# Workshop Programme

## for period 24 - 28 June 2013

### Liquid Crystal Defects and their Geometry, Active and Solid Liquid Crystals, and Related Systems

24 - 28 June 2013

Timetable

 Monday 24 June 09:00-09:35 Registration 09:35-09:45 Welcome by Director, Professor John Toland 09:45-10:30 Kleman, M (Institut de Physique du Globe de Paris) Liquid crystal defects, a critical overview Meeting Room 2, CMS Defects in liquid crystals present an extremely vast set of situations, depending on the nature of the order parameter, elasticity properties, boundary conditions. One distinguishes : defects characteristic of liquid crystalline media with one or two discrete repeat distances (smectic and columnar phases) which can be investigated by pure geometric methods ; defects characteristic of a director order parameter, which employ the Volterra process (for one dimensional defects) and topological methods, those latter providing scope for defects of various dimensionalities ; finally continuous defects whose consideration is essential for a description of defect physical properties. These topics will be confronted with an historical point of view and possible future developments. 10:30-11:00 Morning Coffee 11:00-12:00 Kamien, R (University of Pennsylvania) Pure and Applied Focal Conics Meeting Room 2, CMS The epitaxial assembly of toric focal conic domain (TFCD) arrays of smectic-A liquid crystals onto pillar arrays is studied. The 3D nature of the pillar array is crucial to confine and direct the formation of TFCDs on the top of each pillar and between neighboring pillars, leading to highly ordered square and hexagonal array TFCDs persisting deeply into the bulk. 12:00-12:45 Fukuda, J (AIST) Exotic defect structures in a strongly confined chiral liquid crystal Meeting Room 2, CMS We present our numerical results on the structures of a chiral nematic liquid crystal when it is confined in a thin planar cell with strong anchoring on its surfaces. We are interested in the cases where the liquid crystal exhibit a cholesteric blue phase under no confinement, and the cell thickness is of the order of or smaller than the cholesteric pitch. We show various stable exotic defect structures depending on temperature, cell thickness, and the type of anchoring. They include a hexagonal lattice of Skyrmion excitations, and a regular array of ring defects. These exotic defect structures can be regarded as a result of frustrations between bulk blue phase ordering and surface anchoring that does not allow it. 12:45-13:30 Lunch at Wolfson Court 14:00-14:45 Alexander, GP (University of Warwick) Textures and Topology in Liquid Crystals Meeting Room 2, CMS The textures of liquid crystals have always been central in identifying mesophases and understanding their properties. They are deeply connected with topology, both of the liquid crystal and of the environment that it lives in, so that controlling and describing topological properties provides a key tool in constructing and understanding complex three-dimensional textures. I will describe two applications of topological ideas to studying mesophases: the general characterisation of three-dimensional textures in nematics -- illustrated through the analysis of torons and the Hopf fibration in confined cholesterics -- and the formation of elegant knots and links around colloidal particles representing non-orientable surfaces. 14:45-15:30 Zumer, S (University of Ljubljana) Nematic braids: Effects of chirality and confinement Meeting Room 2, CMS Nematic disclinations can form stable braids when they are stabilized by a confining geometry, chirality, or by interplay of both effects. These are stable or metastable topologically diverse defect structures in the nematic ordering field. Based on the synergy of our theoretical and numerical, approaches we are able to characterize geometries and properties of disclination loops forming braids by winding numbers, lengths, knot or link types, and self-linking numbers. We focus our attention to selected nematic braids of the lowest complexity: knotted 2D colloidal crystals, opal structures permeated by nematics, and knots in cholesteic drops. With this overview I would like to show how topology and geometry enables the assembling of complex soft materials. [1] S. ?opar and S. Žumer, Nematic Braids: Topological Invariants and Rewiring of Disclinations, Phys. Rev. Lett. 106, 177801 (2011). [2] S. ?opar, and S. Žumer, Quaternions and hybrid nematic disclinations, Proc. R. Soc. A 469, 1471 (2013). [3] U. Tkalec, M. Ravnik, S. ?opar, S. Žumer and I. Muševi?, Reconfigurable Knots and Links in Chiral Nematic Colloids, Science 333, 62 (2011). [4] S. ?opar, N. A. Clark, M. Ravnik and S. Žumer, Elementary building blocks of nematic disclination networks in densely packed 3D colloidal lattices, Soft Matter, DOI: 10.1039/C3SM50475A (2013). 