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2013/14 semester 2 events in Mathematics

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Thu 09/01/14 10:00
Fulton G20
Mathematics Seminar
Miss Franca Hoffmann (University of Cambridge)
Bacterial Chemotaxis & Social Forces
abstract

Abstract

How do bacteria communicate? Why does a single bacterium move seemingly randomly at the microscopic level, yet when we look at the whole population we observe a bulk of bacteria displacing themselves in a straight line towards the food source? The classical Keller-Segel model for cell motion reveals some very interesting mathematical phenomena that are in contradiction with the biological context, such as the existence of a critical mass governing the regularity of solutions. We will suggest an alternative model, obtained by a bottom-up scaling approach from the underlying velocity-jump process. The same idea can be generalised to understand more complex pattern formation in animal communities. What are the individual-level behavioural traits governing these features? We will present a new social interaction model in two dimensions for individuals that attract, repulse and align with each other and discuss its properties.

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Mon 13/01/14 14:05
Fulton G20
Mathematics Seminar
Dr. Peter Hinow (University of Wisconsin - Milwaukee, USA)
Algebraic and Topological Indices of Molecular Pathway Networks in Human Cancers
abstract

Abstract

Biological networks have been an active area of research for some years, in particular protein-protein interaction (PPI) networks. We retrieve the protein-protein interaction networks of 11 human cancers from the Kyoto Encyclopedia of Genes and Genomes (KEGG) and determine their relative automorphism group sizes and the dimensions of their cycle spaces. These quantities are commonly taken to be measures of network complexity in physics and computer science. We find evidence that greater network complexity is associated with lower five year survival probabilities. Moreover, we identify several protein families (PIK, ITG, AKT) that are repeated motives in many of the cancer pathways. Our results can aide in identification of promising targets for anti-cancer drugs. This is joint work with Jack A. Tuszynski (Cross Cancer Institute and Department of Physics, University of Alberta, Edmonton, AB, Canada) and Edward A. Rietman (Center for Cancer Systems Biology, Tufts University School of Medicine, Boston, MA, USA).

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Mon 20/01/14 14:05
Fulton G20
Mathematics Seminar
Prof. Ansgar Jungel (TU Wien)
Entropy structure in cross-diffusion models from biology
abstract

Abstract

Multi-particle systems for multiple species or fluid components can be described in the continuum limit by cross-diffusion systems, derived from lattice or fluid-type models. The main feature of these strongly coupled partial differential equations is that the diffusion matrix is often neither symmetric nor positive definite, which makes the mathematical analysis very challenging. In many situations, however, these systems possess an entropy structure, i.e., there exist so-called entropy variables which make the diffusion matrix positive definite. The existence of these variables is equivalent to the existence of a Lyapunov functional (free energy or logarithmic entropy), leading to a priori estimates. Although the maximum principle does not hold for such systems, the entropy variables naturally leads to lower or upper bounds of the solution. This allows for a mathematical theory for certain classes of cross-diffusion systems. We detail this theory for some examples: a variant of the chemotaxis Keller-Segel model; the tumor-growth model by Jackson and Byrne; and Maxwell-Stefan systems for multicomponent mixtures. The existence of global weak solutions is proved and numerical examples are presented.

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Mon 27/01/14 14:05
Fulton G20
Mathematics Seminar
Prof. Jonathan Sherratt (Heriot-Watt University)
How does seasonal forcing affect vole population cycles?
abstract

Abstract

Voles are a classic example of a cyclic population, with peaks and troughs of abundance occurring every 3-5 years. In Northern lattitudes voles are also subject to strong environmental forcing. I will discuss the way in which this external forcing conspires with the intrinsic oscillations to produce the complex population dynamics that are observed in field data. I will compare two significantly different habitats: Fennoscandia and Northern UK. In Fennoscandia, vole cycles are driven by predation by weasels. I will discuss the dynamics of a predator-prey model for this interaction, in which the vole (prey) birth rate is seasonally forced. I will show how a detailed understanding of bifurcations in this forced system enables the rich dynamics to be understood, and I will discuss the applications of our results to the transition from annual to multiannual cycles that is seen as one moves from South to North in Fennoscandia. In Northern UK, empirical data shows that vole cycles are not caused by predation. I will describe the results of a large multi-disciplinary research project that has investigated an alternative possible cause: that the cycles are due to a defence response in grass. When the main grass species in vole habitats is grazed, it regrows with a higher silica content, which reduces its quality as a food source for voles. I will describe a model that shows that this can lead to multi-year cycles, with seasonal forcing being a key factor for the resulting population dynamics.

