Mon 26/01/15 14:00 Fulton G20 Mathematics Seminar  Dr. Gary Mirams (University of Oxford) Uncertainty in cardiac electrophysiology models 
identifiability, parameterisation and model selection  abstractAbstractCardiac electrophysiology models have been used for over 50
years to understand the mechanisms by which the heart beat is
synchronised and adapts to changes in physiological demands. The
success of the field has led to an explosion of different models of
ion currents and cardiac cells. For just one particular potassium
current (the IKr current carried through the hERG channel) we have
counted over 30 mathematical models (or parameterisations of a handful
of structures). We discuss how we went back to the beginning and
attempted to design experiments to select the correct model structure,
as well as to identify each parameter in the models as uniquely as
practical. We will show how this is allowing us to quantify
variability between cells for the first time. hide 

Mon 02/02/15 14:00 Fulton G20 Mathematics Seminar  Dr. Matthew Pitkin (University of Glasgow) Searching for white light flares in Kepler data  abstractAbstractThe Kepler satellite's primary goal has been to search for planets orbiting other stars. To do this it has stared at a fixed patch of sky containing over 100000 stars for several years in the hope that it will catch tiny dips in their light caused by planetary transits. However, this wealth of data enables us to look for other interesting features on these stars, in particular stellar flares. I will present a method we developed to try and efficiently detect flares in this large data set. I will discuss the issues that arise when looking at Kepler data, such as dealing with the variability of stellar light curves and problems with other transient artefacts. I will present some results from looking at a short stretch of Kepler data. Finally, I will talk about what the future plans for the search method are. hide 

Mon 09/02/15 14:10 Fulton G20 Mathematics Seminar  Prof. Andrey Piatnitski (Narvik University College, Norway) Homogenization of low temperature spin systems  

Mon 16/02/15 14:00 Fulton G20 Mathematics Seminar  Dr. Carlos Escudero (Universidad Autónoma de Madrid) Dynamics of a fourth order equation arising in the theory of
nonequilibrium growth  abstractAbstractIn this talk we will introduce a model that arises in the
theory of nonequilibrium phase transitions, in particular in the
description of the growth of selfaffine surfaces. We will briefly
comment on the role that this model is meant to play in this physical
theory. Furthermore, we will mention some open questions of physical
nature related to it. Subsequently we will start with the rigorous
analysis of our model, which is a fourth order partial differential
equation. We will describe our progress in building an existence
theory for the full model, of parabolic nature, and for its stationary
counterpart. For the latter case existence and multiplicity results
are provided, and for the former one we will show local in time
existence of the solution, that can be made global for small enough
data, and cannot if these are large enough. We will show how these
results fit into the physical theory, and what open questions are left
for the future. hide 

Mon 23/02/15 14:00 Fulton G20 Mathematics Seminar  Dr. Joern Warnecke (MaxPlanck Institut for Solar System Research) Understanding the solar dynamo from numerical simulations  abstractAbstractSunspots occurring on the solar surface following a typical pattern during the activity cycle. At the beginning of the cycle they appear at high latitude, whereas at the end they appear close to the equator. This is associated with an underlying strong toroidal field which migrates equatorward. Since a few years this behavior has been reproduced in global convective dynamo simulations.
I will present results from our simulations of global convective dynamos. All of these simulations produce cyclic and migrating mean magnetic fields. Through detailed comparisons, we show that the migration direction can be clearly explained by an alphaOmega dynamo wave following the ParkerYoshimura rule. This lead to the conclusion, that the equatorward migration in this and other work is due to a positive (negative) alphaeffect in the northern (southern) hemisphere and a negative radial gradient of rotation outside the inner tangent cylinder of these models. This idea is supported by a strong correlation between negative radial shear and toroidal field strength in the region of equatorward propagation.
In the Sun the only region, where the rotation rate possesses a negative radial gradient, is in the nearsurface shear layer. A positive alphaeffect there would lead to an equatorward propagating dynamo wave.
Furthermore, I will present results of combined simulation of solar dynamo and a coronal envelope. These simulation give us indication, that the latitudinal temperature variations play an important role in generating the differential rotation profile of the Sun through turbulent Reynold stresses. I will show, that the meridional component of the Reynolds stress can explain the formation of a nearsurface shear layer in the Sun.
This lead to the conclusion, that in Sun the magnetic field is generated and stored just below the surface, and sunspot are generated by local mechanisms of concentration flux. hide 

