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Band Structures Of Layered Carbon/Boron Nitride Materials With Commensurate Lattices, Christopher C. Wells
Band Structures Of Layered Carbon/Boron Nitride Materials With Commensurate Lattices, Christopher C. Wells
Legacy Theses & Dissertations (2009 - 2024)
The electronic structures of systems consisting of hexagonal boron nitride layers and graphite sheets have been investigated in detail using density functional theory methods with two exchange correlation functions (local density approximation and generalized gradient approximation). The experimental data of graphene, graphite, monolayer hexagonal BN, and hexagonal BN were reproduced well with computational models. The commensurate models used in the investigation were generated by taking the averages of the lattice constants for graphite and h-BN.
Lattice Vertex Algebras And Combinatorial Bases, Michael Eugene Leslie Penn
Lattice Vertex Algebras And Combinatorial Bases, Michael Eugene Leslie Penn
Legacy Theses & Dissertations (2009 - 2024)
We explore the structure of a certain ``principal'' subalgebra, $W_L(\mathcal{B})$, of a lattice vertex (super)-algebra, $V_L$, where $L$ is a non-degenerate integral lattice, and $\mathcal{B}$ is a $\mathbb{Z}$-basis of $L$. Under a certain positivity condition on $\mathcal{B}$ we find a presentation of $W_L(\mathcal{B})$ and of $W_L(\mathcal{B})$-modules. In a more general case we also find their combinatorial bases. For both cases we calculate the (multi)-graded dimensions of modules expressed as fermionic $q$-series . This work generalizes some of the results from \cite{CalLM}, which involved a root lattice of type $A-D-E$, and where $\mathcal{B}$ was the set of simple roots.