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2013/14 semester 1 events in Mathematics

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Mon 09/09/13 15:00
Fulton G20
Mathematics Seminar
Dr. Lei Zhang (Shanghai Jiao Tong University)
Construction and analysis of energy based atomistic/continuum coupling methods
abstract

Abstract

We discuss the construction and numerical analysis of energy based atomistic/continuum coupling methods (a/c methods) for modeling crystalline solids with defects, in particular, the issues of consistency (so-called 'ghost force removal') and stability of the coupling method. For general multi-body interactions on the 2D triangular lattice, we show that ghost force removal (patch test consistent) a/c methods can be constructed for arbitrary interface geometries. Moreover, we prove that all methods within this class are first-order consistent at the atomistic/continuum interface and second-order consistent in the interior of the continuum region. The convergence and stability of the method is analyzed and justified with numerical experiments. This is a joint work with Christoph Ornter (Warwick) and Alexandre Shapeev (Minnesota).

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Mon 16/09/13 11:05
Fulton G20
Mathematics Seminar
Dr. John Ward (University of Loughborough)
Modelling Biofilms as a Thin Film
Mon 16/09/13 15:00
Harris LT
Mathematics Seminar
Dr. Lyonell Boulton (Heriot-Watt University )
Mistuned Toeplitz operators and applications
abstract

Abstract

The study of a new family of highly non-self-adjoint operators which is reminiscent of the classical Toeplitz operators arises naturally in the context of evolution problems connected to sandpiles/slow-fast diffusion. The aim of this talk is to describe the difficulties involved in determining general spectral properties of operators in this family and show how to overcome these difficulties. In turns we will establish basisness/non-basisness theorems for general families of 1D periodic functions. We will then apply the latter, in order to examine non-orthogonal projection methods for the p-poisson parabolic time-evolution initial value problem with stochastic forcing.

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Tue 17/09/13 14:15
Fulton G20
Mathematics Seminar
Prof. Hermann Eberl (University of Guelph)
Cross-diffusion in biofilms
abstract

Abstract

Bacterial biofilms are micorbial depositions on immersed surfaces that form whereever environmental conditions sustain microbial growth. They play an important role in medicine (bad), industry (mostly bad), environmental technologies (mostly good), and ecology (good). Biofilms have been characterized both, as spatially structured bacterial populations, and as mechanical objects. We will show how starting from either point of view one arrives as the same density-dependent difusion-reaction model for biofilm growth, with three non-Fickian effects: (i) a porous medium degeneracy that ensures a finite speed of interface propagation, (ii) a super-diffusion singularity that guarantees volume filling, and (iii) cross-diffusion that describes mixing behaviour. We will comment on numerical challenges and suggest a simple semi-implicit scheme to address those. We will use this numerical method to show how the modeling framework is flexible enough to describe a variety of biofilm systems, including pure competition, disinfection with antmicrobials, and allelopathic control.

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Mon 23/09/13 14:00
Fulton G20
Mathematics Seminar
Dr. Ralf Kaiser (Bayreuth University)
Mathematical problems in dynamo theory
abstract

Abstract

The generation of planetary and stellar magnetic fields is generally ascribed to the dynamo effect through which mechanical energy stored in the motion of a conducting fluid is converted in magnetic energy. Mathematically this process is described by the dynamo equation, which constitutes a system of parabolic equations for the magnetic field components with coefficients provided by a velocity field and a conductivity distribution. In general, the velocity field couples these components in a nontrivial way which makes the question for non- decaying solutions (the criterion of a working dynamo) difficult to answer. It is well-known that the dynamo process requires a certain degree of complexity of the velocity field as well as of the magnetic field. These requirements are specified in so-called antidynamo theorems which exclude dynamo action for certain classes of velocity or magnetic fields. The most famous example is Cowling’s theorem ruling out dynamo action for axisymmetric magnetic fields. Another class of antidynamo theorems constrains the velocity field rather than the magnetic field. Its most prominent representative is the “toroidal velocity theorem”, stating that no dynamo action is possible if the divergence-free velocity field is constrained to spheres. My talk is divided into three parts: The first one is a general introduction of the dynamo problem, the second one discusses both prototypical antidynamo theorems mentioned above and the third part is concerned with a more recent antidynamo theorem excluding certain “invisible dynamos”, i.e. dynamos with vanishing external magnetic field.