Mon 02/03/15 14:00 Fulton G20 Mathematics Seminar  Dr. Gabriel Barrenechea (University of Strathclyde) Stabilising some infsup stable pairs on anisotropic quadrilateral meshes  abstractAbstractThe finite element solution of the Stokes problem is subject to the wellknown
infsup condition. This condition usually depends on the domain and the degree of
the polynomial spaces used in the discretisation. Now, when anisotropic finite elements
are used, this infsup condition usually degenerates with the aspect ratio. In this
talk I will present results identifying the part of the pressure space that is responsible
for this degeneration, and present a way to solve that. In the second part of the talk,
this technique will be applied to some, non infsup stable this time, pairs of spaces
for the Stokes and Oseen equations. The work presented in this talk is in collaboration
with Mark Ainsworth (Brown) and Andreas Wachtel (Strathclyde). hide 

Mon 09/03/15 14:00 Fulton G20 Mathematics Seminar  Dr. Mariya Ptashnyk (University of Dundee) Gene Regulatory Network and Functional Analysis  abstractAbstractIn this talk I would like to present some ideas on bifurcation analysis for a very simple model of a gene regulatory network.
This will be a short story about the long way from a simple idea on a sunny morning in Lyon to a beautiful functional analysis. hide 

Mon 16/03/15 14:00 Fulton G20 Mathematics Seminar  Prof. JeanLuc Thiffeault (University of Wisconsin) Random entanglements  abstractAbstractExperiments and numerical simulations provide plenty of data
describing entangled systems arising from dynamics or otherwise. For
example, there are recent experiments studying entangled hair, and
magnetic fields are often modelled as entangled lines. But what is a
good measure of entanglement, and how much entanglement should we
expect? We look at modeling the entanglement of purely random orbits
such as Brownian motion. This is joint work with Marko Budisic and
Huanyu Wen. hide 

Fri 20/03/15 16:30 Baxter Suite Edinburgh Mathematical Society  Prof. Benoit Perthame (Universite de Pierre et Marie Curie) The HeleShaw freeboundary asymptotics for fluid models of tumor growth Tea will be served from 3.45 p.m. in the Lamb Gallery, Tower Building  abstractAbstractThe growth of solid tumors can be described at a number of different scales from the cell to the organ scales. For a large number of cells, the ’fluid mechanical’ approach has been advocated recently by many authors in mathematics or biophysics. Several levels of mathematical descriptions are commonly used, including only elastic effects, nutrients, active movement, surrounding tissue, vasculature remodeling and several other features.
We will focus on the links between two types of mathematical models. The ‘microscopic’ description is at he cell population density level and a more macroscopic, description is based on a free boundary problem close to the classical HeleShaw equation. Asymptotic analysis is a tool to derive these HeleShaw free boundary problems from cell density systems in the stiff pressure limit. This modeling also opens other questions as circumstances in which instabilities develop.
This work is a collaboration with F. Quiros and J.L. Vazquez (Universidad Autonoma Madrid), M. Tang (SJTU) and N. Vauchelet (LJLL).
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Mon 23/03/15 14:00 Fulton J1 Mathematics Seminar  Dr. Reuben O'Dea (University of Nottingham) Multiscale analyses of growing tissue  abstractAbstractThe derivation of continuum models which represent underlying discrete or microscale phenomena is emerging as an important part of mathematical biology: integration between subcellular, cellular and tissuelevel behaviour is crucial to understanding tissue growth and mechanics. I will present a new macroscale description of nutrientlimited tissue growth, which is formulated as a microscale freeboundary problem within a porous medium. A multiscale homogenisation method is employed to enable explicit accommodation of the influence of the underlying microscale tissue structure, and its evolution, on the macroscale dynamics.
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Mon 30/03/15 14:00 Fulton J1 Mathematics Seminar  Dr. Soko Matsumura (University of Dundee) Formation and Compositions of
Terrestrial Planets in the Solar System  abstractAbstractRecent observations started revealing the potential diversity in
compositions of extrasolar planets. With the expectation of the further
constraints in the future, it is crucial to understand how the final
composition of planets is related to planet formation processes. A few
groups have estimated the elemental abundances of simulated Solar System
planets and successfully reproduced a global trend of the compositions of
terrestrial planets. However, most studies were limited to refractory
species and did not consider volatile ones that include biogenic elements
such as C and N. In this talk, we discuss two potential pathways to
deliver biogenic species to terrestrial planets – one of them is the
delivery from the outer region of a protostellar disk and the other is the
incorporation of these species in the inner region of the disk as a result
of the ice line evolution. We test these scenarios by assuming that the
initial elemental abundances of embryos and planetesimals are determined
by the equilibrium condensation model, and by simulating the formation of
terrestrial planets. hide 

