Dr Georg Maierhofer is a Henslow Fellow at Clare Hall and works in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. His research interests lie in Computational Mathematics for Partial Differential Equations (PDEs). PDEs are a central foundation of modern scientific modelling and help describe phenomena as varied as atmospheric processes and the generation and propagation of noise in the form of sound waves. Computational Mathematics is used to simulate nature by solving these PDEs approximately and without such numerical techniques many of humanity’s greatest technological and scientific advances would be impossible – from supercomputers processing terabytes of data on a daily basis for weather forecasting to sophisticated numerical models predicting the movement of atoms in particle accelerators.
Dr Maierhofer’s main research concerns the study of so-called structure-preserving numerical methods for PDEs – algorithms which can replicate the ‘physical behaviour’ of solutions to PDEs, by preserving associated conservation laws such as the preservation of energy. A particular focus lies on the understanding of properties of symplectic methods when applied to infinite-dimensional Hamiltonian systems – differential equations that can be written in a unified formalism that encompasses a powerful mathematical description of many physical systems and their conservation laws. The rigorous understanding of advantages and limitations of such structure-preserving methods could lead to improved simulation tools for example improving the accuracy of weather forecasts.
This research is complemented by a broader interest in the applications of computational mathematics, such as the simulation of extreme ocean waves, and the use of machine learning for the enhancement of classical methods from numerical analysis, for instance in meshing problems and the acceleration of classical solvers for time evolution PDEs.
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The dynamics of infectious disease (ID) require fast accurate diagnosis for effective management and treatment. Without affordable, accessible diagnostics, syndromic or presumptive actions are often followed, where positive cases may go undetected in the community, or mistreated due to wrong diagnosis. In many low and middle income countries (LMICs), this undermines effective clinical decision-making and infectious disease containment.
Unsteady effects occur in many natural and technical flows, for example around flapping wings or during aircraft gust encounters. If the unsteadiness is large, the resulting forces can be quite considerable. However, the exact physical mechanisms underlying the generation of unsteady forces are complex and their accurate prediction remains challenging. One strategy is to identify the dominant effects and describe these with simple analytical models, first proposed a hundred years ago. When used successfully, this approach has the advantage that it also gives us a conceptual understanding of unsteady fluid mechanics.
In this lecture I will explain some of these ideas and demonstrate how they can still be useful today. As a practical example, I will show how the forces experienced in a wing-gust encounter can be predicted – and how the predictions can be used to mitigate the gust effects. The lecture will be illustrated with images and videos from simple, canonical, experiments.
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