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Mon 03/02/14 14:05
Fulton G20
Mathematics Seminar
Dr. Jaroslav Dudik (University of Cambridge)
The Non-Maxwellian Distributions in the Solar Atmosphere
abstract

Abstract

Departures from the Maxwellian distribution of particle energies are routinely observed during solar flares and have also been predicted in the transition region. In the solar corona, presence of impulsive nanoflare heating could also lead to particle acceleration and possibly high-energy tails. Spectroscopic consequences of different types of non-Maxwellian distribution are examined. We searched for possible diagnostics using transition region lines observed by SUMER and IRIS, as well as coronal lines observed by Hinode/EIS. The optically thin nature of the coronal plasma makes the diagnostics of non-Maxwellian distributions difficult. However, the Differential Emission Measures (DEM) recovered are not very sensitive to the presence of the high-energy tail, making them a valuable tool to study the coronal heating problem. In addition to the high-energy tails, dielectronic satellite lines have been observed to be increased with respect to the allowed lines. This phenomenon cannot be explained by the presence of the high-energy tails alone. The bulk of the distribution function at energies of several keV needs to be modified as well. We present diagnostics of quasi-monoenergetic distributions from X-ray spectra observed by RESIK and RHESSI, and the possible physical meaning of such diagnosed distributions.

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Mon 10/02/14 14:05
Fulton G20
Mathematics Seminar
Dr. Jan-Ulrich Kreft (University of Birmingham)
Individual-based modelling of aging in unicellular organisms:specialist versus generalist models
abstract

Abstract

How aging, being unfavourable for the individual, can evolve is an unsolved problem of biology. Evidence for aging in unicellular organisms is far from conclusive. Some studies found aging even in symmetrically dividing unicellular organisms. Others did not find aging in the same, or in different, unicellular organisms, or only under stress. Mathematical models suggested that segregation of non-genetic damage, i.e. aging, would increase fitness. However, these models failed to consider repair as an alternative strategy or did not properly account for the benefits of repair. We used a new and improved individual-based model to rigorously examine the effect of a range of aging strategies on fitness in various environments. Repair of damage emerges as the best strategy despite its fitness costs, since it immediately increases growth rate. There is an optimal investment in repair that outperforms damage segregation in well-mixed, lasting, and benign environments over a wide range of parameter values. Damage segregation becomes beneficial, and only in combination with repair, at high rates of damage accumulation if the damage is toxic and efficiency of repair low. In contrast to previous models, our model predicts that unicellular organisms should have active mechanisms to repair damage. Indeed, as predicted, all organisms have evolved active mechanisms of repair whilst aging in unicellular organisms is absent or accidental under benign conditions, apart from microorganisms with a different ecology, inhabiting short-lived environments strongly favouring early reproduction rather than longevity. In conclusion, aging confers no fitness advantage for unicellular organisms in lasting environments under benign conditions, since repair of non-genetic damage is better than damage segregation.

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Mon 17/02/14 14:05
Fulton G20
Mathematics Seminar
Prof. Darren Wilkinson (Newcastle University)
Stochastic Modelling of Genetic Interaction in Budding Yeast
abstract

Abstract

Saccharomyces cerevisiae (often known as budding yeast, or brewers yeast) is a single-celled micro-organism that is easy to grow and genetically manipulate. As it has a cellular organisation that has much in common with the cells of humans, it is often used as a model organism for studying genetics. High-throughput robotic genetic technologies can be used to study the fitness of many thousands of genetic mutant strains of yeast, and the resulting data can be used to identify novel genetic interactions relevant to a target area of biology. The processed data consists of tens of thousands of growth curves with a complex hierarchical structure requiring sophisticated statistical modelling of genetic independence, genetic interaction (epistasis), and variation at multiple levels of the hierarchy. Starting from simple stochastic differential equation (SDE) modelling of individual growth curves, a Bayesian hierarchical model can be built with variable selection indicators for inferring genetic interaction. The methods will be applied to data from experiments designed to highlight genetic interactions relevant to telomere biology. This is joint work with Jonathan Heydari, Conor Lawless and David Lydall.

