Skip to main content
"By creating we think, by living we learn" Patrick Geddes
Main University menu
 

Templates Top-Level Menu

2015/16 semester 2 events in Mathematics

(Back to previous events)   (Upcoming events)
Mon 18/01/16 14:00
Fulton G20
Mathematics Seminar
Dr. Dmitri Finkelshtein (Swansea University)
Kinetic equations for stochastic dynamics of complex systems: derivation, analysis and ‘refinement’
abstract

Abstract

We describe the so-called statistical approach for the study of stochastic dynamics of complex systems in the continuum that allows deriving of the hierarchical equations for the correlations of all orders. We show how to rigorously reduce an appearing chain of linear equations (which reflect the microscopic behaviour of the systems) to a unique non-linear kinetic equation using mesoscopic scalings; the latter equation describes approximately the density of the rescaled system. We consider results about properties of solutions to such equations, in particular, travelling wave solutions and the front propagation. We present an approach that gives the next order of the approximation for the rescaled density.

hide

Mon 25/01/16 14:00
Fulton G20
Mathematics Seminar
Prof. Ovidiu Radulescu (Université de Montpellier)
Taming the complexity of biochemical networks through model reduction and tropical geometry Taming the complexity of biochemical networks through model reduction and tropical geometry
abstract

Abstract

Biochemical networks are used as models of cellular physiology with diverse applications in biology and medicine. In the absence of objective criteria to detect essential features and prune negligible details, networks generated from data are too big and therefore out of the applicability of many mathematical tools for studying their dynamics and behavior under perturbations. However, under circumstances that we can generically denote by multi-scaleness, large biochemical networks can be approximated by smaller and simpler networks, called dominant subsystems. Model reduction is a way to find these simpler models that can be more easily analyzed. We discuss several model reduction methods for biochemical networks with polynomial or rational rate functions and propose as their common denominator the notion of tropical equilibration, meaning finite intersection of tropical hypersurfaces in algebraic geometry. Using tropical methods, one can strongly reduce the number of variables and parameters of biochemical networks. For multi-scale networks, these reductions are computed symbolically on orders of magnitudes of parameters and variables, and are valid in wide domains of parameter and phase spaces. I'll also discuss applications of this approach to coarse graining and analysis of signal transduction models used in cancer research.

hide

Mon 01/02/16 14:00
Fulton G20
Mathematics Seminar
Prof. Nigel Mottram (University of Strathclyde)
Bending, flexing, wrinkling and snapping of fluid drops
abstract

Abstract

The ability to control the shape of droplets and thin films of liquid, i.e. via an externally applied electric field, has been exploited for technological applications including surface tension measurements, ink-jet printing, optical displays, and optimising the properties of polymer microlenses. Working with experimental collaborators at Nottingham Trent University we consider a system where a sessile droplet or film of liquid is placed on one substrate of a parallel plate capacitor. Our work aims to describe the bending and wrinkling distortions as a function of key experimental parameters (droplet size, capacitor plate separation, electric field magnitude and contact angle). As the applied voltage increases the bending of the interface increases and then suddenly snaps, leaving a droplet that bridges across the capacitor. When we consider anisotropic liquids (nematic liquid crystals) we find that a spontaneous deformation of the free surface occurs, without the need for an applied voltage, and that the deformation of the free surface is out of phase with the flexing of the anisotropic axis.

hide

Mon 08/02/16 14:00
Fulton G20
Mathematics Seminar
Dr. Emmanuil Georgoulis (University of Leicester, UK/ National Technical Univ. of Athens, Greece)
Discontinuous Galerkin Methods for Elliptic Multiscale Problems
abstract

