Solving the generalized indirect Fourier transformation (GIFT) by Boltzmann simplex simulated annealing (BSSA)

Solving the generalized indirect Fourier transformation (GIFT) by Boltzmann simplex simulated... The structure of colloidal particles can be studied with small‐angle X‐ray and neutron scattering (SAXS and SANS). In the case of randomly oriented systems, the indirect Fourier transformation (IFT) is a well established technique for the calculation of model‐free real‐space information. Interaction leads to an overlap of inter‐ and intraparticle scattering effects, preventing most detailed interpretations. The recently developed generalized indirect Fourier transformation (GIFT) technique allows these effects to be separated by assuming various models for the interaction, i.e. the so‐called structure factors. The different analytical behaviour of these structure factors from that of the form factors, describing the intraparticle scattering, allows this separation. The mean‐deviation surface is defined by the quality of the fit for different parameter sets of the structure factor. Its global minimum represents the solution. The former non‐linear least‐squares approach has proved to be inefficient and not very reliable. In this paper, the incorporation of the completely different Boltzmann simplex simulated annealing (BSSA) algorithm for finding the global minimum of the hypersurface is presented. This new method increases not only the calculation speed but also the reliability of the evaluation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Crystallography Wiley

Solving the generalized indirect Fourier transformation (GIFT) by Boltzmann simplex simulated annealing (BSSA)

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Publisher
Wiley
Copyright
Copyright © 2000 Wiley Subscription Services, Inc., A Wiley Company
ISSN
1600-5767
eISSN
1600-5767
DOI
10.1107/S0021889800008372
Publisher site
See Article on Publisher Site

Abstract

The structure of colloidal particles can be studied with small‐angle X‐ray and neutron scattering (SAXS and SANS). In the case of randomly oriented systems, the indirect Fourier transformation (IFT) is a well established technique for the calculation of model‐free real‐space information. Interaction leads to an overlap of inter‐ and intraparticle scattering effects, preventing most detailed interpretations. The recently developed generalized indirect Fourier transformation (GIFT) technique allows these effects to be separated by assuming various models for the interaction, i.e. the so‐called structure factors. The different analytical behaviour of these structure factors from that of the form factors, describing the intraparticle scattering, allows this separation. The mean‐deviation surface is defined by the quality of the fit for different parameter sets of the structure factor. Its global minimum represents the solution. The former non‐linear least‐squares approach has proved to be inefficient and not very reliable. In this paper, the incorporation of the completely different Boltzmann simplex simulated annealing (BSSA) algorithm for finding the global minimum of the hypersurface is presented. This new method increases not only the calculation speed but also the reliability of the evaluation.

Journal

Journal of Applied CrystallographyWiley

Published: Oct 1, 2000

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