Mon 27/04/15 14:00 Fulton G20 Mathematics Seminar  Prof. Oliver Jensen (University of Manchester) Modelling plant cell and tissue growth  abstractAbstract Plant growth typically occurs through the coordinated anisotropic expansion of plant cells. Growth is regulated by hormones and is driven by high intracellular pressures generated by osmosis. This machinery allows a plant primary root, for example, to penetrate soil in a direction guided by gravity, while seeking out nutrients and avoiding obstacles. I will describe the biomechanical aspects of a computational multiscale model for root gravitropism that incorporates descriptions of cell walls as fibrereinforced viscoelastic polymer networks and adopts upscaling approaches to describe the growth of multicellular tissues. hide 

Mon 04/05/15 14:00 Fulton G20 Mathematics Seminar  Dr. Istvan Ballai (University of Sheffield) MHD waves in ionisation nonequilibrium plasmas  abstractAbstractMany space plasmas are in a partially ionised state, where neutrals, heavy ions and electrons are treated as a separate fluids, however they behave in a collective manner.
Usually the standard theory considers that the plasma is in ionisation equilibrium, i.e. the rates of ionisation and recombination are equal and collisions occurring in the plasma are always elastic
However this is an idealistic restriction, the two rates are not always equal and a different approach is needed. In my presentation I will consider the ionisation nonequilibrium of plasmas (with special emphasis on prominences) due to inelastic collisions and construct the rate equation for the excited of atoms and ion/electrons.
Assuming a simple form for the ionisation and excitation rate, I will discuss briefly what changes such considerations will bring into the equations describing the nature of magnetic and magnetoacoustic waves. hide 


Mon 18/05/15 14:00 Fulton G20 Mathematics Seminar  Dr. Sara Jabbari (University of Birmingham) Mathematical modelling of gene regulation networks in Grampositive bacteria  abstractAbstractMathematical models are being used increasingly to understand the roles of particular genes, proteins or signals in the gene regulation networks that govern the behaviour of bacteria. Using examples from Bacillus subtilis, Staphylococcus aureus and Clostridium difficile (ranging through sporulation, toxin production and cellcell communication), we illustrate how numerical and asymptotic approaches to ODE models can elucidate individual roles and highlight the key aspects of a system. The use of asymptotic methods is particularly fruitful in the common situation where there is a lack of data available for model parameterisation. Where possible, we focus on the generation of hypotheses which can be tested in the laboratory. hide 

