three-dimensional oscil- latory waves through a sub-critical bifurcation that exhibits a viscosity depen- dence opposite to the primary instability. The existence of a global bifurcation point is investigated.

2008-12-05	Fri	Viktor Fedun (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-11-28	Fri	Koji Ohkitani (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Magnetic reconnection observed in the Eulerian-Lagrangian analysis of magnetohydrodynamics equations

2008-11-26	Wed	Dr Balazs Pinter (Aberystwyth)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Local helioseismology - How far can we go?

	Abstract: We can see clusters of galaxies millions of light years away in the deep space. However, looking into the interior of the nearest star is impossible even to the deservedly celebrated Hubble Space Telescope. Helioseismology is the only field of physics which offers means to discover the hidden world of the Sun. We will briefly review different techniques together with the greatest results of local helioseismology. The power of observing and analysing oscillations will be apparent also in the second part, which will be a case study in coronal seismology. A filament was visible in the Sun�s atmosphere on 15th October 2002. A part of it was clearly oscillating until the filament erupted. The spatial structure and the temporal variation of the filament oscillations will be studied by using the techniques of wavelet analysis.

2008-11-21	Fri	Johan Anderson (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-11-19	Wed	Francesca Ticconi (Universita degli Studi Roma Tre)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Synthetic aperture radar: its role in remote sensing

	Abstract: The Synthetic Aperture Radar (SAR) is an active sensor that transmits a beam of electromagnetic radiation, in the microwave region of the electromagnetic spectrum, providing high quality image of the Earth�s surface, with a fine resolution independent of the sensor altitude or wavelength. By proper selection of operating frequency, the microwave signal can penetrate clouds, haze, rain, fog and precipitation with very little attenuation, thus allowing operation in unfavourable weather conditions that preclude the use of visible/infrared system. Being an active sensor, that is providing its own source of illumination, SAR is not dependent on light from Sun and therefore it can operate day or night. Moreover, it is able to illuminate with variable look angle and can select wide area coverage. The net result is an instrument that is capable of continuously monitoring geophysical parameters related to the structural and electrical properties of Earth�s surface and also it is capable of observing dynamic phenomena, such as ocean currents, sea ice motion or changing of land cover vegetation. In addition, the topography change can be derived from phase difference between measurement using radar interferometry, achievable due the coherent character of the SAR system that retains both phase and magnitude of the backscattered echo signal. Even if the interpretation on the SAR images is less intuitive compared to the optical ones, SAR has been shown to be very useful over a wide range of applications, including sea and ice monitoring, oil pollution monitoring, oceanography, snow monitoring, forest monitoring and classification of Earth terrain.

2008-11-14	Fri	Sergey Zharkov (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-11-12	Wed	Jennifer Waters (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Data Assimilation into the Wavewatch III model

	Abstract: The assimilation of data into wave models aims to improve the performance of the model by correcting the model state with observations. The area considered in this study is the Celtic Sea region off the coast of South Wales were a Pisces HF radar was deployed between 2002 and 2005. The ultimate aim is to assimilate the HF radar data into Wavewatch III and an initial study is presented where perturbed buoy data is assimilated into the model to test the assimilation scheme configuration.

2008-11-12	Wed	Noel Robertson (SheffieldSheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Modelling of the effect of snow on the hydrology and carbon budget of boreal regions

	Abstract: In the study of global carbon dynamics, the carbon and water cycles are closely related. In order to act as an effective carbon sink, plants must have water as well as sunlight to perform photosynthesis. In cold boreal regions, where some of the world�s largest forests are located, we therefore need to quantify the role of snow water dynamics in the carbon cycle. In this talk I particularly discuss the effect of climate-driven model predictions of snow water equivalent on the hydrology and carbon budget of boreal zones such as Siberia.

2008-11-07	Fri	Gary Verth (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-11-05	Wed	Peter Constantin (Chicago)	Applied Maths Colloquium
14:00	LTA	Complex Fluids

	Abstract: I will describe recent results concerning melts of complex particles. Time permitting, I will describe some mathematical results concerning suspensions in fluids.

2008-10-31	Fri	Nicolas Leprovost (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-10-29	Wed	Elizabeth Winstanley (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Furry black holes

	Abstract: My aim in this seminar is to explain what furry black holes are, and why they might be interesting. There will not be a lot of detail on the relativity side of things, but I will explain the mathematics behind the proof of the existence and stability of furry black holes in a particular matter model.

