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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 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)
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)
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)
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)
We present the results of a high-statistics Monte Carlo simulation of a phantom crystalline (fixed-connectivity) membrane with free boundary. We verify the existence of a flat phase by examining lattices of size up to 128 2. The Hamiltonian of the model is the sum of a simple spring pair potential, with no hard-core repulsion, and bending energy. The only(More)
We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure(More)
The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Results of experiments on endocytosis in yeast show general agreement that 1) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it, and 2) the large-scale membrane deformation is tubular in shape. In(More)
We introduce and investigate numerically a minimal class of dynamical tri-angulations of two-dimensional gravity on the sphere in which only vertices of order five, six or seven are permitted. We show firstly that this restriction of the local coordination number, or equivalently intrinsic scalar curvature, leaves intact the fractal structure characteristic(More)