Tue 02/06/15 14:00 Fulton G20 Mathematics Seminar  Dr. Pascal Démoulin (Paris Observatory  LESIA) Tracking magnetic helicity in the solar atmosphere and interplanetary space  abstractAbstractMagnetic helicity is a valuable quantity in MHD since has two unique properties: it is almost conserved and it cascades to large scales. However, observations provide only 1D or 2D cuts of magnetic field configurations while computation of helicity requires the knowledge of the 3D magnetic field and its vector potential. First, I will review how theory is rescuing observations to derive magnetic helicity from different types of magnetic data. Second, I will describe cases where helicity was tracked during eruptions. Third, I will focus on the helicity estimation in magnetic clouds where precise magnetic field measurements are available but only along the spacecraft trajectory. Finally, I will compare helicity budgets realized over one solar cycle. hide 

Tue 09/06/15 14:00 Fulton G20 Mathematics Seminar  Dr. Gherardo Valori (MSSL  University College London) Non linear forcefree field modelling of a
circularribbon flare  abstractAbstractOn October 22, 2011, a circular ribbon, shortly preceded by localized
inner and remote compact brightening, was observed in AR11324 using
SDO/AIA. The global evolution of such peculiarly shaped flares is believed
to be caused by reconnection at a coronal null point, with the circular
ribbon being the footprint of the domeshaped fan, and the inner and
remote brightening tracing the two photospheric anchoring of the spines.
The high spatial resolution and time cadence of AIA observations give the
unique opportunity to explore the details of this flare event, which is
globally agreeing with, but not entirely explained by, the null/slipping
reconnection model. In particular, preflare brightening and a threephase
time evolution of EUV signals do not have straightforward interpretations.
Also, the noneruptive character of the flare makes standard
interpretations inadequate.
In this talk I will briefly introduce the nonlinearforcefree field
(NLFFF) extrapolation technique, and apply it to the interpretation of
that event. In particular, I will show how the combination of the NLFFF
extrapolation with a topological analysis based on quasiseparatrix layers
(QSL) allows to interpret the AIA observation of the dynamic of the flare.
In addition to the expected topological features of a standard
circularribbon flare model, we find a flux rope and a complex QSL
internal to the dome, which are connected with the brightening locations.
Guided by the AIA observation, we are able to provide a coherent
description of the specific dynamic of this event that, because of its
noneruptive nature, has a peculiar reconnection pattern. The different
peaks in the EUV signals are then explained by the cooling of specific
sets of reconnected field lines that are matching both the reconnection
process evinced by our modeling and the multiwavelengths observations.
The combination of highresolution observations with powerful modeling and
analysis techniques allow us to interpret very complex observations with
realistic models of the coronal field, helping us to deepen the
theoretical understanding of flare dynamics. hide 

Mon 15/06/15 14:00 Fulton G20 Mathematics Seminar  Dr. Chris Prior (Durham University) Contorted flux tubes and decorating ribbons  abstractAbstractThis talk will be in two parts. In the first part I will introduce recent
work exploring the behaviour of braided magnetic flux ropes with contorted
geometry. This work extends the work of several members of the Dundee MHD
research group on straight braided flux tubes; where it has been
demonstrated that the evolution of braided fields differ significantly
to those of twisted tubes. The additional freedom of the tube to distort
in the atmosphere is crucial here. The complexity of the braided fields
implies the are more likely to be prevented form expanding, where their
twisted counterparts are not, this is confirmed in the simulations. Much
of the work relies on the geometry of tubes and ribbons commonly used in
elasticity and biophysics...
The second topic concerns an explanation for the mechanism by which thin
ribbons can be sheared with a pair of scissors to create ornamental coils
for gifts. I report on experiments in which we identify key parameters
which dictated the final coiling radius, namely the blade sharpness, the
force applied against the blade and the speed at which the ribbon is
pulled over the blade. We develop a viscoplastic thin ribbon model to
explain this phenomenon and find very reasonable fits to the data. hide 
