Department of Mathematics

Research projects in Applied Mathematics

Our staff are engaged in ground breaking research which is recognised internationally.

  • Manifolds of systems with multiple time scales

    Systems with slow and fast variables have so-called slow manifold (curves and surfaces) that are invariant for only a finite time. This project explores the role of truly invariant manifolds, such as (un)stable manifolds of equilibria or periodic orbits, in the presence of slow manifolds.

  • Intrinsic excitability and other transient effects

    Applications of dynamical systems theory in a finite-time context, with a particular focus on understanding mechanisms that induce large-amplitude oscillations caused by small external perturbations.

  • The geometry of chaos

    When invariant manifolds (e.g., special surfaces) interact, they can generate chaotic dynamics. Exactly how this happens is poorly understood. Using advanced numerical methods, we can now visualise and study this behaviour in exceedingly more detail.

  • Excluded volume diffusion

    The modelling of diffusion of particles where the particle size is taken into account leads to nonlinear PDEs for the collective dynamics.

  • Earth Impactors

    Modelling how often asteroids and other small bodies hit Earth.

  • Dynamics of climate models

    Climate models range in complexity from those containing a few differential equations to huge models that require a vast amount of computational power