2008-10-24	Fri	Sergey Shelyag (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-10-22	Wed	Dr Rosa Diaz-Sandoval (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Solar activity and human health

	Abstract: We will show the most important results of statistical studies regarding the relationship between solar activity and cardiac and mental diseases, as well as the physiological parameters of healthy individuals. In order to establish a plausible physical mechanism, the whole system from the sun to the human body is studied. The methodology used to find correlations between solar and health parameters is based mainly upon the spectral analysis of solar and medical data because it has been suggested that a possible physical mechanism might be related to solar periodicities. To compare the geomagnetic activity, caused by the solar activity itself, and health parameters, the Superposed Epochs Method is used. The Forbush decreases in cosmic rays and the geomagnetic index Ap are the phenomena most commonly analyzed because of previous results reported in the literature. We will show, based on the Mexican results, that solar activity could well be a risk factor that affects the vulnerable population by a factor of 2 in the occurrence of myocardial infarction diseases.

2008-10-17	Fri	Eun-Jin Kim (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2008-10-10	Fri	Takashi Sakajo (Department of Mathematics at Hokkaido University, JAPAN)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	N-vortex problem on a sphere

2008-10-07	Tue	Tom Bridgeland (Sheffield)	SoMaS Colloquium
17:00	LT7	Mirror Symmetry

	Abstract: Since its discovery by string theorists in the early 90s mirror symmetry has become a huge area of research with connections to many areas of mathematics. I'll try to give a rough feel for the subject by introducing Calabi-Yau manifolds and explaining what it means for two such manifolds to be mirror.

2008-10-03	Fri	Istvan Ballai (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Ten years of solar physics at Sheffield University

2008-10-01	Wed	Professor Keke Zhang (Exeter)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Linear and nonlinear instabilities in rotating cylindrical Rayleigh-Bénard convection

	Abstract: Motivated by the wish to understand the fundamental dynamics taking place in planetary/stellar fluid interiors and atmospheres, convection in rotating cylindrical geometry has been extensively studied. We shall present some new analytical and numerical results on linear and nonlinear convection in cylindrical systems heated from below and rotating about its vertical axis. In particular, we shall discuss asymptotic solutions of inertial convection in rotating cylinders and nonlinear counter-traveling waves in connection with the Eckhaus-Benjamin-Feir-type instability and with the saddle-node-type bifurcation in rotating cylindrical channels.

2008-09-25	Thu	Brian Sawford (Monash)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre 5	Relative Dispersion and Richardson's Constant

	Abstract: This talk will describe some very recent analysis of Direct Numerical Simulation results for turbulent relative dispersion over a wide range of Reynolds numbers. We will start with some background discussion of the nature and significance of relative dispersion and of the role of Kolmogorov's similarity theory, leading to the introduction of Richardson's constant as a fundamental parameter of relative dispersion. Although it is of great fundamental and practical significance, Richardson's constant has not been well-quantified, and model estimates for it range from 0.01 to 4. We will describe first a traditional analysis of relative dispersion data, concluding that this approach does not yield a good estimate for Richardson's constant even at the highest Reynolds number currently available. We then use a modified version of a new approach developed by Ott and Mann (JFM, 422, 207, (2000)) to show that a welldefined Richardson scaling range exists in our data. We estimate Richardson's constant over a range of Reynolds numbers showing that it decreases weakly with Reynolds number to an asymptotic value at large Reynolds number of 0.55 - 0.57.

2008-06-06	Fri	Marialejandra Luna (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-06-04	Wed	Yuri Shtessel (Alabama)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Higher Order Sliding Mode Control with Application to Blood Glucose Level Regulation