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Mon 03/03/14 14:05
Fulton G20
Mathematics Seminar
Dr. Stanislav Gunar (University of St Andrews)
Quiescent prominence fine structure modelling
abstract

Abstract

Unprecedented amount of detailed, high-resolution observations of prominence fine structures provided by present space-borne and ground-based observatories represents a significant challenge for prominence modelling. Today's models have to cope with the increasingly finer dimensions and ever better resolved dynamics of the observed fine structures. However, the increasing complexity of the prominence fine structure models opens new opportunities for deepening our understanding of these spectacular solar features. Currently, prominence fine structure modelling stands on three main pillars: simulations of prominence magnetic field configurations, modelling of radiative transfer in the prominence plasma, and modelling of prominence fine structure dynamics. We will review the state-of-the-art and achievements of the present models and show the capabilities of the new generation of prominence fine structure models, combining the prominence magnetic field simulations with realistic representation of the prominence plasma and radiative transfer computations.

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Mon 10/03/14 14:05
Fulton G20
Mathematics Seminar
Dr. Eduard Kontar (University of Glasgow)
Solar flares and recent X-ray observations
abstract

Abstract

During periods of sporadic flare activity, the Sun releases energy stored in the magnetic field into the plasma of the solar atmosphere. This is an extremely efficient process, with a large fraction of the magnetic energy going into plasma particles. The solar flares are accompanied by prompt electromagnetic emission virtually over the entire electromagnetic spectrum from gamma-rays down to radio frequencies. The Sun, through its activity, also plays a driving role in the Sun-Earth system that substantially influences geophysical space. Solar flare energetic particles from the Sun are detected in interplanetary space by in-situ measurements making them a vital component of the single Sun-Earth system. Although a qualitative picture is generally agreed upon, many processes solar flare processes are poorly understood. Specifically, the processes of acceleration and propagation of energetic particles interacting on various physical scales remain major challenges in solar physics and basic plasma physics. In the talk, I will review the current understanding of solar flare physics focusing on recent observational progress toward the understanding of energy release and particle acceleration in solar flares, which became possible due to the numerous spacecraft and ground-based observations.

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Fri 14/03/14 15:00
Fulton G20
Mathematics Seminar
Prof. Robert Krasny (University of Michigan (Ann Arbor))
A Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver for Solvated Proteins
abstract

Abstract

We present a treecode-accelerated boundary integral (TABI) solver for electrostatics of solvated proteins described by the linear Poisson-Boltzmann equation. The method uses a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated by MSMS and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES and the matrix-vector product is carried out by a Cartesian treecode which reduces the cost from $O(N^2)$ to $O(N\log N)$, where $N$ is the number of faces in the triangulation. The code is applied to two test cases, the Kirkwood sphere and a medium sized protein. We compare TABI results with those obtained using the grid-based APBS code, in terms of error, CPU run time, and memory usage, and we also present parallel TABI simulations. The TABI solver exhibits good serial and parallel performance combined with relatively simple implementation, efficient memory usage, and geometric adaptability. This is joint work with Weihua Geng (Southern Methodist University).

