The DOS, and its predecessor BOS, network unites researchers with an interest in anisotropy or directionality in materials, be they solids or liquids. The network brings together for the first time leading research groups in continuum mechanics from Durham, Oxford and Strathclyde.
Anisotropy means the "existence of special or distinguished directions" and "reduced symmetry" since all directions are not physically equivalent. This, in turn, implies directional physical, optical, mechanical and rheological properties that pave the way for new applications. Nematic liquid crystals are classical examples of anisotropic complex fluids for which the constituent asymmetric molecules have translational freedom but tend to align along certain preferred directions, leading to long-range orientational order.
Apala Majumdar leads the Strathclyde side, and specializes in the mathematics and modelling of nematic liquid crystals, in particular spatio-temporal pattern formation for nematics in confined geometries and how their orientational anisotropy may be tailored by material properties, geometrical properties and temperature using techniques from the calculus of variations, algebraic topology, dynamical systems approaches and numerical studies. Her work is largely motivated by questions in the display industry or new experiments on nano-confined systems.
Ian Griffiths leads the Oxford side, and has recently started to specialize in anisotropic solids, for example, porous media with non-periodic pores and spatially dependent permeabilities. This can be mathematically studied using new techniques in homogenization theory, with new applications in filtration and environmental problems. A recently studied example concerns a porosity-graded filter, whose porosity varies with depth, such as fibrous filters and ceramic filters. Each of these materials offers the possibility of improved performance either by filtering out particles more uniformly in the depth or by reducing the pressure required to drive fluid through the filter, and there is ample scope for new mathematical insights from asymptotics, analysis and up-scaling methods.
Nigel Mottram co-led the Strathclyde side until his recent move to the University of Glasgow. He specializes in the mathematics and applications of nematic liquid crystals, with a more recent interest in bio-inspired active liquid crystals. Active liquid crystals are inherently non-equilibrium systems, constantly producing and dissipating energy with striking and unique mechanical and rheological responses, such as low Reynolds number turbulence, rapid density fluctuations and exotic singularities. Active liquid crystals are ubiquitous in biology, common examples being the cell cytoskeleton and the human DNA and a lot remains to be understood about the active terms in the phenomenological theories for active systems and the new resulting anisotropies.
Halim Kusumaatmaja leads the Durham side, and is interested in a wide range of soft matter and biological problems which often show anisotropic behaviour. Examples of current interest include phase behaviour on non-uniform curved surfaces, spreading dynamics on structured surfaces, and reconfigurable elastic structures. His work is largely motivated by a strong interest to understand and mimic nature for engineering and industrial applications. He uses a combination of analytical and numerical techniques. The latter include Monte Carlo, Molecular Dynamics, lattice Boltzmann and energy landscape exploration techniques.