Methods of mathematical modelling & A brief introduction to ordinary differential equation modelling with chemical kinetics
Day 3 – Foundations of Data Science I (AM)
10.00-12.00 Methods of mathematical modelling
Mathematical models of the physical world often lead to descriptions based on differential equations. In this session we will work through the modelling process for an example system, from the initial formulation of the governing equations to the model analysis, reduction and solution. During the process I will introduce some of the basic methods of mathematical modelling, including differential equations, dimensional analysis and asymptotic techniques. The lectures will be illustrated with hands-on sessions.
Matlab installed. (If not available, Octave or Octave online may suffice ( https://octave-online.net/ )
Speaker biography: I am an applied mathematician with a particular interest in fluid mechanics and elasticity. I work in the Department of Mathematics and Statistics at the University of Limerick, Ireland, and I am a supervisor in the SFI Centre for Research Training in Foundation of Data Science. I am interested in mathematical modelling of real-world systems, and primarily in fluid and solid mechanics. My research focuses primarily on the dynamics of thin viscous, elastic and plastic sheets, motivated by applications such as glass manufacture, elastic wrinkling, and metal forming processes. I am also interested in fluid-structure interactions and in fluid flow and reactions inside porous media – this includes decontamination problems and battery modelling. My mathematical modelling approach primarily uses differential equations, perturbation methods and numerical methods. Prior to joining UL I was a postdoctoral researcher at the University of Oxford, where I also completed my PhD in Mathematics. I have a BSc in Theoretical Physics from University College Dublin and an MSc in Mathematical Modelling and Scientific Computing from Oxford.
12.00-13.00 A brief introduction to ordinary differential equation modelling with chemical kinetics
A range of applications require modelling of the interactions of multiple species or populations to determine how these interactions drive changes in the abundance of each species or population. If the populations are assumed to be well-mixed in some sense, the population dynamics may be described by a set of ordinary differential equations evolving in time. Applications include modelling predator-prey systems, disease spread and evolution of species concentration in chemical reactions.
In this talk, such ordinary differential equation models will be introduced in the context of chemical kinetics. Some basic concepts needed to derive the governing equations will be outlined and applied to a classical enzyme-catalysed reaction. The equations will be non-dimensionalised and reduced to arrived at the so-called Michaelis-Menten approximation. If time allows, some asymptotic results may be presented as well as the possibility of geometric analysis on the phase-plane for this system.
The mode of delivery will be lecture style. Participants may wish to bring their laptops with MATLAB installed if they would like to look at or run the code during the lecture. Where access to MATLAB is not possible, Octave or Octave online may be used (https://octave-online.net/ ).
Speaker biography: Kevin Moroney is a lecturer in industrial and applied mathematics at the University of Limerick. He holds an BSc in Mathematical Sciences from University College Cork and an MSc in Mathematical Modelling from University of Limerick. In 2017 he completed his PhD in Applied Mathematics from University of Limerick. He is interested in various topics in applied mathematics with industrial applications, including mathematical modelling of transport processes in porous media with applications in coffee brewing and drug dissolution. These topics require modelling of multiphysics phenomena including multiphase fluid flow, chemical transport and phase change (dissolution and precipitation).
Participants are welcome to join in person (S206 Schumann Building, University of Limerick) or remotely. A Zoom link will circulate to remote participants on Wednesday 24th of August.
There is a 0.5 deduction from the training unit allocation per Enterprise Alliance member joining this session.
The SFI Centre for Research Training in Foundations of Data Science will train a cohort of PhD students with world-class foundational understanding in the horizontal themes of Applied Mathematics, Statistics, and Machine Learning.
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