2026-09-20T11:18:46Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/82357 2023-07-11 col_2142_5131 col_2142_11615 com_2142_5130 com_2142_9130 com_2142_8903

Nikolaos Sahinidis Vaia, Anastasia 2015-09-25T20:43:17Z 2015-09-25T20:43:17Z 10000-01-01 2003 2003 "Finally, the last part of the thesis considers the ""phase problem"" in X-ray crystallography. In particular, we address the problem of estimating the three-dimensional atomic positions of crystal structures from diffraction measurements alone. Starting from the ""minimal principle"" model, we develop novel optimization formulations and algorithms that exploit the special model structure of the problem. For the case of centrosymmetric structures, we first formulate the problem as a 0--1 linear programming problem and suggest a branch-and-bound algorithm for solving it. Based on empirical observations regarding the nature of the solutions of this model, we then propose to solve it through a system of linear equations for which we develop a fast Gaussian elimination algorithm. For noncentrosymmetric structures, we reduce the phase problem to a mixed-integer quadratic problem and utilize a branch-and-bound algorithm for its solution." Made available in DSpace on 2015-09-25T20:43:17Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3101985.pdf: 5770289 bytes, checksum: 0f0b89123e47f9a9a40bb2838a73c14e (MD5) Previous issue date: 2003 Embargo set by: Seth Robbins for item 83638 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 136 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003. http://hdl.handle.net/2142/82357 (MiAaPQ)AAI3101985 eng Engineering, Chemical Global Optimization in Least Squares Problems in FTIR Spectroscopy and X -Ray Crystallography text Chemical and Biomolecular Engineering Chemical and Biomolecular Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.