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Wed 25/09/13 17:00
Dalhousie
Celebration
Prof. Mark Chaplain (University of Dundee)
Creating a Virtual Tumour: Are We Nearly There Yet?
Mon 30/09/13 15:00
Fulton G20
Mathematics Seminar
Prof. David Needham (University of Birmingham)
The Existence of self-similar structures in a simple model for the spread of morphogens and solvent-polymer diffusion
abstract

Abstract

This talk focuses on the existence and qualitative properties of self-similar structures in a simple model for solvent diffusion in a polymer matrix.

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Tue 15/10/13 14:00
Fulton G20
Mathematics Seminar
Dr. Anthony Yeates (Durham University)
The Internal Topology of Magnetic Flux Tubes
abstract

Abstract

Many plasmas - ranging from stellar atmospheres to controlled fusion devices - have such high electrical conductivity that the topology (connectivity and linking) of their magnetic field lines is closely preserved during dynamical evolution. As such, magnetic reconnection events that locally break these topological constraints play a controlling role in the overall behaviour. In this talk, I will introduce a "topological flux function" to quantify the topological structure of a single magnetic flux tube. I will discuss how this function relates to magnetic helicity, to winding numbers, and to measures of reconnection. Flux tubes are the building blocks of astrophysical plasmas, yet their behaviour already depends on their internal structure in ways that are not yet fully understood. (joint work with Gunnar Hornig, Dundee and Chris Prior, Durham)

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Mon 21/10/13 14:15
Fulton G20
Mathematics Seminar
Prof. Graeme Houston (University of Dundee)
Haemodynamics; Reintroducing normal blood flow patterns in medical devices
Mon 28/10/13 15:00
Fulton G20
Mathematics Seminar
Dr. Philip Murray (University of Dundee)
Mathematical modelling of the somitogenesis oscillator
Thu 31/10/13 11:00
Harris LT
Mathematics Students
Mathematics Careers Talk ()
Wed 06/11/13 14:00
Accountancy LT
Careers Service
JP Morgan  ()
As one of the biggest financial services companies in the world, J.P. Morgan offers a variety of areas of careers.
Mon 11/11/13 15:00
Fulton G20
Mathematics Seminar
Dr. Kevin Painter (Heriot-Watt University)
Movement in oriented environments: from cells to animals
abstract

Abstract

Successful navigation, whether by cells or organisms, requires the detection, integration and response to numerous external and internal cues. In this talk I will discuss a multiscale model to describe movement in oriented environments. Starting with an individual level model, I will introduce the scaling limits to derive a fully macroscopic model. The modelling framework will be illustrated through applications to glioma growth and hilltopping butterflies.

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Wed 13/11/13 14:00
Accountancy LT
Careers Service
Black Rock ()
Internships, graduate schemes and careers in the investment industry
Mon 18/11/13 15:00
Fulton G20
Mathematics Seminar
Prof. Jose Carrillo (Imperial College)
Stability and pattern formation in nonlocal interaction models
abstract

Abstract

I will review some recent results for first and second order models of swarming in terms of patterns, stationary states, and qualitative properties. I will discuss the stability of these patterns for the continuum and discrete particle cases. These non-local models appear in collective behavior for animals, control engineering, and molecular structures among others. We first concentrate in the spatial shape of these patterns and the dynamics when inertia terms are neglected. The mathematical question behind consists in finding properties about local minimizers of the total interaction energy. Concerning 2nd order models, we will discuss particular properties of two patterns: flocks and mills. We will discuss the stability of these patterns in the discrete case. In both cases, we will describe the properties obtained for the continuum limits.