Abstract

We shall review some recent results on the use of discontinuous Galerkin methods for elliptic multiscale problems. The first part of the talk will be concerned with a-priori error analysis for a multiscale discontinuous Galerkin method for elliptic problems with multiscale diffusion coefficients, as well as the possible use of polytopic meshes for the resolution of the respective geometries with reduced number of degrees of freedom. The second part of the talk will be concerned with a stochastic collocation discontinuous Galerkin method for elliptic multiscale problems involving randomness, based on a recent high-dimensional quadrature scheme.

hide

Mon 15/02/16 14:00
Fulton G20
Mathematics Seminar
Prof. Mariana Haragus (Universite de Franche-Comte)
Stability of gravity-capillary periodic water waves
abstract

Abstract

We study the stability of two-dimensional gravity-capillary periodic water waves in the case of large surface tension. In this parameter regime, predictions based on model equations suggest that periodic traveling waves are stable with respect to two-dimensional perturbations, and unstable with respect to three-dimensional perturbations which are periodic in the direction transverse to the direction of propagation. In this talk we show that these predictions are confirmed for the full Euler equations describing this hydrodynamic problem.

hide

Mon 22/02/16 15:00
Fulton H2
Mathematics Seminar
Dr. Patrick Antolin (National Astronomical Observatory of Japan / University of St Andrews)
Alfvénic Vortices in the Solar Atmosphere
abstract

Abstract

Magnetohydrodynamic (MHD) waves are interesting agents ubiquitously present in the solar atmosphere through which several aspects of the observed heating, dynamics and morphology may be explained. Recently we have shown that a subset of these waves, known as transverse MHD waves, can lead to fine-scale structure, braiding, heating, characteristic Doppler motions and line broadening through the combination of resonant absorption and dynamic instabilities. Such combination may allow an efficient conversion of the wave energy into thermal energy through viscous and resistive dissipation in the generated turbulence. In this talk I will present recent developments of this model, how it can explain recent observations of decay-less coronal loop oscillations, and how it can explain several of the observed features in chromospheric spicules. A possible extension to Alfvénic vortex shedding in prominences will also be discussed.

hide

Mon 29/02/16 14:00
Fulton G20
Mathematics Seminar
Dr. Valentina Balbi (University of Manchester)
Modelling morphogenesis of the Gastro-Intestinal system
abstract

Abstract

Among the fundamental processes involved in the development of an organism, morphogenesis is one of the most complex. During the past centuries, an amount of experimental studies have improved our actual knowledge of the mechanisms which drive many morphogenetic processes in living organisms. Only recently, experiments have been complemented with mathematical modeling as a tool for proving novel insights on morphogenesis in soft tissues. In this context, this work aims at developing a new mathematical model for the embryonic development of the Gastro-Intestinal system in vertebrates. A macroscopic approach is adopted, where the embryonic tissue is considered as a continuum body undergoing growth and remodeling. The main idea behind the proposed model is that during growth and remodeling, residual stresses can arise and once they exceed a critical value, an elastic instability can occur in the tissue and lead to a morphological change. Therefore, the morphoelastic model is developed integrating the modern theories of growth and remodeling within the framework of the thermo-mechanics of open systems. The occurrence of the elastic instability is investigated using the method of incremental deformations superposed on finite deformations. The critical thresholds for the onset of the instability are determined together with the modes of the associated instability pattern. Moreover, numerical simulations are implemented in Abaqus in order to investigate the evolution of the established instability pattern.

hide

Mon 07/03/16 14:00
Fulton G20
Mathematics Seminar
Dr. James McLaughlin (University of Northumbria)
First Direct Measurements of Transverse Waves in Solar Polar Plumes Using SDO/AIA
abstract

