Diffusion Fundamentals (E-Journal)
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Unravelling intermittent features in single particle trajectories by a local convex hull method
Get PDFSemi-analytical solutions of boundary value problems for the stationary diffusion equation in three-dimensional canonical domains
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Fast and Slow, Restricted or Free, Correlated or Random: The Complex World of Li Diffusion as Seen by Solid State NMR
Get PDFChemical Kinetic Processes in Oxides Studied by Relaxation Experiments of Optical Absorption and Electrical Conductivity
Get PDF7Li Ion Diffusion in Isotope-diluted Glassy Li2Si3O7 – The Generation of pure Spin-3/2 Spin-alignment NMR Echoes
Get PDFWhat are, and what are not, Inverse Laplace Transforms
Get PDFTime-domain NMR, in one and higher dimensionalities, makes routine use of inversion algorithms to generate results called \T2-distributions\u27 or joint distributions in two (or higher) dimensions of other NMR parameters, T1, diffusivity D, pore size a, etc. These are frequently referred to as \Inverse Laplace Transforms\u27 although the standard inversion of the Laplace Transform long-established in many textbooks of mathematical physics does not perform (and cannot perform) the calculation of such distributions. The operations performed in the estimation of a \T2-distribution\u27 are the estimation of solutions to a Fredholm Integral Equation (of the First Kind), a different and more general object whose discretization results in a standard problem in linear algebra, albeit suffering from well-known problems of ill-conditioning and computational limits for large problem sizes. The Fredholm Integral Equation is not restricted to exponential kernels; the same solution algorithms can be used with kernels of completely different form. On the other hand, (true) Inverse Laplace Transforms, treated analytically, can be of real utility in solving the diffusion problems highly relevant in the subject of NMR in porous media
FID NMR Studies of Suspensions and Porous Media
Get PDFNuclear Magnetic Resonance is used for the determination of the properties of porous media in Geophysics and oil exploration. As it stands, there is a challenge in understanding the connection between the times measured in Free Induction Decay Nuclear Magnetic Resonance experiments and the shape of samples. In this work, suspensions and watersaturated densely-packed porous media with the volume fraction of the glass solid phase in the range from 10–4 to ∼1 are found to exhibit FID decay rates proportional to the square root of the volume fraction of the solid phase of the samples. A model of spheres in liquid is proposed for the description of such behavior