Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 3, 2010, Pages

  Sausset, François ^a   Tarjus, Gilles ^b   Nelson, David R ^c  

^a DIF   (France)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC CONFIGURATION; ATOMIC LIQUIDS; CONTINUUM THEORY; DISCLINATIONS; GLASSY LIQUIDS; HYPERBOLIC PLANE; LOW-TEMPERATURE REGIME; MOLECULAR DYNAMICS SIMULATIONS; STRUCTURE AND DYNAMICS; TOPOLOGICAL DEFECT;

CONTINUUM MECHANICS; DEFECT DENSITY; GRAIN BOUNDARIES; GRAIN SIZE AND SHAPE; LIQUIDS; MOLECULAR DYNAMICS;

DEFECTS;

EID: 77949762842     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.031504     Document Type: Article

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27. Disclinations with such high charge magnitude have always a nonzero probability to be present at finite temperature, which is given by the Boltzmann factor + |q| k T, as the energy of a free disclination is proportional to its charge magnitude. For the system studied here, in the range of temperatures shown in Fig. and for all curvatures, the total density of disclinations with charge magnitude strictly larger than π / 3 is always less than 5.10 - 3, whereas the density of fivefold and sevenfold disclinations is roughly two orders of magnitude bigger.
28. By using standard hyperbolic trigonometry (see Appendix C in Ref.), one can compute the cell area of any { p, q } tiling and deduce from it the associated density of vertices. A {3,7} crystal of disclinations can only appear if the density of vertices of the { p, q } tiling corresponding to the chosen periodic boundary condition is equal to the density of irreducible disclinations.