Projects per year
Abstract
This thesis presents a reformulation of existing problems in materials science in terms of wellknown methods from applied mathematics: graph theory, computational geometry, and mixed integer programming.
The centrosymmetry parameter is reformulated as a graph matching problem, and resolves the inconsistencies in the existing calculation methods as a consequence. By formulating the distance function of lattices as a bipartite graph matching problem, it is shown that the similarity between crystal lattices (root mean square distance, RMSD) can be calculated in polynomial time, which improves upon the existing factorialtime bound. This method is subsequently extended to twodimensional monolayers.
A method is presented for the identication of ordered crystalline phases in molecular dynamics simulations. A robust classication is obtained by the use of template matching, also formulated as a bipartite matching problem on geometric graphs. This method is adapted for twodimensional materials, in order that e.g. defect structures in polycrystalline graphene can be studied.
Matrix decompositions are used to develop a geometric lattice matching algorithm, which can exhaustively identify all lowstrain interfaces. The stable, lowenergy interfaces which are found as a result are intended for use in the design and construction of topological superconductors, which have important applications in quantum computing.
Cluster expansion models are used to nd groundstate structures in goldsilver nanoparticles, which are used in a variety of catalysis processes. In addition to this concrete application, theoretical methods are developed for the optimal construction of cluster expansion models, the exact determination of ground states in a large model, and the exhaustive determination of all possible ground states in a small model.
Lastly, a method for nearlyoptimal sampling of orientations is presented. Whilst this has many applications in science and engineering, the usecase described here is the indexing of diffraction patterns for experimental materials characterization. Signicantly improved sampling is achieved by applying methods from computational geometry.
The centrosymmetry parameter is reformulated as a graph matching problem, and resolves the inconsistencies in the existing calculation methods as a consequence. By formulating the distance function of lattices as a bipartite graph matching problem, it is shown that the similarity between crystal lattices (root mean square distance, RMSD) can be calculated in polynomial time, which improves upon the existing factorialtime bound. This method is subsequently extended to twodimensional monolayers.
A method is presented for the identication of ordered crystalline phases in molecular dynamics simulations. A robust classication is obtained by the use of template matching, also formulated as a bipartite matching problem on geometric graphs. This method is adapted for twodimensional materials, in order that e.g. defect structures in polycrystalline graphene can be studied.
Matrix decompositions are used to develop a geometric lattice matching algorithm, which can exhaustively identify all lowstrain interfaces. The stable, lowenergy interfaces which are found as a result are intended for use in the design and construction of topological superconductors, which have important applications in quantum computing.
Cluster expansion models are used to nd groundstate structures in goldsilver nanoparticles, which are used in a variety of catalysis processes. In addition to this concrete application, theoretical methods are developed for the optimal construction of cluster expansion models, the exact determination of ground states in a large model, and the exhaustive determination of all possible ground states in a small model.
Lastly, a method for nearlyoptimal sampling of orientations is presented. Whilst this has many applications in science and engineering, the usecase described here is the indexing of diffraction patterns for experimental materials characterization. Signicantly improved sampling is achieved by applying methods from computational geometry.
Original language  English 

Publisher  Department of Physics, Technical University of Denmark 

Number of pages  151 
Publication status  Published  2017 
Fingerprint
Dive into the research topics of 'Structural Analysis Algorithms for Nanomaterials'. Together they form a unique fingerprint.Projects
 1 Finished

Characterization of Nanomaterials with Experimental Measurements and Atomistic Simulations
Larsen, P. M., Schiøtz, J., Thygesen, K. S., Goedecker, S., Ferrando, R. & Schmidt, S.
Technical University of Denmark
01/09/2014 → 15/11/2017
Project: PhD