Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2008.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2009
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| Online Access: | http://hdl.handle.net/1721.1/44383 |
| _version_ | 1811080864686145536 |
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| author | Okan, Osman Burak |
| author2 | Gerbrand Ceder. |
| author_facet | Gerbrand Ceder. Okan, Osman Burak |
| author_sort | Okan, Osman Burak |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2008. |
| first_indexed | 2024-09-23T11:38:08Z |
| format | Thesis |
| id | mit-1721.1/44383 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:38:08Z |
| publishDate | 2009 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/443832019-04-12T09:52:47Z Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians Okan, Osman Burak Gerbrand Ceder. Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. Materials Science and Engineering. Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2008. Includes bibliographical references (p. 46-48). We present a general outline for automating cluster expansions of configurational energetics in systems with crystallographic order and well defined space group symmetry. The method presented herein combines constrained optimization techniques of positive-definitive quadratic forms with the mathematical tool of Tikhonov regularization (kernel smoothing) for automated expansions of an arbitrary general physical property without compromising the underlying physics. Throughout the thesis we treat formation energy as the fundamental physical observable to expand on since the predominant application of cluster expansions is the extraction of robust approximations for configurational energetics in alloys and oxides. We therefore present the implementational aspects of the novel algorithmic route on a challenging material system NaxCoO2 and reconstruct the corresponding GGA ground state line with arbitrary precision in the formation energy-configuration space. The mathematical arguments and proofs, although discussed for cases with arbitrary spin assignments and multiple candidate species for single site occupancy, are eventually formulated and illustrated for binary systems. Various numerical challanges and the way they are resolved in the framework of kernel smoothing are addressed in detail as well. However, the applicability of the procedure described herein is more universal and can be tailored to probe different observables without resorting to modifications in the algorithmic implementation or the fundemantal mathematical construction. The effectiveness in recovering correct physics shall than be solely tied to the presence of superposable nature (of the physical property of interest) of local atomic configurations or lackthereof. by Osman Burak Okan. S.M. 2009-01-30T16:39:45Z 2009-01-30T16:39:45Z 2008 2008 Thesis http://hdl.handle.net/1721.1/44383 277139570 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 48 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Materials Science and Engineering. Okan, Osman Burak Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians |
| title | Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians |
| title_full | Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians |
| title_fullStr | Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians |
| title_full_unstemmed | Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians |
| title_short | Merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice Hamiltonians |
| title_sort | merging quadratic programming with kernel smoothing for automated cluster expansions of complex lattice hamiltonians |
| topic | Materials Science and Engineering. |
| url | http://hdl.handle.net/1721.1/44383 |
| work_keys_str_mv | AT okanosmanburak mergingquadraticprogrammingwithkernelsmoothingforautomatedclusterexpansionsofcomplexlatticehamiltonians |