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Mon 25/11/13 15:00
Fulton G20
Mathematics Seminar
Dr. Andrew Goryachev (University of Edinburgh)
How the budding yeast got its septin ring
abstract

Abstract

Budding yeast is an ideal model organism to study biophysical principles underlying eukaryotic cellular morphogenesis. Rather than dividing its cell in halves, this unicellular fungus proliferates by constructing every new daughter cell de-novo, on the side of mother cell. This process is an amazing example of building a cell from scratch. It starts with the establishment of a new cell polarity axis, which is physically marked by a membrane domain, presumptive bud site (PBS), whose protein-lipid composition is distinctly different from the rest of the cell. This and the whole cascade of downstream morphogenetic processes are controlled by a single master regulator – small GTPase Cdc42. Its biological activity is directly responsible for the assembly of the PBS and the following formation of the septin ring, a dense polymeric organelle that serves as the boundary between mother and daughter until they are finally split apart by cytokinesis. Septin rings are found at the cytokinetic sites of fungi, in the tails of spermatozoa as well as at the base of neural spines and eukaryotic cilia – all places where contiguous membrane has to be divided into two non-mixing domains with distinct biological properties and developmental fates. Yet, despite the utmost importance of this organelle for eukaryotic cells, molecular mechanisms responsible for the formation of these rings are not known in any system. As often before, budding yeast comes to the rescue again. In this talk I will present the results of our recent experiment-theory study aimed to unravel the mystery of septin ring emergence in budding yeast. Among others, I will answer a long-standing question: How does it become a ring in the first place?

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Mon 02/12/13 15:00
Fulton G20
Mathematics Seminar
Dr. Isaac V. Chenchiah (University of Bristol)
Surprises in monoclinic-I martensite
abstract

Abstract

We study the zero-energy states of monoclinic-I martensite, which is a material with twelve phases and the most-common shape memory alloy. We have two surprising results: First, there is an open set in which the energy minimising microstructures are infinite-rank laminates (commonly known as T3s). This is, to our knowledge, the first "real-world" occurrence of these non-(finite)-laminate microstructures. (We suspect that, as a consequence, the symmetrized rank-one convex hull/envelope of monoclinic-I martensite is strictly larger/lower than the lamination convex hull/envelope. If so, this would be the first material for which this is known to be true.) Second, there are in fact two types of monoclinic-I martensite, indistinguishable in their symmetry but differing as to their convex-polytope structure. Curiously all known materials belong to one of these types. Since these differ in their zero-energy states, it is possible that the other type would have superior mechanical properties. Our analysis is in the context of geometrically-linear elasticity and ignores interfacial energy. A novel feature is the use of algebraic methods, primarily the theory of convex polytopes. This is joint work with Anja Schloemerkemper, University of Wuerzburg.

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Wed 04/12/13 11:00
Fulton G20
Mathematics Seminar
Prof. Xuecheng Tai (University of Bergen)
Image segmentation: diffusive or sharp interfaces and some global minimization techniques
abstract

Abstract

Image segmentation and a number of other problems from image processing and computer vision can be regarded as interface problems. Recently, diffusive and sharp interface techniques have been used for these problems. In this talk, we will first briefly explain these models and compare the advantages and disadvantages of these models. Numerically, these models can be solved through some PDEs. In the end, we will show some recent results on how to use graph cut to solve these interface problems. Moreover, the global minimizer can be guaranteed even the problem is nonconex and nonlinear. The use of max-flow in a network setting and also in an infinite dimensional setting will be explained.

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Mon 09/12/13 15:00
Fulton G20
Mathematics Seminar
Dr. Lehel Banjai (Heriot-Watt University)
Coupling of finite and boundary element methods in the time domain
abstract

Abstract

We will discuss the numerical simulation of acoustic wave propagation with localized inhomogeneities. To do this we will apply a standard finite element method (FEM) in space and explicit time-stepping in time on a finite spatial domain containing the inhomogeneities. The equations in the exterior computational domain will be dealt with a time-domain boundary integral formulation discretized by the Galerkin boundary element method (BEM) in space and convolution quadrature in time. We will give the analysis of the proposed method, starting with the proof of a positivity preservation property of convolution quadrature as a consequence of a variant of the Herglotz theorem. Combining this result with standard energy analysis of leap-frog discretization of the interior equations will give us both stability and convergence of the method. Numerical results will also be given.

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