	Abstract: Control under uncertainty is one of the main topics of the modern control theory. In spite of the extensive and successful development of robust adaptive control and backstepping technique, sliding mode control (SMC) stays, probably, the main choice in handling bounded uncertainties/disturbances and unmodeled dynamics. The idea is in stirring the system trajectory to properly chosen constraints (sliding manifold) and keeping it thereafter by means of high-frequency switching control, exploiting the main features of the sliding mode: its insensitivity to external and internal disturbances matched by control and ultimate accuracy and finite-time reaching transient. Stabilization of the sliding variable in SISO systems by means of the traditional SMC, designed as a switching control with respect to the so-called sliding variable, requires the system relative degree to be equal to one with respect to the sliding variable. Also, high frequency control switching leads to the so-called chattering effect, which is exhibited by high frequency vibration of the controlled plant that can be dangerous in applications and difficult to avoid or attenuate. The intrinsic difficulties of the traditional SMC are mitigated by the higher order sliding mode control (HOSM) that stabilizes at zero not only the sliding variable, but also its successive derivatives (kth order HOSM). HOSM is a new generation of SMC that is based on a general discontinuous-control approach. The unique power of the approach is revealed by the development of practical arbitrary-order real-time robust exact differentiator, which performance is proved to be asymptotically optimal in the presence of small Lebesgue-measurable input noises. 1k- Applications of HOSM control and observation to blood glucose regulation (diabetes control) are discussed.

2008-05-30	Fri	Jamie Douglas (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 11

2008-05-28	Wed	Rekha Jain (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Interaction of p Modes with a Thin Magnetic Flux Tube

	Abstract: The Sun's magnetic active regions, composed of sunspots and plage, are topologically complex. The magnetic field is highly structured, forming a tangle of fibrils within the plage and more compact, regimented bundles within sunspot umbrae. The fragmented nature of the field makes helioseismic observations within active regions rather difficult to interpret. We choose to study the propagation of acoustic waves through regions of plage, modelling the magnetic field therein as a collection of thin flux tubes. In this talk I will present the first results of this research; the computation of the absorption coefficient from a single tube. The incoming acoustic waves interact with the flux tube, exciting sausage and kink tube waves which propagate downward and upward carrying away energy, thereby producing absorption. The tube response further scatters the incoming wave into a variety of f modes and p modes. We treat plage as a collection of noninteracting flux tubes. I will present the resulting theoretically calculated absorption coefficients and compare with the most recent observations.

2008-05-28	Wed	Rekha Jain (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	tbd

2008-05-23	Fri	Andrew Newton (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-05-21	Wed	Michael Atiyah (Edinburgh)	SoMaS Launch Event
09:00	Lecture theatre 7	Soliton dynamics

	Abstract: Many important physical problems involve non-linear PDE. Simplified models may admit exact analytical solutions, which can provide some guidance, but usually this has to be augmented by simulation, backed by physical insight. There is scope here for a really interdisciplinary approach. I will illustrate this by the example of magnetic monopoles and the Skyrmion model of protons and neutrons, showing in particular the underlying role of topology.

2008-05-21	Wed	Douglas Gough (Cambridge)	SoMaS Launch Event
10:00	Lecture theatre 7	Resonant waves in a deformed sphere

	Abstract: The resonance conditions for one-dimensional waves on a line are easy to derive and state. Brillouin, and perhaps Einstein, tried to generalize them to three dimensions in the early days of quantum theory. Unfortunately, their analyses were incomplete. It was only after Keller, nearly forty years later, recognized the importance of caustic surfaces that useful estimates of the eigenvalues of wave-like boundary-value problems were obtained, and then the resonance procedure became widely used to solve complicated problems. But I shall keep it simple. After describing the basic procedure, and applying it to acoustic waves in a spherical system, which could be a nonrotating star, I shall demonstrate how small deformations caused by rotation or a magnetic field can be accounted for, yielding asymptotic formulae which provide more insight than do more accurate numerical solutions.

2008-05-21	Wed	Terry Lyons (Oxford)	SoMaS Launch Event
11:30	Lecture theatre 7	Rough paths

	Abstract: Calculus is the main mathematical tool used to describe systems with a local interaction. Examples of this abound throughout mathematics. Even the simplest case of a control problem without feedback has a huge importance. Differential equations of the form dyⁱ = ∑_i f^i,j dx_i express the relationship between a controlling process x and a response y; x could be a path in a Lie algebra and y its development into a Lie group; x could represent the evolution of massive particles exerting a gravitational influence on the evolution of a satellite, whose state is represented by y. However, an examination of many real world situations leads one to conclude that in many contexts, the controls that influence evolution are highly oscillatory and not at all adequately modelled on normal scales by classical tools of calculus. The theory of rough paths considers the relationship between the control and the response, and identifies natural metrics making this functional uniformly continuous, and so well-defined on the completion. The completion of the smooth paths in these metrics are called rough paths; they are tractable and not particularly abstract objects (it is important to understand that they are a generalisation of the concept of a smooth path, rather than a restriction of the concept of a continuous path). They allow one to describe what is important about x on normal scales and to do numerical analysis on these scales, rather than tunnel deep into fine structure to use classical calculus. A key feature of this approach is a natural and universal representation of the class of paths in Rⁿ with concatenation into a subgroup of the free tensor algebra.

