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Full-Text Articles in Physical Sciences and Mathematics
Self-Assembly On A Cylinder: A Model System For Understanding The Constrain Of Commensurability, D. A. Wood, Christian Santangelo, A. D. Dinsmore
Self-Assembly On A Cylinder: A Model System For Understanding The Constrain Of Commensurability, D. A. Wood, Christian Santangelo, A. D. Dinsmore
Christian Santangelo
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to structures with a chiral seam known as a ‘line slip’ phase, neither of which is stable for isotropic particles in equilibrium on flat surfaces. In this study, we use molecular dynamics simulations to find the steady-state structure of spherical particles with short-range repulsion and long-range attraction far below the melting temperature. We vary the range of attraction using the Lennard-Jones and Morse potentials and …
Nambu-Goldstone Modes And Diffuse Deformations In Elastic Shells, Christian Santangelo
Nambu-Goldstone Modes And Diffuse Deformations In Elastic Shells, Christian Santangelo
Christian Santangelo
I consider the shape of a deformed elastic shell. Using the fact that the lowest-energy, small deformations are along infinitesimal isometries of the shell's mid-surface, I describe a class of weakly stretching deformations for thin shells based on the Nambu–Goldstone modes associated with those isometries. The main result is an effective theory to describe the diffuse deformations of thin shells that incorporate stretching and bending energies. The theory recovers previous results for the propagation of a “pinch” on a cylinder. A cone, on the other hand, has two length scales governing the persistence of a pinch: one governing the relaxation …