Title

Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

Author(s)/Creator(s)

Mark Bowick, Department of Physics, Syracuse University, Syracuse, NYFollow
Luca Giomi, Syracuse University

Document Type

Article

Date

2-20-2007

Keywords

Crystalline Order

Language

English

Acknowledgements

Luca Giomi:

https://orcid.org/0000-0001-7740-5960

Disciplines

Physics

Description/Abstract

We investigate the zero temperature structure of a crystalline monolayer constrained to lie on a two-dimensional Riemannian manifold with variable Gaussian curvature and boundary. A full analytical treatment is presented for the case of a paraboloid of revolution. Using the geometrical theory of topological defects in a continuum elastic background we find that the presence of a variable Gaussian curvature, combined with the additional constraint of a boundary, gives rise to a rich variety of phenomena beyond that known for spherical crystals. We also provide a numerical analysis of a system of classical particles interacting via a Coulomb potential on the surface of a paraboloid.

Additional Information

12 pages, 8 figures More information at http://arxiv.org/abs/cond-mat/0702471

Recommended Citation

Bowick, Mark and Giomi, Luca, "Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary" (2007). Physics - All Scholarship. 147.
https://surface.syr.edu/phy/147

Source

Harvested from Arxiv.org

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.