Research

Here you will find an overview of my present research interests. A significant component of my work is collaborative and spans experimental, engineering, pure and applied mathematics, as well as industrial groups. This has led to strong cross-fertilisation of ideas and approaches which have matured into significantly more than the sum of their parts. A few examples and additional interactive material will soon be included as deep dive subpages into some of the more beautiful (and subtle) aspects of the respective work.

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High-speed flows and drop impact

The canonical problem of drop impact provides a striking example of a deceivingly simple fundamental setup with a history of almost a century and a half (Worthington, 1876). The highly violent evolution of the gas-liquid interface continues to inspire new approaches in matched asymptotics and complex analysis, while numerically it represents a stern test for even the most capable numerical platforms. For the past five years I have worked towards the inclusion of rigorous mathematical insight into phenomena such as pre-impact deformation, liquid jet formation and secondary drop generation and break-up.

I have also worked as part of large scale projects pertaining to laminar-turbulent transition and contributed to the modelling of the effect of thin liquid films on boundary layer separation using extensions to multiple deck theory.

Small scale multi-physics modelling

Using a combination of reduced-order modelling, asymptotic analysis and direct numerical simulations, I aim to identify and extend the range of validity of existing theoretical approaches for the manipulation of small liquid volumes in confined geometries which are difficult to access non-invasively. Using electric fields as driving force, I then use the developed hybrid framework to efficiently access nonlinear regimes involving complex interfacial dynamics and topological transitions such as coalescence or dripping. The ultimate aim of these methods is to provide functionalities over lengthscales ranging from microns to millimetres, pertaining to applications such as lab-on-a-chip devices and precision coating.

More recently I have started looking into feedback control methodologies using mechanical techniques involving for example blowing/suction, acoustic and electrohydrodynamical effects.

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Computational acoustics

My early efforts in modelling high-intensity focused ultrasound have shaped my understanding of the challenges in designing reflectionless boundary conditions for wave propagation problems in finite domains. These issues became immediately apparent in view of the large wavenumbers and inhomogeneous media involved in the respective context. Together with colleagues at the University of Manchester we have developed a robust and efficient way to use perfectly matched layers in a manner that avoids the numerous parameters which usually burden such a setup. This has been successful in the context of both acoustic and elastic waves.

Our progress in this direction is summarised in this publication. The oomph-lib tutorial here describes the general implementation steps.

Industrial mathematics

A representative example is the construction of a method to integrate multi-scale statistical information into a predictive model for specialised port terminal operations. The specific geography and restrictions, as well as long-term logistics planning horizons, made this endeavour both engaging and immediately applicable in terms of addressing key expansion scenarios. The interaction with colleagues at the University of Limerick and RUSAL Aughinish has been shortlisted for the Irish Lab Awards - Collaboration Achievement category back in 2014.

The developed data-rich model and its predictions on the potential improvements on the operational activity can be found here.

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