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2014/15 semester 1 events in Mathematics

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Mon 01/09/14 18:30
D'Arcy Thompson
Public Lecture
Dr. Lucie Green (Mullard Space Science Laboratory)
Solar Max
abstract

Abstract

There is more to our Sun than meets the eye. Observations from spacecraft have, over the last 50 years, revealed astonishing activity that cannot be seen from the Earth. This talk will discuss where we are in the solar cycle and whether the Sun has indeed reached the maximum in its cycle. It will also show you the science behind the activity including how eruptions of magnetic field from the Sun’s atmosphere are formed and how these eruptions can be linked to other activity known as solar flares and even sunquakes.

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Tue 16/09/14 14:00
Fulton G20
Mathematics Seminar
Dr. Alessandro de Moura (University of Aberdeen)
Mon 22/09/14 15:00
Fulton G20
Mathematics Seminar
Dr. Andrea Cangiani (University of Leicester)
Extending Finite Element Methods to Polytopic Meshes
abstract

Abstract

Can we extend the FEM to general meshes while maintaining the ease of implementation and computational cost comparable to that of FEM? Within this talk, I will present two approaches that achieve just that (and much more): the Virtual Element Method (VEM) and the discontinuous Galerkin method. The Virtual Element spaces are like the usual (polynomial) finite element spaces with the addition of suitable non-polynomial functions. The novelty of the VEM approach is that it avoids expensive evaluations of the non-polynomial (virtual) functions by basing all computations on a set of carefully chosen degrees of freedom. In doing that we can easily deal with complicated element geometries and/or higher continuity conditions (like C1, C2, etc.), while maintaining the computational complexity comparable to that of standard finite element computations. As you might expect, the choice and number of the degrees of freedom depends on the continuity requirements. If mesh flexibility is the goal, while one is ready to give up on regularity, other approaches can be considered. For instance, the discontinuous Galerkin method is naturally suited to deal with polygonal/polyhedral meshes, as we shall show.

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Sat 27/09/14 14:00
Fulton H2
Mathematics Open Day
Mathematics Staff (Open Day)
Chaos, Randomness and Chance: Getting order from Disorder
Mon 29/09/14 14:00
Fulton G20
Mathematics Seminar
Dr. Emanuele Tassi (Aix-Marseille UniversitĂ©)
Hamiltonian models for plasma physics
abstract

Abstract

The theoretical description of both laboratory and astrophysical plasmas is very often based on fluid or kinetic reduced models. Typically, such models are obtained by more general models after performing operations such as truncations, averagings or asymptotic expansions. In the non-dissipative limit, all such models are supposed to possess a Hamiltonian structure. In this talk I will show how some fluid and kinetic models of interest for plasma physics can be formulated as infinite-dimensional Hamiltonian systems, identified by a conserved Hamiltonian functional and a Poisson bracket, often of noncanonical type. From a fundamental point of view, this approach provides a unifying framework for treating a large number of models. From a more practical point of view, it helps in obtaining information on the dynamics of the system, in terms, for instance, of conservation laws and stability properties. I will also discuss some applications of this formulation related, for instance, to the phenomenon of magnetic reconnection.

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Mon 06/10/14 14:00
Fulton G20
Mathematics Seminar
Dr. Hugh Hudson (UC Berkeley / University of Glasgow)
The Role of Particles in Solar Magnetic Activity
abstract

Abstract

The various aspects of solar magnetic activity include the topics of coronal heating, flares, CMEs, "space weather" and many other phenomena largely seen in the solar atmosphere. These often involve the acceleration of non-thermal particles, in large numbers and far outside the energies that particles would have in any fluid description of the process. I will describe our knowledge of these inherently non-thermal effects and ask how they relate to our theoretical descriptions, many of which simply ignore energy and momentum transport by the particles.

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Mon 13/10/14 15:00
Fulton G20
Mathematics Seminar
Dr. Sorin Pop (Eindhoven University of Technology )
Dissolution and precipitation in porous media: from pore scale to Darcy scale
abstract

Abstract

In this presentation we consider a mathematical model for dissolution and precipitation in porous media. The model is a coupled evolution system involving reaction, diffusion, transport, and ordinary differential equations. Compared to similar models for reactive flows, the particularity encountered here is in the modeling of the dissolution. This involves a multi-valued rate and can explain the occurrence of dissolution fronts. After addressing some modeling details, we present results concerning the existence and uniqueness of a weak solution at the pore scale. Next, we employ upscaling techniques to derive the corresponding model at the core (laboratory) scale, for which existence and uniqueness results are provided. Further, the convergence of numerical discretization techniques (FEM/MFEM) is discussed. We conclude the presentation with related results on domains with rough boundaries, or evolving surfaces at the pore scale. This is a joint work with C.J. van Duijn (Eindhoven), , K. Kumar (Texas), A. Mikelic (Lyon), T.L. van Noorden (Comsol), M. Neuss-Radu (both Erlangen), and F.A. Radu (Bergen)

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Mon 20/10/14 14:00
Fulton G20
Mathematics Seminar
Prof. Roger Fletcher (University of Dundee)
Iterative regularisation of large scale inverse problems
abstract

Abstract

Inverse problems arise when we wish to compute parameters in a mathematical model that give rise to a given observed or desired effect. They occur widely in fields such as machine learning, geophysics, medical imaging, remote sensing, non-destructive testing, astronomy, computer vision, statistical inference, and many others. The problems are difficult to solve as they are almost invariably large, ill-posed (we may not be able to exactly characterise a solution) and ill-conditioned (small perturbations in the data give rise to large changes in the solution). The talk will review the various iterative methods (Lanczos, Conjugate gradients, Spectral gradients) that are at our disposal for solving such problems. Regularisation techniques such as Tikhonov regularisation, Truncated SVD, and "early stopping" are described, which attempt to give some meaning as to what constitutes an acceptable solution to an inverse problem. Some numerical experiments on an image de-blurring problem are presented which show the effect of the various regularisation techniques. Some new iterative methods for solving these and other problems are proposed.