2008-05-21	Wed	Jon Keating (Bristol)	SoMaS Launch Event
14:00	Lecture theatre 7	Random matrices and number theory

	Abstract: I will review some conjectural connections between the zeros of the Riemann zeta function and random matrix theory, which underpins our understanding of complex quantum systems. I will then describe how these conjectures shed interesting new light on some deep and long-standing problems relating to the size of the Riemann zeta function and other L-functions, and the number of rational points on elliptic curves.

2008-05-21	Wed	Paul Blackwell (Sheffield)	SoMaS Launch Event
15:00	Lecture theatre 7	Random tessellations - models, inference and applications

	Abstract: Tessellations with various kinds of symmetry and regularity are well known in mathematics and in art, but tessellations generated by random processes are also important, and have been widely used as models of observed spatial patterns. Statistical inference for such processes can enable us to choose between models or theories, to reconstruct patterns or images, or to estimate underlying parameters. I will talk about a range of tessellations of the plane, including the well-known (and often re-invented) Dirichlet or Voronoi tessellation and variants obtained by for example varying the distance function used, regarding the plane as a section of a three-dimensional space, or using a form of duality-giving the Delaunay triangulation. The random process driving the tessellation will typically be a point process on some suitable space; in practice, a further modelling step is needed to describe the way in which the tessellation is observed, for example the `noise' in an image. Carrying out the actual inference involves modern computer-intensive `Markov chain Monte Carlo' techniques, which are partly derived from simulation techniques in physics. I will illustrate the models and methods with examples from ecology and a selection of possible other areas including material science, physiology, geography and astronomy.

2008-05-21	Wed	Koji Ohkitani (Sheffield)	SoMaS Launch Event
16:10	Lecture theatre 7	Recent progress in the basic problems of fluid equations

	Abstract: In this talk geared for non-specialists, we address the fundamental issues of fluid dynamics. Besides their mathematical interest as nonlinear PDEs, we explain the esoteric connection with developed fluid turbulence, centering on the so-called Onsager's conjecture. We then review what have been known mathematically regarding the 3D incompressible Euler and Navier-Stokes equations and point out the differences from what physicists and engineers expect about them. We recall how the existing methods fail to show, for example, regularity of the Navier-Stokes equations or singularity of the Euler equations. We also emphasise how studying the Euler equations may help in making possible progress in the Navier-Stokes theory. Some examples of numerical experiments are shown for illustration, where appropriate.

2008-05-21	Wed	Neil Strickland (Sheffield)	SoMaS Launch Event
16:50	Lecture theatre 7	Thoughts on toric topology

	Abstract: In this talk I'll discuss a construction that starts with some combinatorial and algebraic data and produces a manifold, called a toric variety. There are many beautiful examples, and connections with combinatorics, commutative algebra, geometry, topology and physics, so this topic lies in the intersection of many of the most active areas of research in the pure mathematics department.

2008-05-16	Fri	Alan Zinober (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10	The Big Picture in Control and Estimation with Application to Satellite Attitude Control

2008-05-09	Fri	Carlos Jaimes (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-05-07	Wed	Remi Tailleux (Reading)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Are incompressible Navier-Stokes equations valid for describing turbulent diabatic motions?

	Abstract: According to classical turbulence theory, there exists two possible pathways to dissipation for kinetic energy in a turbulent stratified fluid, a viscous and a diffusive one. The viscous pathway is well known and associated with the work of molecular viscous stresses. The second one is envisioned as a two steps process. In the first step, kinetic energy is converted into available potential energy (APE) adiabatically, without modification of the mean gravitational potential energy (GPEr). In a second step, lateral molecular diffusion is thought to irreversibly convert the APE into GPEr. Thus, according to the diffusive pathway, kinetic energy is dissipated into mean GPE. In this talk, I will present different line of arguments aiming at demonstrating that this view is invalid. Ultimately, the arguments will lead to the conclusion that the incompressible description of hydrodynamics of fluid flows at low Mach number must be invalid too for representing diabatic irreversible motions. A modification of the incompressible Navier-Stokes equations will be proposed that is more physically consistent, and how existing incompressible hydrodynamics codes can be modified will be discussed. We will also show that the above results provide a simple solution to the existing "ocean heat engine controversy".