15:30-16:00 Afternoon Tea 16:00-17:00 Lubensky, T (University of Pennsylvania) Rigidity, Zero Modes, States of Self Stress, and Surface Phonons in Periodic and Diluted Periodic Networks near their Instability Limit Sem 1 Frames consisting of nodes connected pairwise by rigid rods or central-force springs, possibly with preferred relative angles controlled by bending forces, are useful models for systems as diverse as architectural structures, crystalline and amorphous solids, sphere packings and granular matter, networks of semi-flexible polymers, and protein structure. The rigidity of these networks depends on the average coordination number z of the nodes: If z is small enough, the frames have internal zero-frequency modes, and they are "floppy"; if z is large enough, they have no internal zero modes and they are rigid. The critical point separating these two regimes occurs at a rigidity threshold, which corresponds closely to what is often referred to as the isostatic point, that for central forces in d-dimensions occurs at coordination number zc = 2d. At and near the rigidity threshold, elastic frames exhibit unique and interesting properties, including extreme sensitivity to boundary conditions, power-law scaling of elastic moduli with (z- zc), and diverging length and time scales. This talk will explore elastic and mechanical properties and mode structures of model periodic and diluted periodic lattices, such as the square and kagome lattices with central-force springs, that are just on verge of mechanical instability, and 4-coordinated lattices in two and three dimensions that are stabilized by bending forces. It will discuss the origin and nature of zero modes of these structures under both periodic (PBC) and free boundary conditions (FBC), and it will derive general conditions under which (a) the zero modes under the two boundary conditions are essentially identical and (b) under which zero modes do not appear in the periodic spectrum but do appear as surface Rayleigh waves in the free spectrum. In the former situation, lattices are generally in a type of critical state that admits states of self-stress in which there can be tension in bars with zero force on any node, and distortions away from that state give rise to surface modes under free boundary conditions whose degree of penetration into the bulk diverges at the critical state. This general phenomenon also occurs in sub-isostatic lattices like the honeycomb lattice. The talk will also explore diluted 4-coordinated lattices as models for networks of semi-flexible polymers, discuss the special properties that result when constituent polymers adopt strictly straight configurations. 17:00-18:00 Welcome wine reception
 Tuesday 25 June 09:00-09:45 Smalyukh, I (University of Colorado) Topological colloids and particle-induced defects in liquid crystals Meeting Room 2, CMS We fabricate colloidal particles with nontrivial surface topology, including colloidal handlebodies, knots, links, Mobius strings, and Seifert surfaces. When introduced into a nematic liquid crystal with a uniform far-field director, these particles induce three-dimensional director fields and topological defects around them. We use director switching by electric fields, laser tweezing of defects, and local photothermal melting of the liquid crystal to promote transformations among many stable and metastable particle-induced director configurations and then explore them by means of a direct label-free three-dimensional nonlinear optical imaging. This reveals many peculiarities of the interplay between topologies of colloidal surfaces, director fields, and defects, which we find being in agreement with Gauss-Bonnet and Poincaré-Hopf index theorems. The lecture will conclude with a brief discussion of how these findings may lay the groundwork for new types of topology-di ctated elastic self-assembly in liquid crystals and experimental study of low-dimensional topology. 