Professor in the
School of Mathematics;

Member of the
Manchester Centre for Nonlinear Dynamics;

University of Manchester.

I am broadly interested in the study of continuum mechanics, principally fluid and solid mechanics, with application to both biological and physical phenomena. Many complex fluid, solid and fluid-solid interaction problems occur naturally in the human body; for example, the veins in the arm collapse when raised above the level of the heart. Fluid-structure interaction is also important in pathologies of the body. The collapse and occlusion of the airways in the lung is driven by an interplay between the elastic properties of the airway wall and the surface tension of the lung-lining fluid.

The behaviour of the coupled continuum systems can be described by nonlinear differential equations, which must be often be solved numerically. After discretisation, the model consists of a large (up to tens of millions for three-dimensional problems) number of coupled equations. Since 2004, Matthias Heil and I (and many students, postdocs and colleagues ) have been developing oomph-lib, an object-oriented library of C++ functions designed specifically to make it "easy" to formulate and solve multi-physics problems. One of the main design aims of the library is to allow calculation of steady and unsteady solutions and their stability, including bifurcation detection and tracking, without a change in problem formulation.

- a study of the modes of bubble propagation in rectangular tubes containing localised constrictions in their cross-section; with Anne Juel
- bifurcations and instabilities in cellular solids; with Tom Mullin
- an investigation into the applicability of exact solutions of the Navier--Stokes equations (e.g. stagnation-point flows) in finite domains; with Rich Hewitt
- development of computational methods for the fast evaluation of unit-cell problems in homogenisation theory; with Will Parnell
- the simulation of the non-linear evolution of interfacial instabilities; with Anne Juel and Matthias Heil
- a study of the motion of rigid and deformable bodies in bounded fluid domains.

I am interested in all aspects of fluid and solid mechanics and
particularly coupled or multi-physics problems. Much of my work is
motivated by ** biological fluid mechanics, **
over a variety of scales from
millimetric (blood flow in large arteries, airway reopening and
collapse) to microscopic (flow on cellular lengthscales, swimming of
micro-organisms). I have spent a lot of time in recent years
studying ** interfacial flows and instabilities ** particularly
instabilities induced by geometric changes that may be a consequence of
the presence of elastic boundaries.
Typically, I take a combined experimental and theoretical
approach to solve physical problems, but my particular expertise is in
** numerical methods. ** I have a
fondness for finite, spectral and boundary element methods, as well
as expertise in parallel computation and object-oriented scientific
computing.