Academic webpage Title: The Role of Geometry, Topology and Mechanics in Physiology and Disease Abstract: Molecular networks underpin all cellular functions, including metabolism, division, and migration. These networks are frequently altered in disease and are common targets for therapeutic intervention. Many key molecular components are associated with the plasma membrane or are localized within organelles…

Academic webpage Title: Adaptive methods and explicit time-stepping Abstract: Aposteriori error analysis for Galerkin finite element methods have proven very successful tool in developing mathematically rigorous adaptive mesh refinement algorithms for implicit/space-time evolution equations.  In this work we extend rigorous adaptivity principles to explicit time-stepping for the wave equation. I will review in the first…

Academic webpage Title: Decayless kink oscillations of solar coronal loops as a self-oscillatory process Abstract: Kink oscillations of the decayless class are detected as small amplitude (< 1 Mm) persistent transverse repetitive displacements of solar coronal plasma loops, occurring without any association with solar flares, eruptions, or other impulsive energy releases. The linear correlation of the…

Academic webpage Title: Oscillatory Reconnection Abstract: Magnetic reconnection is a fundamental plasma process at the heart of many dynamic events such as solar flares. These are clearly time-dependent events, and so we require time-dependent reconnection models to capture this dynamic behaviour. In this talk, I will describe ongoing investigations into “Oscillatory Reconnection”: a type of…

Academic webpage Title: Untangling waves and mean flows via PDE-based Lagrangian filtering Abstract: Oceanic flows are typically composed of wave and mean motions with a wide range of overlapping temporal scales, making separation between the two types of motion in wave resolving numerical simulations challenging. Lagrangian filtering – whereby a temporal filter is appliedin the frame…

Academic webpage Title: Postponed to a later date.

Academic webpage Title: What can flow down a pipe teach us about the geodynamo (and other nonlinear stability problems)? Abstract: The Geomagnetic field is generated in the rapidly rotating fluid outer core of the Earth on a vast range of temporal scales. This leads to the presence of slow balanced motions and fast waves, which…

Academic webpage Title: Multicellular Calculus Abstract: The disordered and granular nature of multicellular tissues endows them with exotic mechanical properties and presents challenges to continuum modelling frameworks.  To address this, many researchers use the vertex model as a convenient computational tool with which to simulate epithelia, the cell layers that coat developing embryos or provide protective…

Academic webpage Title: Turbulent damping of fast oscillations by a convective flow Abstract:Traditional mixing-length models describe tidal dissipation in convective flows as a large-scale oscillation damped by an effective turbulent viscosity that is artificially reduced when the oscillation period is much shorter than the convective turnover time.  This yields dissipation rates far below observational constraints. From first principles,…

Academic webpage Title: Phase transitions from the viewpoint of an applied mathematician Abstract: Evaporation, supercooling, and related phenomena can be described using hydrodynamic, kinetic, or mixed models – which yield results differing by up to two orders of magnitude.  Furthermore, these theoretical predictions disagree with at least some experimental results, which themselves are not mutually consistent:…