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Mon 17/03/14 14:05
Fulton G20
Mathematics Seminar
Dr. Ivana Gudelj (University of Exeter)
A tragedy of the commons: the role of metabolic constraints in the evolution of microbial diversity, cooperation and drug resistance
abstract

Abstract

Seventy, or so, years after the empirical and theoretical formulation of the competitive exclusion principle (CEP), microbial evolutionary ecologists provided the first experimental counterexample to the CEP: an experimental evolution approach showing that multiple lineages of different bacterial ecotypes can stably coexist in a chemostat. At the time this was published, the many available theories of chemostat dynamics could not explain how diverse microbial communities could exist in simple, homogeneous environments containing a single limiting carbon source. In this talk, I present a mathematical formulation that proposes a new mechanism supporting stable diversity maintenance in environments where diversity was previously thought impossible. The mechanism requires intermediate mutation rates and metabolic and physiological constraints, in particular a trade-off seems to be needed between the rate and efficiency of bringing extracellular nutrients into the cell and assembling those nutrients into offspring. Subsequently, I will demonstrate the varied role this rate-efficiency trade-off plays in the evolution of microbial cooperation and when understanding the complexities of selection for antimicrobial drug resistance in multi-species fungal communities.

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Thu 20/03/14 14:05
Fulton G20
Mathematics Seminar
Prof. Yihong Du (University of New England)
Spreading profile and nonlinear Stefan problems
abstract

Abstract

In this talk I will report some recent progresses on the study of a general nonlinear Stefan problem, used as a model for the understanding of a variety of spreading phenomena, where the unknown function u(t,x) represents the density of concentration of a certain (chemical or biological) species at time t and space location x, with the free boundary standing for the spreading front. Such spreading problems are usually modeled by the corresponding Cauchy problem, which has attracted extensive research starting from the well-known 1937 paper of Kolmogorov-Petrovski-Piskunov. We will discuss the similarity and differences of the long-time behavior of these two types of mathematical models by closely examining their spreading profiles.

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Mon 24/03/14 14:05
Fulton G20
Mathematics Seminar
Dr. Ruth Baker (University of Oxford)
Experimental and modelling investigation of monolayer development with clustering
abstract

Abstract

Standard differential equation models of collective cell behaviour, such as the logistic growth model, invoke a mean-field assumption which is equivalent to assuming that individuals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, that aim to account for the dynamics of individuals, pairs of individuals, triplets of individuals, and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean-field model to both data sets. Our results indicate that the mean-field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean-field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.

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Tue 01/04/14 11:00
Fulton G20
Mathematics Seminar
Dr. Antonia Savcheva (CfA, Harvard University)
Solar Sigmoidal Active Regions: From Formation to Eruption
abstract

Abstract

The formation, evolution and eruption of solar active regions is a main theme in solar physics. Ultimately the goal is predicting when, where and how an eruption will occur, which will greatly aid space weather forecasting. S-shaped active regions (sigmoids) facilitate this line of research, since they provide conditions that are easier to disentangle and have a high probability for erupting as flares and/or coronal mass ejections. This talk explores the behavior of solar sigmoids via both observational and magnetic modeling studies. Data from the most modern space-based solar observatories are utilized in addition to data-constrained magnetic field modeling to gain insight into the physical processes controlling the evolution and eruption of solar sigmoids. We use X-ray ans spectroscopic observations and magnetic field models to introduce the underlying magnetic and plasma structure defining these regions. By means of a large comprehensive observational study we investigate the formation and evolution mechanism. Specifically, we show that flux cancellation is a major mechanism for flux rope formation and evolution. We make use of topological analysis to describe the magnetic field structure of the sigmoids. We show that when data-constrained models are used in sync with MHD simulations and observations we can arrive at a consistent picture of the scenario for CME onset, namely the positive feedback between reconnection at a generalized X-line and the torus instability. In addition we show that topological analysis is of great use in analyzing the post-eruption flare- and CME-associated observational features. Such analysis is used to extend the standard 2D flare/CME models to 3D and to find potentially large implications of topology to understanding 3D reconnection and energetic particles production in flares.

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Mon 28/04/14 11:30
Fulton G20
Mathematics Seminar
Prof. Ke Chen (University of Liverpool)
Effective Variational Models for Restoration of images with blur and noise
abstract