Abstract

There is intense interest in determining the precise contribution of Alfvénic waves propagating along solar structures to the problems of coronal heating and solar wind acceleration. Since the launch of SDO/AIA, it has been possible to resolve transverse oscillations in off-limb solar polar plumes and recently McIntosh et al. concluded that such waves are energetic enough to play a role in heating the corona and accelerating the fast solar wind. However, this result is based on comparisons to Monte Carlo simulations and confirmation via direct measurements is still outstanding. Thus, this presentation reports on the first direct measurements of transverse wave motions in solar polar plumes. Over a four hour period, we measure the transverse displacements, periods, and velocity amplitudes of 596 distinct oscillations observed in the 171 Å channel of SDO/AIA. We find a broad range of non-uniformly distributed parameter values which are well described by log-normal distribution with peaks at 234 km, 121 s, and 8 km/s, and mean and standard deviations of 407 ± 297 km, 173 ± 118 s, and 14 ± 10 km/s. Within standard deviations, our direct measurements are broadly consistent with previous results. However, accounting for the whole of our observed non-uniform parameter distribution we calculate an energy flux of 9-24 W/m^2, which is 4-10 times below the energy requirement for solar wind acceleration. Hence, our results indicate that transverse magnetohydrodynamic waves as resolved by SDO/AIA cannot be the dominant energy source for fast solar wind acceleration in the open-field corona.

hide

Mon 14/03/16 15:00
Fulton G20
Mathematics Seminar
Prof. Mitch Berger (University of Exeter)
Geometry of field lines in elasticity and MHD
abstract

Abstract

I will explore two topics concerning the geometry of field lines. In elasticity theory, a solid in equilibrium has a divergence-free stress tensor. We can regard rows of the stress tensor as vector fields; mapping where their field lines go provides a picture of how forces flow through a solid. This leads to a method for finding average stress and strain in a volume in a way which automatically preserves the elastic energy. The linking of magnetic field lines provides a conserved quantity in MHD known as magnetic helicity. I will discuss recent proposals for defining an absolute measure of helicity when the field lines are not closed, but instead have endpoints (e.g. on the surface of the sun).

hide

Fri 18/03/16 15:45
LT2 Dalhousie
EMS Meeting
Prof. Claud Le Bris (Ecole des Ponts and Inria, Paris)
Modern materials science: mathematical theory and computational approaches
abstract

Abstract

The talk, intended for a general audience, will survey some challenging problems, in terms of modeling, theory or computation, in contemporary materials science. A selection of such problems will be presented. Questions such as the insertion of uncertainties, heterogeneities and defects in the models will be examined, both from the perspective of mathematical analysis (theory of partial differential equations, stochastic processes, homogenization theory) and computational approaches (finite element methods, Monte Carlo methods).
The works presented are joint works with Xavier Blanc (Paris 7), Frédéric Legoll (ENPC-Inria), Pierre-Louis Lions (Collège de France) and other collaborators

hide

Mon 21/03/16 14:10
Fulton G20
Mathematics Seminar
Dr. Gibelli Livio (Politecnico di Torino)
Stochastic numerical schemes for kinetic equations
abstract

Abstract

Kinetic equations provide a statistical description of systems composed of many interacting entities, and, as such, they are used to describe a variety of phenomena in different fields, ranging from rarefied gas dynamics and plasma physics to biology and crowd dynamics. The numerical solution of kinetic equations represents a challenge since they are usually in the form of nonlinear integro-differential equations whose unknown function may depend on more than seven variables. In order to deal with the high dimensionality of the problem, numerical schemes based on Monte Carlo methods have been developed over the years. In this talk, the Monte Carlo quadrature is introduced in its simplest form and sampling and variance reduction techniques are briefly discussed. The basic numerical stochastic schemes for solving kinetic equations are then illustrated and the possibility to implement them on Graphics Processing Units (GPUs) is briefly discussed. Finally, two applications are presented to demonstrate the effectiveness of the stochastic approach, namely the formation of liquid menisci between planar surfaces of micro-electro-mechanical systems, and the crowd evacuation from a venue with a complex time dependent geometry.

hide

Thu 31/03/16 14:00
Fulton G20
Mathematics Seminar
Dr. Konstantina-Stavroula Giannopoulou (University of Crete, Greece)
Construction of an approximate solution of the Wigner equation by uniformization of WKB functions
abstract