2008-05-02	Fri	Kara Burke (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-04-30	Wed	Robert Rothschild (Lancaster)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Should airlines code-share or should they merge?

	Abstract: This seminar compares the profits from 'contractual' relationships amongst competing firms, with those obtainable when the parties formally merge. The emphasis throughout is on the essentially game-theoretic nature of the decision, and the strategic equilibria that result.

2008-04-28	Mon	Simon Willerton (Sheffield)	Quantisation
16:10	J11	K-theory

2008-04-25	Fri	Mark Douglas (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-04-23	Wed	Nicolas Leprovost (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Shear stabilisation and turbulent mixing

	Abstract: In order to explain the turbulent mixing in the solar tachocline and also the occurrence of differential rotation in the convection zone, we study the effect of rotation on sheared turbulence. By solving quasi-linear equations for the fluctuating fields, we derive turbulence amplitude and turbulent transport coefficients (turbulent viscosity and diffusivity), taking into account the effects of shear and rotation on turbulence. The interaction between the shear and the rotation is shown to give rise to a novel non-diffusive flux of angular momentum (known as the Lambda effect), possibly offering a mechanism for the occurrence of a strong shear region in the solar interior. We also discuss the effect of stratification and magnetic fields on turbulent mixing."

2008-04-18	Fri	Sergei Zharkov (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-04-17	Thu	Vappu Reijonen (Helsinki)
13:00	E39, Hicks Building

2008-04-16	Wed	A Thyagaraja (UKAEA/EURATOM Fusion Association, Culham Science Centre)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Two-fluid theory of axisymmetric toroidal equilibria

	Abstract: An introduction to key issues in the magnetic confinement to fusion power production will be given. This is followed by an overview account of a recently developed, novel approach to axisymmetric toroidal equilibria with strong flows will be presented, essentially from an analytical point of view.

2008-04-11	Fri	Philippe Caillol (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-04-09	Wed	Zhivko Stoyanov (Bath)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Clustering and ordering of large networks, and sensitivity analysis

	Abstract: Clustering is the problem of dividing a network into two or more balanced and well-connected subnetworks with only a few links between them. This is a discrete problem, which is intractable for most real-life networks, due to their size. We give a brief overview of some of the methods, available in the literature, for clustering large networks. Another discrete problem on networks, which can not be solved exactly in real-life examples, is that of ordering. For example, the problem which Google solves is that of ordering the webpages in the internet, respecting the criteria of their authority, that is, how many webpages link to a given webpage. We give a brief overview of the basics of the techique, which Google uses, in order to solve the problem of ordering. In the second half of the talk we motivate the sensitivity analysis of networks and consider the effects, which small perturbations of the data can produce on the clustering of the network.

2008-04-04	Fri	Daniel Rees (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-03-19	Wed	Anne Juel (Manchester)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Interfacial wave growth in oscillating two-phase flow

	Abstract: When a closed vessel containing two stably stratified, immiscible liquids is oscillated sinusoidally in the horizontal direction, the at interface between the two liquids loses stability to two-dimensional `frozen waves' through a mech- anism analogous to that of the KelvinHelmholtz instability). The onset of `frozen waves' occurs through a supercritical pitchfork bifurcation, but for larger values of the forcing parameters, a qualitative change in the wave growth takes place. In terms of the inverse vibrational Froude number, W (ratio of vibrational to gravity forces, proportional to the square of the forcing velocity), there is a critical value, Wc, beyond which the experimental data collapses onto a single curve that exibits a linear dependence on W. We find that this collapse is indicative of a bifurcation to an inviscid solution at Wc. Our investigation of the evolution of the interface shape suggests that this second bifurcation is associated with a transition from gravity to capillary dominated waves, which is consistent with the wavelength reaching a minimum for W = Wc. For larger values of the forcing parameters, the two-dimensional array of waves becomes unstable to three-dimensional oscillatory waves through a sub-critical bifurca- tion. The response frequency of the three-dimensional oscillatory waves is found to be locked to the forcing frequency. Secondary transition to three-dimensional waves underpin the dynamics of a variety of fluid flows, e.g. the oscillatory instability of rolls in thermal convection and the formation of streamwise vortices in mixing layers. We characterise the secondary instability of our oscillating interface by comparison with these systems and discuss the physical mechanism that leads to the onset of three-dimensional waves.