Abstract

In recent years, the interdisciplinary field of imaging science has been experiencing an explosive growth in active research and applications. In this talk I shall present some recent and new work of modeling the inverse problem of removing noise and blur in a given and observed image. Here we assume the Gaussian additive noise is present and the blur is defined by some linear filters. Inverting the filtering process does not lead to unique solutions without suitable regularization. There are several cases to discuss: Firstly I discuss the problem of how to select optimal coupling parameters, given an accurate estimate of the noise level, in a total variation (TV) optimisation model. Secondly I show a new algorithm for imposing the positivity constraint for the TV model for the case of a known blur. Finally I show how to generalise the new idea to the blind deconvolution where the blur operator is unknown and must be restored along with the image. Again the TV regularisers are used. However with the splitting idea, our work can be extended to include other high order regularizers such as the mean curvature. Once an observed image is improved, further tasks such as segmentation and co-registration become feasible. There will be potentially ample applications to follow up. Joint work with B. Williams, J. P. Zhang, Y.Zheng, S. Harding (Liverpool) and E. Piccolomini, F. Zama (Bologna). Other collaborators in imaging in general include T. F. Chan, R. H. Chan, B. Yu, N. Badshah, H. Ali, L. Rada, C. Brito, L. Sun, F. L. Yang, N. Chumchob, M. Hintermuller, Y. Q. Dong, X. C. Tai, etc.

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Tue 29/04/14 14:00
Fulton G20
Mathematics Seminar
Prof. Thomas Hillen (University of Alberta)
Mathematical Modelling of Cancer
abstract

Abstract

Hanahan and Weinberg recently defined what is known as the hallmarks of cancer. I will use these hallmarks to motivate the understanding of cancer as an ecosystem. I will use this perspective to present mathematical modelling of specific cancers, including glioma spread, optimization of radiation treatment, and the relevance of cancer stem cells.

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Thu 01/05/14 09:00
Fulton Building
Workshop
 (Third Systems Biology Workshop)
Northern Research Partnership
Contact Dr. Fordyce Davidson for further details
Mon 05/05/14 14:05
Fulton G20
Mathematics Seminar
Dr. Rosemary Dyson (University of Birmingham)
Modelling plant growth
abstract

Abstract

Understanding the growth of plants is fundamental to current efforts in food security and bioenergy. Cellular level growth is driven by a high internal turgor pressure, which causes viscous stretching of the cell wall, combined with new material deposition, whilst growth at the level of e.g. a root involves coordination across multiple cells. The cell wall is a complex material with a highly ordered microstructure, producing non-linear anisotropic mechanical behaviour that can be manipulated under enzymatic control to alter the cellular growth rate. We present a series of models across multiple spatial scales, from the cell wall microstructure to whole organ level, aiming to ellucidate the mechanical mechanisms underpinning plant growth.

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Mon 19/05/14 14:05
Fulton G20
Mathematics Seminar
Dr. Fabio Del Sordo (Paris-Saclay University)
Helical and turbulent motion in the interstellar medium
abstract

Abstract

In this talk I will focus on some elements of the dynamics of the interstellar medium. Many different kinds of astrophysical phenomena take place in the interstellar medium: I will focus on the effect of supernovae explosions and galactic winds on the evolution of turbulence and magnetic field. In the first part of this talk I will show why events like supernovae explosions can be modeled as spherical expansion, i. e. irrotational flows. Such flows can develop vorticity when they occur in environments affected by rotation or shear, or that are not barotropic. Secondly, helical flows are taken into account. They are of basic importance for the phenomenon of the amplification of magnetic fields, namely the dynamo, as helicity plays a role both in the growth and in the saturation and decay of a magnetic field. I will speak about the effect of advection on helical dynamos and analyze how dynamos are affected by advection of magnetic fields and material away from the domain in which they operate. It will be shown that the presence of an outflow, like stellar or galactic winds in real astrophysical cases, alleviates the so-called catastrophic quenching, that is the damping of a dynamo in highly conductive media, thus allowing the dynamo process to work better.

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Thu 22/05/14 11:00
Fulton G20
Mathematics Seminar
Prof. Jens Lang (TU Darmstadt)
Adaptivity in Numerical Methods for ODEs and PDEs
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Abstract

In this talk I will emphasize on the use of adaptive strategies in numerical algorithms to solve systems of ordinary and partial differential equations more efficiently and reliably. After a brief introduction to local and global error control for time integrators general approaches to combine adaptivity in space and time are discussed. Finally, I will speak about recent developments in using adaptive multilevel strategies for PDE-constrained optimization and uncertainty quantification. Throughout my talk I will present numerical results for academic as well as real-life applications including chemical reaction-diffusion systems, regional hyperthermia, electrocardiology, magnetoquasistatics, steel hardening and complex turbulent flows.

