Advanced optimal control methods for spin systems
Advanced optimal control methods for spin systems
Work within this thesis advances optimal control algorithms for application to magnetic resonance systems. Specifically, presenting a quadratically convergent version of the gradient ascent pulse engineering method. The work is formulated in a superoperator representation of the Liouville-von Neumann equation.
A Newton-grape method is developed using efficient calculation of analytical second directional derivatives. The method is developed to scale with the same complexity as methods that use only first directional derivatives. Algorithms to ensure a well-conditioned and positive definite matrix of second directional derivatives are used so the sufficient conditions of gradient-based numerical optimisation are met.
A number of applications of optimal control in magnetic resonance are investigated: solid-state nuclear magnetic resonance, magnetisation-to-singlet pulses, and electron spin resonance experiments.
University of Southampton
Goodwin, David L.
349b642d-bc15-4a8d-b1d7-98691a39e069
October 2017
Goodwin, David L.
349b642d-bc15-4a8d-b1d7-98691a39e069
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065
Goodwin, David L.
(2017)
Advanced optimal control methods for spin systems.
University of Southampton, Doctoral Thesis, 250pp.
Record type:
Thesis
(Doctoral)
Abstract
Work within this thesis advances optimal control algorithms for application to magnetic resonance systems. Specifically, presenting a quadratically convergent version of the gradient ascent pulse engineering method. The work is formulated in a superoperator representation of the Liouville-von Neumann equation.
A Newton-grape method is developed using efficient calculation of analytical second directional derivatives. The method is developed to scale with the same complexity as methods that use only first directional derivatives. Algorithms to ensure a well-conditioned and positive definite matrix of second directional derivatives are used so the sufficient conditions of gradient-based numerical optimisation are met.
A number of applications of optimal control in magnetic resonance are investigated: solid-state nuclear magnetic resonance, magnetisation-to-singlet pulses, and electron spin resonance experiments.
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PhD Thesis 2017
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Published date: October 2017
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Local EPrints ID: 423078
URI: http://eprints.soton.ac.uk/id/eprint/423078
PURE UUID: 00598d27-e067-49ef-b481-cfad52f0a790
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Date deposited: 13 Aug 2018 16:31
Last modified: 16 Mar 2024 04:11
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Author:
David L. Goodwin
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