Two dimentional lattice vibrations from direct product representations of symmetry groups

J. N. Boyd and P. N. Raychowdhury

International Journal of Mathematics and Mathematical Sciences, 1983, vol. 6, 1-12

Abstract:

Arrangements of point masses and ideal harmonic springs are used to model two dimensional crystals. First, the Born cyclic condition is applied to a double chain composed of coupled linear lattices to obtain a cylindrical arrangement. Then the quadratic Lagrangian function for the system is written in matrix notation. The Lagrangian is diagonalized to yield the natural frequencies of the system. The transformation to achieve the diagonalization was obtained from group theorectic considerations. Next, the techniques developed for the double chain are applied to a square lattice. The square lattice is transformed into the toroidal Ising model. The direct product nature of the symmetry group of the torus reveals the transformation to diagonalize the Lagrangian for the Ising model, and the natural frequencies for the principal directions in the model are obtained in closed form.

Date: 1983
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/6/371643.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/6/371643.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:371643

DOI: 10.1155/S0161171283000666

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().