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Mon 03/11/14 14:00
Fulton G20
Mathematics Seminar
Dr. Lloyd Bridge (University of Swansea)
Modelling the impact of plant shoot architecture on leaf cooling: coupled heat and mass transfer simulations
abstract

Abstract

Plants display a range of striking architectural adaptations when grown at elevated temperatures. In the model plant Arabidopsis thaliana, these include elongation of petioles and increased petiole and leaf angles from the soil surface. The potential physiological significance of these architectural changes remains speculative. We address this issue computationally by formulating a mathematical model and performing finite element simulations, investigating the hypothesis that elongated and elevated plant configurations may reflect a leaf-cooling strategy. This sets in place a new basic model of plant water use and interaction with the surrounding air, using a transpiration term which depends on saturation, temperature and vapour concentration. A two-dimensional multi-petiole shoot geometry is considered, with added leaf-blade shape detail. Our simulations show that increased petiole length and angle generally result in enhanced transpiration rates and reduced leaf temperatures in well-watered conditions. Furthermore, our computations also reveal plant configurations for which elongation may result in decreased transpiration due to decreased leaf liquid saturation. We offer further qualitative and quantitative insights into the role of architectural parameters as key determinants of leaf cooling capacity.

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Mon 17/11/14 14:00
Fulton G20
Mathematics Seminar
Dr. Anotida Madzvamuse (University of Sussex)
An optimal control approach for modelling Neutrophil cell migration
abstract

Abstract

Cell migration is of vital importance in many biological studies, hence robust cell tracking algorithms are needed for inference of dynamic features from (static) in vivo and in vitro experimental imaging data of cells migrating. In recent years much attention has been focused on the modelling of cell motility from physical principles and the development of state-of-the art numerical methods for the simulation of the model equations. Despite this, the vast majority of cell tracking algorithms proposed to date focus solely on the imaging data itself and do not attempt to incorporate any physical knowledge on cell migration into the tracking procedure. In this study, we present a mathematical approach for cell tracking, in which we formulate the cell tracking problem as an inverse problem for fitting a mathematical model for cell motility to experimental imaging data. The novelty of this approach is that the physics underlying the model for cell migration is encoded in the tracking algorithm. To illustrate this we focus on an example of Zebrafish (Danio rerio's larvae) Neutrophil migration and contrast an ad-hoc approach to cell tracking based on interpolation with the model fitting approach we propose in this talk.

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Tue 18/11/14 16:00
Fulton G20
Mathematics Seminar
Prof. Christina Surulescu (University of Kaiserslautern )
Mathematical models for anisotropic glioma invasion: a multiscale approach
abstract

Abstract

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. Since they are highly invasive they are hard to remove by surgery, as the tumor margin it most often not precisely enough identifiable. The understanding ofglioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. We propose a multiscale framework for glioma growth including interactions of the cells with the underlying tissue network, along with proliferative effects. Relying on experimental findings, we assume that cancer cells use neuronal fibre tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we deduce on the macroscale effective equations characterizing the evolution of the tumor cell population and perform numerical simulations based on DTI data.

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Mon 24/11/14 14:00
Fulton G20
Mathematics Seminar
Dr. Andreas Dedner (University of Warwick)
Discontinuous Galerkin nethods for surface PDEs
abstract

Abstract

The Discontinuous Galerkin (DG) method has been used to solve a wide range of partial differential equations. Especially for advection dominated problems it has proven very reliable and accurate. But even for elliptic problems it has advantages over continuous finite element methods, especially when parallelization and local adaptivity are considered. After introducing the notation and analysis for DG methods in Euclidean spaces, we will extend the DG method to general surfaces. The surface finite-element method with continuous ansatz functions was analysed some time ago; we extend this results to a wide range of DG methods where the non-smooth approximation of the surface introduces some additional challenges. Both a-priori and a-posteriori analysis is presented together with numerical experiments.

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Mon 01/12/14 14:00
Fulton G20
Mathematics Seminar
Dr. David MacTaggart (Abertay University )
Topological flux emergence
abstract

Abstract

Dynamic activity in the solar atmosphere is driven, in part, by the emergence of magnetic flux from beneath the solar surface. Once in the atmosphere, these magnetic regions can create a plethora of interesting phenomena, including some of the most violent eruptions in the solar system. In this talk, I'll discuss how to model flux emergence and exploit the topological properties of the magnetoplasma in order to study certain eruptive phenomena.

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Mon 08/12/14 14:00
Fulton G20
Mathematics Seminar
Dr. Brendan Owens (University of Glasgow)
The topology of knots
abstract

Abstract

The aim of this talk is to give an introduction to mathematical knot theory. I will try to indicate why knots are of central importance in the study of low-dimensional topology, and also mention a few applications. I will discuss various quantities or invariants associated to knots and give some examples. No expertise in topology will be assumed.

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