09:45-10:30 Cates, M (University of Edinburgh) Colloidal Doping of Cholesterics and Blue Phases Meeting Room 2, CMS At the interface between a cholesteric phase and an isotropic fluid, an array of defects arises. This creates for embedded colloidal particles a free energy landscape that depends on the ratio of colloid size to cholesteric pitch and on the strength of anchoring at the colloid-cholesteric interface. I shall outline recent experiments and simulations that probe this landscape. A somewhat similar situation arises when colloids are added to blue phases, for which the defect array is not interfacial but permeates the bulk phase. Preliminary simulations suggest a variety of structures, many metastable, with interesting transitions inducible by external fields and/or flow. 10:30-11:00 Morning Coffee 11:00-11:45 Marenduzzo, D (University of Edinburgh) Modelling actomyosin droplets, and their consequences for cell motility Meeting Room 2, CMS We present a lattice Boltzmann study of the dynamics of an actomyosin droplet, described in terms of a continuum model which follows the time evolution of actomyosin density, actin polarisation and flow. This analysis offers a simple representation of a “cell extract”, which is a highly simplified system used in vitro to understand cell dynamics, and which essentially only comprises the actin cytoskeleton and an enclosing cell membrane. In the absence of polymerization and depolymerization processes (‘treadmilling’), the dynamics of our actomyosin droplet arises solely from the contractile motion of myosin motors; this should be unchanged when polarity is inverted. Our results suggest that motility can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry. This motility mode driven by myosin contractility alone may be relevant to cell motion in three dimensions, where frictional forces, which are crucial to convert actin polymerisatino into motion, are likely to be modest. We also show of active droplets crawling on a substrate, when both treadmilling and contractility are taken into account. Our droplets can adopt a number of morphologies and motility modes found experimentally in cells, such as lamellipodia, pseudopodia and oscillatory cell motion. 11:45-12:30 Liverpool, T (University of Bristol) Polar Active LCs: Non-equilibrium steady states and fluctuations Meeting Room 2, CMS 12:30-13:30 Lunch at Wolfson Court 14:00-14:45 Yeomans, J (University of Oxford) Active Nematics Meeting Room 2, CMS Active systems, such as the cytoskeleton and bacterial suspensions, provide their own energy and hence operate out of thermodynamic equilibrium. Continuum models describing active systems are closely related to those describing liquid crystal hydrodynamics, together with an additional ‘active’ stress term. We discuss how the behaviour of the active continuum models depends on model parameters, such as the strength of the activity and the liquid crystal tumbling parameter, and we compare our results to recent experiments on cytoskeletal gels. 14:45-15:30 Dogic, Z (Brandeis University) Hierarchical active matter: from extensible bundles to active gels, streaming liquid crystals and motile emulsions Meeting Room 2, CMS The emerging field of active matter promises an entirely new category of materials, with highly sought after properties such as autonomous motility and internally generated flows. In this vein, I will describe recent experiments that have focused on reconstituting dynamical structures from purified biochemical components. In particular I will describe recent advances that include: (1) assembly of a minimal model of synthetic cilia capable of generating periodic beating patterns, and conditions under which they exhibit metachronal traveling waves, (2) study of 2D active nematic liquid crystals whose streaming flows are determined by internal fractures and self-healing as well as spontaneous unbinding and recombination of oppositely charged disclination defects, (3) reconstitution of active gels characterized by highly tunable and controllable spontaneous internal flows, and (4) assembly of active emulsions in which aqueous droplets spontaneously crawl when in contact with a hard wall. 15:30-16:00 Afternoon Tea 16:00-16:45 Toner, J (University of Oregon) Rice, Locusts and Chemical Waves: A Hydrodynamic Theory of Polar Active Smectics Meeting Room 2, CMS We present a hydrodynamic theory of polar active smectics, by which we mean active striped systemsactive systems, both with and without number conservation. For the latter, we find quasi long-ranged smectic order in $d=2$ and long-ranged smectic order in $d=3$. In $d=2$ there is a Kosterlitz-Thouless type phase transition from the smectic phase to the ordered fluid phase driven by increasing the noise strength. For the number conserving case, we find that giant number fluctuations are greatly suppressed by the smectic order; that smectic order is long-ranged in $d=3$; and that nonlinear effects become important in $d=2$. 17:00-21:00 Walk to Grantchester, pub dinner* (either on Tues or Thu)