Seminars this semester



Feb 8	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.


Feb 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.


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


Feb 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.


Mar 7	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.


Mar 8	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.


Mar 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.


Mar 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.


Mar 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.


Mar 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.


Apr 2	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/.


Apr 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.


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


May 4	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


May 9	Wed	Dr Anantanarayanan Thyagaraja (Culham)
14:00	LT6


May 9	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.


May 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.


May 18	Fri	Alistair Williamson (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9	Resonant damping of kink waves in a loop with a time dependent density

	Abstract: Resonant absorption is a popular and viable mechanism to model the twin problems of MHD wave damping in solar coronal structures (e.g. coronal loops or prominences) and the heating of the plasma in the magnetised corona. Earlier modelling applied the concept of resonant absorption of slow and Alfven waves in stationary plasma where the background equilibrium is time-independent. However, high-resolution observations of the current cohort of solar instruments clearly indicate that often there is a time-dependent plasma behaviour associated with loop oscillations. In this presentation we show the first steps made to address the challenges in the development of resonant MHD wave theory in a time-dependent plasma. Expressions for the decrease in wave amplitude and wave dissipation across both the Alfven and slow resonant points have been found for plasma structures within time-dependent models. This work also aims to show how the wave amplitude across the resonant point changes in time and contributes to the rapid damping of resonantly coupled driven MHD kink waves.


May 23	Wed	Jingsong He (Ningbo University, China)	Applied Maths Colloquium
14:00	Lecture Theatre 10	Some new patterns of the higher order rogue waves of the NLS equation

	Abstract: The rogue wave of the Nonlinear Schrodinger equation is one kind of hot topic in the studies of water wave, plasma, nonlinear optics and mathematical physics. One core problem is the generating mechanism of this very novel phenomenon. In this talk I shall discuss how to make different patterns (including circular, triangle and their combinations) of the higher order rogue waves of the NLS from breather solutions, which provides a new insight of the mechanism of the rogue wave. I also hope to show similar results of Hirota equation if the time is sufficient.


Jun 8	Fri	Stuart Mumford (University of Sheffield)	SP2RC Friday Seminars
13:05	Lecture Theatre 9