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Mon 02/06/14 14:05
Fulton G20
Mathematics Seminar
Dr. Eamonn Gaffney (University of Oxford)
Exploring The Mechanics Of Swimming Flagellates
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Abstract

Mammalian spermotozoa motility is a subject of growing importance, due to rising human infertility and the possibility of improving animalbreeding for livestock and conservation, while understanding how bacterial motility contributes to colonisation and biofilm initiation is of fundamental concern in numerous fields. Fluid and filament mechanics offers many opportunities to provide novel insights concerning the mechanics of such swimming cells. Examples of the information that can be extracted by combining imaging and continuum mechanics will be highlighted together with studies of how mechanical effects can influence cell behaviour especially near surfaces.

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Mon 09/06/14 14:00
Fulton G20
Mathematics Seminar
Dr. Jamal Uddin (University of Birmingham)
Multilayer liquid curtain coating
abstract

Abstract

In this talk I will describe our recent attempts to investigate stability and break-up of multilayer curtain coating with the overall aim of examining stability windows for multi-layer liquid curtains comprised of Newtonian fluids, where the properties of each layer can be kept constant or varied. For a single-layer curtain it is known that the minimum flow rate required for initial stability can be violated by carefully reducing the flow rate below this point, which defines a hysteresis region. However, when two or three layers are used to form a composite curtain, the hysteresis window can be considerably reduced depending on the experimental procedure used. The talk will concentrate on new experimental results we have obtained at the High Speed Fluids Lab at KAUST along with a theoretical model to investigate the stability of a multilayer curtain with the use of surfactants.

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Fri 20/06/14 15:30
Fulton G20
Mathematics Seminar
Dr. Mahboubeh Asgari-Targhi  (CfA, Harvard-Smithsonian)
Coronal Heating by Dissipation of Energy in Braided Magnetic Structure
Tue 19/08/14 11:00
Fulton G20
Mathematics Seminar
Dr. Deb Baker (MSSL - University College London)
Revisiting plasma composition in the Hinode era
abstract

Abstract

Plasma composition is a critical plasma parameter linking coronal source regions to solar wind streams. We typically characterize plasma composition using first ionization potential (FIP ) bias which is the ratio of elemental abundance in the upper atmosphere to that in the photosphere. Though the in situ determination of plasma composition is well established, the solar side has not significantly evolved since the seminal Skylab results. Hinode/EIS has provided a new opportunity to re-examine plasma composition and it's evolution in a variety of solar structures at the highest temporal and spatial resolutions using large field of view composition maps. Using these pioneering Hinode/EIS composition maps, we will examine in unprecedented detail: 1. FIP bias in an active region-coronal hole complex and 2. FIP bias evolution in a decaying active region. We will finish by exploring what clues plasma composition can provide about the magnetic topology in a sigmoid channel.

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Tue 19/08/14 14:00
Fulton G20
Mathematics Seminar
Prof. George Baravdish (Linkoping University)
Applications of inverse problems: expanding diffusion models
abstract

Abstract

Inverse problems often arise in the context of information reconstruction from a set of known, measurable, and possibly noisy data. Even though inverse problems have been extensively studied, many theoretical and practical problems remain unsolved. In this talk we will briefly review classical mathematical models for inverse problems and present methods for information recovery in image processing applications such as deblurring, inpainting and image enhancement. Particularly, we consider the Cauchy-problem for elliptic equations and inverse diffusion models with an emphasize on ill-posedness and the importance of regularization. In the second part of the talks we concentrate on Tikhonov-type regularization, which is subject to an extensive discussion from an image analysis perspective. Specifically, we formulate and present tensor-based variational models with a focus on image enhancement. The talk is concluded with an outlook for future work and extensions to other problem domains such as tumor growth.

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Tue 19/08/14 15:00
Fulton G20
Mathematics Seminar
Mr. Freddie Astrom (Linkoping University)