2008-03-14	Fri	Sergey Shelyag (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-03-10	Mon	Richard Hepworth (Sheffield)	Quantisation
16:10	J11	The Hirzebruch Signature Theorem

2008-03-07	Fri	Nicolas Leprovost (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-03-05	Wed	Gene Ryan (Bath)	Applied Maths Colloquium
13:30	Hicks Lecture Theatre 7	Input-to-State Stability of Differential Inclusions with Application to Hysteretic Feedback Systems

	Abstract: Input-to-state stability is a concept that captures �nice� properties of dynamical systems with input (e.g. bounded input implies bounded state, input �eventually small� implies state �eventually small�, input convergent to zero implies state convergent to zero). Input-to- state stability (ISS) of a class of differential inclusions is described. Every system in the class is of Lur�e-type: a feedback interconnection of a linear system and a (set-valued) nonlinearity. Applications of the ISS results, in the context of feedback interconnections with a hysteresis operator in the feedback path, are developed.

2008-02-29	Fri	James McLaughlin (St Andrews University)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-02-26	Tue	Michael Thompson (Sheffield)	SoMaS Colloquium
17:00	Hicks Lecture Theatre 7	Forward and Inverse Problems of Solar Seismology

	Abstract: The Sun oscillates simultaneously in more than a million resonant modes, the oscillations being manifest in small-amplitude motions of the Sun's surface. The measured properties of the observed oscillations can be used to infer conditions inside the Sun, a study known as helioseismology. In this colloquium I shall describe the forward problem of modelling the oscillations and the inverse problems that arise in using the oscillations to infer properties of the solar interior and its physics.

2008-02-22	Fri	Youra Taroyan (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 10

2008-02-20	Wed	Chris Jones (Leeds)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Convection driven zonal flows in giant planets

	Abstract: The large scale zonal flows on Jupiter and Saturn may be due either to deep convection or to forcing in the stably stratified zone near the surface. Boussinesq simulations of deep convection in a rapidly rotating spherical shell have been successful in reproducing the strong eastward flowing current and the alternating bands of eastward and westward flow. We are currently developing an anelastic compressible model to see how the large density variation between the deep interior and the near-surface layers affects these results. A further issue is whether the magnetic field can affect the nature of the surface flows on giant planets.

2008-02-18	Mon		Quantisation
16:00	J11	Organisational Meeting

2008-02-13	Wed	Philippe Caillol (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Nonlinear singular Kelvin modes within a barotropic vortex

	Abstract: This study considers the propagation of helical neutral modes within a barotropic and axisymmetric vortex with an arbitrary azimuthal velocity profile. The singular mode/mean flow interaction leads to strongly nonlinear critical layers around the radius where the angular velocity of the mean flow and the disturbance frequency are comparable. Strong analogies can be done with the theory of critical layers in a stratified flow. We formulate a theory valid when the analogous local Richardson number is small at the critical radius but is nevertheless larger than the mode amplitude, and at a long time asymptotic steady state after the formation of the critical layer. The problem is tackled by removing the apparent singularity by retaining nonlinear terms in the equations of motion inside the critical layer. Viscosity is also introduced in order to render the nonlinear critical layer solution unique, but the inviscid limit is eventually taken. The result from the interaction is the emergence of a multipolar vortex whose poles are located on the critical radius, spiral around the basic vortex axis and are embedded in a distorted mean flow caused by a slow diffusion of the three-dimensional vorticity field from the critical layer in a transitional stage due to the very weak viscosity of the flow. This study gives an analytical description of these vortices.

