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Order Out of Disorder
Defects and Topology
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amorphous structures angle atoms average bond broken symmetry chain Chap components condensed matter configuration consider continuous group coordinates correlation function corresponding covariant derivative crystalline curvature curved space defined denote density disclinations dislocation element entropy equilibrium ergodicity Euclidean example expansion fluctuations fluid Frank-Kasper free energy gauge field geometry given group G homotopy group hydrodynamic hydrodynamic equations icosahedral illustrated incommensurate integers invariant isomorphic Kleman Landau theory lattice Lie group line defects liquid crystals loop magnetic mapping molecules nematic obtained orbit order parameter order-parameter space orientational order orientational symmetry pair parallel transport pattern Penrose tiling phase space Phys Physics plane polytope possible projection quasicrystals quasiperiodic referred regular relation rotation Sadoc Sect smectic solid sphere spin subgroup surface symmetry breaking symmetry group temperature tensor tessellation tetrahedra thermodynamic topological defects topological space trajectory transformation transition translational order unit cell variables vector