Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media
Momot, Konstantin I., Powell, Sean K., & Tourell, Monique C. (2015) Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media. Microporous and Mesoporous Materials, 205, pp. 24-30.
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Magnetic resonance is a well-established tool for structural characterisation of porous media. Features of pore-space morphology can be inferred from NMR diffusion-diffraction plots or the time-dependence of the apparent diffusion coefficient. Diffusion NMR signal attenuation can be computed from the restricted diffusion propagator, which describes the distribution of diffusing particles for a given starting position and diffusion time.
We present two techniques for efficient evaluation of restricted diffusion propagators for use in NMR porous-media characterisation. The first is the Lattice Path Count (LPC). Its physical essence is that the restricted diffusion propagator connecting points A and B in time t is proportional to the number of distinct length-t paths from A to B. By using a discrete lattice, the number of such paths can be counted exactly. The second technique is the Markov transition matrix (MTM). The matrix represents the probabilities of jumps between every pair of lattice nodes within a single timestep. The propagator for an arbitrary diffusion time can be calculated as the appropriate matrix power. For periodic geometries, the transition matrix needs to be defined only for a single unit cell. This makes MTM ideally suited for periodic systems.
Both LPC and MTM are closely related to existing computational techniques: LPC, to combinatorial techniques; and MTM, to the Fokker-Planck master equation. The relationship between LPC, MTM and other computational techniques is briefly discussed in the paper. Both LPC and MTM perform favourably compared to Monte Carlo sampling, yielding highly accurate and almost noiseless restricted diffusion propagators. Initial tests indicate that their computational performance is comparable to that of finite element methods. Both LPC and MTM can be applied to complicated pore-space geometries with no analytic solution. We discuss the new methods in the context of diffusion propagator calculation in porous materials and model biological tissues.
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|Item Type:||Journal Article|
|Keywords:||diffusion-sensitive Nuclear Magnetic Resonance spectroscopy, restricted diffusion, finite element methods, Lattice Path Count, Markov Transition Matrix|
|Subjects:||Australian and New Zealand Standard Research Classification > PHYSICAL SCIENCES (020000) > OTHER PHYSICAL SCIENCES (029900) > Complex Physical Systems (029902)|
|Divisions:||Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > Institutes > Institute of Health and Biomedical Innovation
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||2014 Elsevier Inc|
|Copyright Statement:||This is the author’s version of a work that was accepted for publication in Microporous and Mesoporous Materials. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Microporous and Mesoporous Materials, [VOL 205, (2015)] DOI: 10.1016/j.micromeso.2014.08.037|
|Deposited On:||06 Feb 2015 00:45|
|Last Modified:||27 Feb 2015 06:01|
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