2008-02-06	Wed	Yi Li (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	A restricted Euler model for small scale intermittency in fluid turbulence

	Abstract: Small-scale intermittency in fluid turbulence refers to the infrequent but strong bursts in the signals of small scale parameters. These bursts display highly non-Gaussian statistics, and its prediction poses serious challenges to turbulence research. Based on the restricted Euler approximation, we derive in this talk a simple system of equations for the short-time Langrangian evolution of velocity and passive scalar increments. The system reproduces several important intermittency trends observed in turbulence, and thus provides a simple dynamic explanation for the observations.

2008-01-30	Wed	Jesse Andries (Katholieke Universiteit Leuven, Belgium)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A	Decoherence of MHD wave packets: a simple example

	Abstract: Magnetohydrodynamic waves have been studied extensively in the literature. They have received much attention lately in efforts to indirectly extract information about the solar coronal plasma by combining theoretical models with data of (spaceborne) instruments that record ample evidence of MHD waves in the solar atmosphere. We will provide a rigorous treatment of linear MHD oscillations in a very simple model emphasizing the self-adjointness and the origin and implications of the existence of continuous parts in the eigenmode spectrum. This will illustrate an important idea which is mathematically and conceptually very easy to understand but which has not yet received enough attention in the context of 'coronal seismology'. Roughly speaking, the output of a system is a convolution between the input and the system. So if you want to draw conclusions based on the output of a system, either you need some information about the input which allows to determine the system, or you need some information on the system in order to draw conclusions on the input. 'Coronal seismology' has so far mainly focussed on discrete trapped waveguide modes and has therefore not payed much attention to this. However, it provides a unifying conceptual framework for the interpretation and comparison of several mechanisms which are often invoked to explain the observed wave behavior and which are often interpreted as being conceptually different (e.g. phase mixing, resonant absorption and leakage). Certainly, within the current understanding that coronal waves are coupled and driven by oscillations in the lower layers of the solar atmosphere and at the solar surface, it is important to appreciate that the characteristics of the solar coronal waves may depend crucially on the characteristics of the driver/exciter and not only on the characteristics of the medium itself.

2007-12-14	Fri	Eamon Scullion (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-12-12	Wed	Professor Steve Decent (Birmingham)	Applied Maths Colloquium
16:00	Hicks Lecture Theatre 6	Unstable Jets, Threads and Curtains

2007-12-10	Mon	Dave Applebaum (Sheffield)	Quantisation
17:00	J11	The Heat Equation

2007-12-07	Fri	Daniel Rees (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-11-30	Fri	Philippe Caillol (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-11-28	Wed	Professor John Brown (Glasgow)	Applied Maths Colloquium
15:00	Hicks Lecture Theatre 6	\'The High Energy Sun and NASA\'s Award Winning RHESSI Mission\'

2007-11-23	Fri	Stephen Fletcher (Sheffield Hallam)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-11-21	Wed	Mahesan Niranjan (Sheffield)	Applied Maths Colloquium
16:00	Hicks Lecture Theatre 6	Some fun problems that simultaneously excite Biologists, Applied Mathematicians and Computer Scientists

2007-11-16	Fri	Viktor Fedun (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-11-14	Wed	Keiichi Ueda (Kyoto University)	Applied Maths Colloquium
16:00	Hicks Lecture Theatre 6	Stripe splitting in reaction-diffusion systems on uniformly growing domains

2007-11-09	Fri	Youra Taroyan (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-11-07	Wed	Dr C.J.Howls (Southampton)	Applied Maths Colloquium
16:00	Hicks Lecture Theatre 6	'Why is a Shock Not a Caustic?

2007-11-02	Fri	Gemma Attrill (MSSL)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-10-31	Wed	Professor Alan Zinober (Sheffield)	Applied Maths Colloquium
16:00	Hicks Lecture Theatre 6	'Optimal Control and Some Applications in Operations Research'

2007-10-26	Fri	Sergei Zharkov (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-10-22	Mon	Paul Mitchener (Sheffield)	Quantisation
17:00	J11	Motivation and Introduction to the Index Theorem

	Abstract: We will look at de Rham cohomology, the Euler characteristic, differential operators, and the Gauss-Bonnet formula in an attempt to motivate the Atiyah-Singer index theorem before stating the theorem in its general form. The plan is for this to be a short talk; we will work out organisational details for the rest of the semester afterwards.

