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2018/19 semester 1 events in Mathematics

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Mon 10/09/18 15:00
EduZone@Library
Mathematics Seminar
Prof. Cristophe Letellier (University of Rouen)
Tumor growth - From mathematical models to clinical applications
abstract

Abstract

Tumor growth is difficult to predict for at least two reasons: i) there are many parameters or variables that are not know, and ii) the dynamics is possibly sensitive to initial conditions. Such a lack of knowledge makes difficult the development of individualized therapies and follow-up. The use of mathematical models is one of the very promising ways towards an individualized oncology. In this talk, I will describe how we used model for reproducing some clinical features and used theoretical analysis for developing a new follow-up. The applications will be focused on lung and prostate cancers.

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Mon 17/09/18 15:00
OMS 2.03
Mathematics Seminar
Dr. Sven Van Loo (University of Leeds)
Numerical modelling of molecular shocks in the interstellar medium
abstract

Abstract

Molecular clouds are large reservoirs of gas and dust, which collapse under gravity to form dense star-forming cores. As stars form, jets and winds are produced and interact with the molecular cloud surrounding them. Shocks are then driven into the clouds sweeping up material. Observations often reveal bow-shaped structures, but the nature and structure of these shocks depends strongly on the local ionisation fraction of the gas and the magnetic field. The feedback from the outflows determines whether stars continue to form within molecular clouds. Often SiO emission is associated with shocks propagating through molecular clouds and it has been the subject of extensive observational programs. The presence of silicon in the gas phase is attributed to sputtering of siliconated-material from grains and to grain-grain interactions. I will present models of C-type shocks and their resulting SiO emission calculated with a time-dependent numerical code including a chemical model and dust microphysics. Furthermore, bow shock structures are currently reproduced from a superposition of one-dimensional plane-parallel shocks and not as a coherent, self-consistent structure. I will show the first results of a 3D simulation generating a molecular bow shock.

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Mon 24/09/18 15:00
EduZone@Library
Mathematics Seminar
Dr. David MacTaggart (University of Glasgow)
The non-modal onset of the tearing instability
abstract

Abstract

I will discuss the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, I will demonstrate that the operators of the linear equations are highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number S increases. In particular, I will show evidence that the maximum possible transient growth, measured in the L2-norm, for the classical setup of current sheets unstable to the TI, scales as O(S1/4) on time scales of O(S1/4) for S≫1. This behaviour is much faster than the time scale O(S1/2) when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. I will decribe the form of the optimal initial conditions for the maximum possible transient growth. Further, I will examine how the structure of the eigenvalue spectrum relates to physical quantities.

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Mon 01/10/18 15:00
Dalhousie 1G05
Mathematics Seminar
Dr. Maria Lopez-Fernandez (Universita di Roma)
Variable time-stepping approximation of convolution equations arising in wave scattering problems
abstract

Abstract

I will present the generalized Convolution Quadratures (gCQ) for the numerical approximation of convolution equations arising in wave scattering problems. The gCQ is a family of time-stepping procedures which allows to use variable steps, possibly driven by some error control mechanism. The derivation of the gCQ is accomplished by working in the Laplace domain and its implementation relies on contour integral techniques in the complex plane. Numerical experiments are presented to show the potential of our approach.

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Fri 05/10/18 15:00
Harris LT
Mathematics Seminar
Prof. Elsa Maria Cardoso-Bihlo (Memorial University of Newfoundland)
Variable time-stepping approximation of convolution equations arising in wave scattering problems
abstract

Abstract

I will present the generalized Convolution Quadratures (gCQ) for the numerical approximation of convolution equations arising in wave scattering problems. The gCQ is a family of time-stepping procedures which allows to use variable steps, possibly driven by some error control mechanism. The derivation of the gCQ is accomplished by working in the Laplace domain and its implementation relies on contour integral techniques in the complex plane. Numerical experiments are presented to show the potential of our approach.

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Mon 08/10/18 15:00
EduZone@Library
Mathematics Seminar
Dr. Tristan Pryer (University of Reading)
Model adaptivity in geophysical flows
abstract

Abstract

As computational capacity grows, simulations of geophysical phenomena become more and more complicated. The additional computational power allows for investment in increased resolution, more ensemble runs to account for uncertainty and the addition of PDEs governing new physical processes. This has a massive impact on the computational complexity. Indeed, a new problem arising in simulations is the power cost of the total ensemble runs. The next generation of high performance numerical methods will require considerable innovation for them to be viable. Adaptivity is crucial in the success of algorithms for geophysical multiscale problems. One of the novelties introduced in this talk is the idea of 'model adaptivity', the automatic switching between models of different complexity in real time as and when required.

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Mon 15/10/18 15:00
Fulton H2
Mathematics Seminar
Dr. Nikos Katzourakis (University of Reading)
On the existence and uniqueness of vectorial absolute minimisers in Calculus of Variations in L∞
abstract

Abstract

The Calculus of Variations in L∞ has a relatively short history in Analysis. The scalar-valued theory was pioneered by the Swedish mathematician G. Aronsson in the 1960s and since then has developed enormously. The general vector-valued case delayed considerably to appear and its systematic development began in the 2010s. One of the most fundamental problems in the area which was open until today (and has been attempted by many researchers) concerned that of the title. In this talk I will discuss the first result in this direction, which is based on joint work with my research associate Giles Shaw.

