A minimum metric basis is a minimum set W of vertices of a graph G(V,E) such that for every pair of vertices u and v of G, there exists a vertex w ∈ W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. The honeycomb and hexagonal networks are popular mesh-derived parallel architectures. Using the duality of these networ...

We outline the small amplitude asymptotic approximation for breathers for one-dimensional chains, and two-dimensional lattices with square, triangular/hexagonal, and honeycomb geometries. Two-dimensional lattices are complicated due to the resulting NLS-type equation being either elliptic or hyperbolic in nature. This gives rise to an additional constraint in addition to the usual condition on ...

We study the dynamics of waves in honeycomb lattices. Wave dynamics in honeycomb lattices exhibits unique phenomena that cannot be observed in any other periodic system, such as conical diffraction [1] and Klein tunneling. The origin of these intriguing phenomena is the conical intersection between the two bands and the presence of two atoms in each unit cell. These two properties make it possi...

This report contains the results of attempting to improve on the results of Scott R. Sawyer and Alan M. L’Esperance research paper “Investigation of Paraffin Wax as an Energy Storage Medium Within a Shell-and-Tube Heat Exchanger.” The overall goal of the paper mentioned was to investigate the usefulness of wax as an energy storage medium. Scott R. Sawyer and Alan M. L’Esperance determined that ...

Most conventional materials expand in transverse directions when they are compressed uniaxially resulting in the familiar positive Poisson's ratio. Here we develop a new class of two dimensional (2D) metamaterials with negative Poisson's ratio that contract in transverse directions under uniaxial compressive loads leading to auxeticity. This is achieved through mechanical instabilities (i.e., b...

Using a hybrid method based on fermionic diagonalization and classical Monte Carlo techniques, we investigate the interplay between itinerant and localized spins, with competing double- and superexchange interactions, on a honeycomb lattice. For moderate superexchange, a geometrically frustrated triangular lattice of hexagons forms spontaneously. For slightly larger superexchange a dimerized gr...