2007-10-19	Fri	Urmila Mitra-Kraev (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-10-12	Fri	Johan Anderson (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-10-10	Wed	Dr Matthew P.Juniper (University of Cambridge)	Applied Maths Colloquium
16:00	Hicks Lecture Theatre 6	'Absolute Stability in Fuel Injectors'

2007-10-09	Tue	David Applebaum (Sheffield)	SoMaS Colloquium
17:00	Hicks Lecture Theatre 7	Some Random Thoughts on the Laplacian

	Abstract: The Laplacian is one of the most important linear operators in mathematics. One reason for this is its ubiquitous role in important second order partial differential equations (pdes) and this lecture will focus mainly on the heat equation. I'll describe the probabilistic method of solving this pde using Brownian motion and show how this relates to the modern analytical approach via semigroup theory. In the last part of the talk, we'll bring in some geometry and I'll describe how the Laplacian on a compact Riemannian manifold can yield information about the curvature.

2007-10-05	Fri	Mykola Gordovskyy (Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9

2007-06-06	Wed	Reza Tavakol (Queen Mary)	Applied Maths Colloquium
16:00		Dynamo models and differential rotation in the Sun and late-type rapidly rotating stars

2007-05-30	Wed	Daniel Brown (Aberystwyth)	Applied Maths Colloquium
16:00		The onset of x-ray bright points in the solar corona

2007-05-23	Wed	Johan Anderson (Sheffield)	Applied Maths Colloquium
16:00		Comparison of theoretical models to zonal flow generation and the effects of back-reaction of zonal flows on ITG turbulence

2007-05-16	Wed	Roddy Vann (York)	Applied Maths Colloquium
16:00		A burning fusion plasma: theoretical challenges

2007-05-09	Wed	Sergei Nazarenko (Warwick)	Applied Maths Colloquium
16:00		Leith-type model of 2D turbulence and its predictions

2007-05-02	Wed	Tom Van Doorsselaere (Warwick)	Applied Maths Colloquium
15:00		Recent results in coronal loop seismology: determination of the non-ideal damping mechanism and the density scale height

2007-04-25	Wed	Christian Boehmer (Portsmouth)	Applied Maths Colloquium
16:00		Does the cosmological constant imply the existence of a minimal energy density?

2007-04-18	Wed	Patrick Fowler (Sheffield (Chemistry Department))	Applied Maths Colloquium
16:00		Mapping currents in molecules

2007-03-21	Wed	May-Win Thein (New Hampshire)	Applied Maths Colloquium
16:00		Celestial Navigation (CelNav): Lunar Surface Navigation

2007-03-07	Wed	T. Talipova (Institute of Applied Physics, Russian Academy of Sciences)	Applied Maths Colloquium
16:00		The Gardner equation in nonlinear theory of wave motion in stratified medium

2007-02-28	Wed	Tony Arber (Warwick)	Applied Maths Colloquium
16:00		Emergence of flux through into the Solar corona: the effect of partially ionized layers

2007-02-21	Wed	Silvia Dalla (Manchester)	Applied Maths Colloquium
16:00		Solar science with AstroGrid

2007-02-14	Wed	Rich Kerswell (Bristol)	Applied Maths Colloquium
16:00		Transition to Turbulence in a Pipe

2007-02-07	Wed	Jitesh S.B. Gajjar (Manchester)	Applied Maths Colloquium
16:00		Global stability calculations of some separated flows

0000-00-00	Wed	Andrew Newton (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A

0000-00-00	Wed	Chutiphon Pukdeboon (Sheffield)	Applied Maths Colloquium
14:00	Hicks Lecture Theatre A

0000-00-00	Wed	Nick Monk (Sheffield)	Applied Maths Colloquium
14:00	LT10

0000-00-00	Wed	Alex Best (Sheffield)	Applied Maths Colloquium
14:00	LT10	Modelling disease dynamics: the coevolution of parasites and their hosts

	Abstract: Understanding the dynamics of infectious disease poses a major challenge for modern science with a range of health, social and financial implications. Mathematical models of host-parasite interactions provide key tools for our understanding of disease dynamics. In this talk I shall introduce the classic S-I-R infectious disease model, as well as the evolutionary modelling framework of adaptive dynamics, and use these to investigate the evolution and coevolution of parasite virulence and host defence. Specifically I shall focus on factors that select for high virulence and defence, and on the evolution of diversity in host-parasite systems through evolutionary branching.