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Mon 22/10/18 15:00
Fulton G20
Mathematics Seminar
Dr. Georgios Minas (University of St Andrews)
How does the noisy NF-kB signalling pathway distinguish between simultaneously received signals?
abstract

Abstract

Cells constantly receive a multitude of different signals from their external environment. They use networks of interacting molecules to respond to these signals and trigger the appropriate actions. An important target of molecular biology is to identify and study the key components of these networks that are often found to be therapeutic targets. An important example is the NF-κB protein complex that is found to respond to a variety of different signals related to stress and inflammation in order to activate a large number (>500) of different genes including those regulating the immune system and the cell cycle. The NF-κB network is noisy and complex with oscillatory dynamics involving multiple feedback loops and therefore it is mathematically very interesting. In this talk, I am going to introduce the NF-kB signalling pathway, discuss stochastic models describing its dynamics and then attempt to develop a mathematical framework for assessing its ability to distinguish between simultaneously received signals.

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Mon 29/10/18 15:00
Fulton G20
Mathematics Seminar
Dr. Penny Wu (Queen's University)
von Karman decay and intermittent dissipation in kinetic collisionless plasma
abstract

Abstract

Collisionless plasma turbulence may be described by magnetohydrodynamics (MHD) at large scales, but requires kinetic description at ion and electron scales in order to include dissipative processes that terminate the cascade. We performed the first kinetic demonstration of von Karman similarity decay (in a formulation adapted to MHD from hydrodynamics) for 2.5-D collisionless plasmas. The profound implication is that decay/dissipation rate is determined in the outer scale by energy containing eddies, independent of the microscopic viscosity, resistivity, and details of dissipation mechanisms. Kurtosis of magnetic field increments indicates that kinetic scale coherent structures are present, with some suggestion of incoherent activity near ion scales. Proton temperature distributions suggest heating associated with coherent (non-Gaussian) structures: intermittent heating. Further, simulations render that at small turbulence amplitudes the electrons are preferentially heated, whilst at larger amplitudes proton heating is the dominant effect. In the solar wind and corona the protons are typically hotter, suggesting that these natural systems are in the large amplitude turbulence regime.

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Mon 12/11/18 15:00
Fulton G20
Mathematics Seminar
Prof. Nicola Bellomo (Politecnico di Torino)
Behavioural Crowd Dynamics by Kinetic Theory Methods
abstract

Abstract

This lecture aims at providing an answer that can be given to the following five key questions:
• Why a crowd is a “social, hence complex,” system?
• How mathematical sciences can contribute to understand the “behavioral dynam- ics of crowds”?
• How the crowd behaves in extreme situations such as panic and how models can depict them?
• Can a crowd be subject to large deviations (black swan)?
• Which are the methods and tools to deal with the multiscale features of a crowd can?
The answer to the key question takes advantage of recent research activity. The answer opens to challenging research perspectives.

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Thu 22/11/18 14:00
Fulton G20
Mathematics Seminar
Dr. Rui Travasso (Centro de Fisica Computacional, University of Coimbra)
Mathematical modeling of cell movement and angiogenesis
abstract

Abstract

Biochemical processes are often tightly coupled with physical mechanisms. For example, the way cells organize in a tissue is dependent on their epigenetic states but also on the properties of the adhesion forces between the cells and with the extracellular matrix. Vessel formation and remodelling depend on blood flow, vessel mechanics, tissue mechanics, growth factor diffusion, and matrix mechanical properties and degradation. In this talk I will present several examples of computational models that simulate cell migration and vessel formation taking into account the mechanical interplay between the cells and their microenvironment. I will focus on the ability for these models to suggest testable hypothesis and to provide new insights into the mechanisms that drive the dynamics in these biological systems.

REFERENCES
[1] Santos-Oliveira, P., Correia, A., Rodrigues, T.,Ribeiro-Rodrigues, T.M., Matafome, P., Rodríguez-Manzaneque, J. C., ... Travasso, R. D. (2015). The force at the tip-modelling tension and proliferation in sprouting angiogenesis. PLoS computational biology, 11(8), e1004436.
[2] M. Moreira-Soares, R. Coimbra, L. Rebelo, J. Carvalho, R. D. M. Travasso, Angiogenic factors produced by hypoxic cells drive anastomoses in sprouting angiogenesis – a computational study. (2018). Scientific Reports, 8, 8726
[3] Ramos, J. R., Travasso, R., Carvalho, J. (2018). Capillary network formation from dispersed endothelial cells: Influence of cell traction, cell adhesion, and extracellular matrix rigidity. Physical Review E, 97(1), 012408.
[4] Gandica, Y., Schwarz, T., Oliveira, O., Travasso, R. D. (2014). Hypoxia in vascular networks: a complex system approach to unravel the diabetic paradox. PloS one, 9(11), e113165.

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