10:30 to 11:00 Registration 11:00 to 11:10 Introduction (John Toland and John Ball) INI 1 11:10 to 11:30 L Corson ([Strathclyde])Liquid dielectrophoresis and wrinkling on the surface of a fluid layer There is a growing technology-driven interest in using external forces to move or shape small quantities of liquids. One existing technique, electrowetting, involves the application of an electric field to a conducting liquid. A disadvantage of this technique is that the liquid must remain in contact with the electrodes. However, this is not the case in liquid dielectrophoresis, where a dielectric (i.e. non-conducting) liquid is used. A common aspect to both these techniques is that electrical surface stresses at liquid-air or liquid-liquid interfaces play an important role. In this work we consider a layer of dielectric liquid of non-dimensional depth $h(x,t)$ wetting a horizontal electrode with a hydrodynamically passive dielectric fluid (e.g. air) above. A second electrode is located at a distance $d>h$ above the lower substrate. When the applied voltage is increased past a critical value, an instability occurs on the free surface of the liquid. We investigate how the material and cell geometry parameters affect the critical applied voltage and the form of the instability. Using linear stability analysis, we find that there exists a critical spacing $d_{c}$ above which the fastest growing unstable mode has a non-zero wave number, so that undulations (wrinkles'') form on the free surface. Below this critical spacing, the fastest growing unstable mode has a zero wave number, so that wrinkles do not form. In general, we also find that higher values of the inverse Bond number $\tau$ (proportional to the surface tension) lead to a stab ilisation of the zero wave number mode, i.e. higher values of $d$ are required for wrinkling to occur. Furthermore, if the inverse Bond number is sufficiently low, a second critical spacing \$\tilde{d}_c INI 1 11:30 to 11:50 T-S Lin ([Loughborough])Hydrodynamic description of thin nematic films We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal. Firstly, we clarify how the elastic energy enters the evolution equation for the film thickness. We show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. Secondly, based on a gradient dynamics approach, we propose a film thickness evolution equation that describes a free surface thin film of nematic liquid crystals on a solid substrate under weak anchoring conditions at the free surface. We show that in the intermediate film thickness range anchoring and bulk energies compete what may result in a linear instability of the free surfa ce of the film. INI 1 11:50 to 12:10 S Bedford (University of Oxford)Variational problems for cholesteric liquid crystals - Function spaces and competing theories Generally chiral nematic liquid crystals have been seen as an aside to nematics, and have been studied less as a result. However they can exhibit many and varied patterns in the form of cholesteric fingers or filaments. If these behaviours were understood and controllable it could prove to be a valuable advance in industry devices. The notion of cholesteric frustration appears to be what drives the existence of the complicated minima, as a result boundary conditions, cell geometry and surface energies are all extremely important in the creation of a tractable problem, but so too is the function space in which we choose to minimise. More generally it might be possible, in some cases, to see different theories (Oseen-Frank, Ericksen, Q-Tensor) as merely minimisations in different function spaces. INI 1 12:10 to 12:30 M Bowick ([Syracuse])Open Problems Session INI 1 12:30 to 13:30 Lunch at Wolfson Court 13:30 to 13:50 M Blow ([Lisbon])Interfacial motion in flexo- and order-electric switching between nematic filled states We consider a nematic liquid crystal, in coexistence with its isotropic phase, in contact with a substrate patterned with rectangular grooves. In such a system, the nematic phase may fill the grooves without the occurrence of complete wetting. There may exist multiple (meta)stable filled states, each characterised by the type of distortion (bend or splay) in each corner of the groove and by the shape of the nematic-isotropic interface, and additionally the plateaux that separate the grooves may be either dry or wet with a thin layer of nematic. Using numerical simulations, we analyse the dynamical response of the system to an externally-applied electric field, with the aim of identifying switching transitions between these filled states. We find that order-electric coupling between the fluid and the field provides a means of switching between states where the plateaux between grooves are dry and states where they are wet by a nematic layer, without affecting the configu ration of the nematic within the groove. We find that flexoelectric coupling may change the nematic texture in the groove, provided that the flexoelectric coupling differentiates between the types of distortion at the corners of the substrate. We identify intermediate stages of the transitions, and the role played by the motion of the nematic-isotropic interface. We determine quantitatively the field magnitudes and orientations required to effect each type of transition. INI 1 13:50 to 14:10 M Nieuwenhuis (University of Oxford)A description of the smectic phase using statistical mechanics Many different interaction potentials have been used in order to model phase transitions for liquid crystals. One of the most fundamental theories used for numerical simulations is the density functional theory. However, the main task in this theory is to find a suitable approximation for the energy functional which is in general very difficult. In this short presentation I would like to give a brief overview over the techniques that can be used in order to capture the mathematical characteristics of the smectic phase. INI 1 14:10 to 14:30 R Lund ([Bristol])Domain wall motion in magnetic nanowires: an asymptotic approach We develop a systematic asymptotic description of domain wall motion in a magnetic nanowire. The Landau--Lifshitz--Gilbert equation is linearized about a static solution and the magnetization dynamics investigated via a perturbation expansion. We compute leading order behaviour, propagation velocities, and first order corrections of both travelling waves and oscillatory solutions, and find bifurcation points between these two types of solutions. INI 1 14:30 to 15:30 Individual discussions INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 16:20 R Foldes ([Minneapolis])Boundary-roughness effects in nematic liquid crystals Paolo Biscari and Stefano Turzi considered a plate with an undulatory pattern. They replace the corrugation with sinusoidal boundary conditions, and use formal asymptotics for the analysis. I would like to use the method of gamma convergence to determine the effective energy and its minimizers for this problem. INI 1 16:20 to 16:40 E Virga (Università degli Studi di Pavia)Open Problems Session INI 1 16:40 to 17:00 C Newton (University of Bristol)Open Problems Session INI 1 17:00 to 18:00 Reception