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We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the minimum-energy configurations of particles with arbitrary repulsive interactions on curved surfaces. Above a critical(More)
We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying(More)
We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature the physics of interacting disclinations is mapped to a Laplacian Sine-Gordon Hamiltonian suitable for numerical simulations. We then specialize to the case of a(More)
Toroidal templates such as vesicles with hexatic bond orientational order are discussed. The total energy including disclination charges is explicitly computed for hexatic order embedded in a toroidal geometry. Related results apply for tilt or nematic order on the torus in the one Frank constant approximation. Although there is no topological necessity for(More)
We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we(More)
Engineering synthetic materials that mimic the remarkable complexity of living organisms is a fundamental challenge in science and technology. We studied the spatiotemporal patterns that emerge when an active nematic film of microtubules and molecular motors is encapsulated within a shape-changing lipid vesicle. Unlike in equilibrium systems, where defects(More)
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology dictates certain broad features of the defect structure of the ground state but curvature-driven energetics controls(More)
The production of strings (disclination lines and loops) has been observed by means of the Kibble mechanism of domain (bubble) formation in the isotropic-nematic phase transition of the uniaxial nematic liquid crystal 4-cyano-4'-n-pentylbiphenyl. The number of strings formed per bubble is about 0.6. This value is in reasonable agreement with a numerical(More)
Liquid crystals inevitably possess topological defect excitations generated through boundary conditions, through applied fields, or in quenches to the ordered phase. In equilibrium, pairs of defects coarsen and annihilate as the uniform ground state is approached. Here we show that defects in active liquid crystals exhibit profoundly different behavior,(More)
Mesoscale objects with unusual structural features may serve as the analogues of atoms in the design of larger-scale materials with novel optical, electronic or mechanical behaviour. In this paper we investigate the structural features and the equilibrium dynamics of micrometre-scale spherical crystals formed by polystyrene particles adsorbed on the surface(More)