Abstract

A systematic approach for model unification of cluster expansion models is developed and demonstrated. The method builds on previous work with the Manifold Boundary Approximation Method (MBAM) to identify supremal models. The work is motivated by the exercise of unifying cluster expansion models – characterized by Π matrices – for two binary alloys that share one atomic species to form a model for the ternary alloy. The result is the Supremal Π Algorithm, a systematic unification algorithm that relies on an MBAM-informed understanding of models and on the singular value decomposition. The algorithm yields ΠΛ, a Π matrix for the unified cluster expansion model. The algorithm also enables construction and investigation of these unified models in polynomial time, achieving a combinatorial reduction in computational time over the aforementioned previous work.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Physics and Astronomy

Rights

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