Abstract

The Wigner equation is a linear, non-local, kinetic evolution equation, governing the Wigner func- tion. The Wigner function is defined as the Fourier transform of the two-point spatial correlation of the wavefunction in configuration space in classical wave propagation or as the Weyl symbol of the density operator in quantum mechanics. This function, in spite of its quantum-mechanical origin, has been proved an extremely powerful tool for the construction of high-frequency asymptotics and the homogenization of classical wavefields. The basic idea is that the integral of the Wigner function with respect to the momentum in the phase space provides, in principle, caustic-free probability amplitudes and mean values of quantum observables or wave amplitudes in paraxial wave propagation. We present the construction of a high-frequency approximate solution of the Wigner equation, by uniformization of WKB approximations of the Schrödinger eigenfunctions, in combination with ideas from the deformation quantization method.

hide

Mon 16/05/16 14:15
Fulton G20
Mathematics Seminar
Dr. Luca Albergante (University of Dundee)
Robustness and evolutionary optimization in cell survival: examples from gene regulation and DNA replication
Thu 19/05/16 14:15
Fulton G20
Mathematics Seminar
Prof. Angela Stevens (Universität Münster)
Mathematical modelling of cell motility and the polymerisation/depolymerisation of the cellular cytoskeleton.
Mon 23/05/16 14:00
Fulton G20
Mathematics Seminar
Dr. Duncan Forgan (University of St Andrews)
Structure and Chemistry in Smoothed Particle Hydrodynamics Simulations
abstract

Abstract

Hydrodynamic simulations of star (and planet) formation will soon encounter its own version of the "big data" problem. As simulations grow in scale and file size, identifying regions of interest can no longer be done "by eye", and must become the province of structure classification algorithms. I will describe my recent work in developing several numerical techniques for assaying structures in smoothed particle hydrodynamics (SPH) data. I will show how these methods can be applied to simulations of large scale star formation in molecular clouds, and small scale star formation in protostellar discs. These algorithms are in fact applicable to any Lagrangian hydrodynamic simulation, including moving mesh simulations. If time permits, I will present some very preliminary work in combining SPH simulations with sophisticated chemical networks, containing hundreds of molecular species. Understanding the interplay between the hydrodynamics of cold dust-gas mixtures and the resulting physical chemistry has obvious ramifications for imaging star forming regions, as well as the young stars and planets which inhabit them.

hide

Thu 04/08/16 10:00
Tower Building
Computational Biology Workshop
Dr. Alex Fletcher (Chaste (University of Sheffield))
Computational Biology
abstract

Abstract

Chaste (Cancer, Heart and Soft Tissue Environment) is a general purpose, open source simulation package aimed at multi-scale, computationally demanding problems arising in biology and physiology. Current functionality includes tissue and cell level electrophysiology, discrete tissue modelling, and soft tissue modelling. The package is being developed by a team mainly based in the Computational Biology Group at the Department of Computer Science, University of Oxford, and development draws on expertise from software engineering, high performance computing, mathematical modelling and scientific computing. While Chaste is a generic extensible library, software development to date has focused primarily on two distinct application areas: continuum modelling of cardiac electrophysiology (Cardiac Chaste); and individual-based modelling of cell populations, with specific application to tissue homeostasis and carcinogenesis (Cell-based Chaste). In this workshop, we will learn how to use Chaste to solve cell-based modelling problems. If you would like to attend then please email pmurray@dundee.ac.uk.

hide

Mon 08/08/16 15:00
Fulton H2
Mathematics Seminar
Prof. Rebecca Waldecker (Martin Luther University Halle-Wittenberg)
Finding and using symmetry
abstract

Abstract

In this talk we will look at situations where a scientific problem exhibits some symmetry. How can this symmetry be used to understand the problem better or to solve it faster? I will comment on a wide range of applications of this method and discuss some examples in detail.

hide