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The proposed method shortens the diffusion time by applying a single refocused bipolar diffusion gradient on one side of a refocusing RF pulse, instead of a set of diffusion sensitizing gradients, separated by a refocusing RF pulse, while reducing the impact of magnetic field inhomogeneity by using a spin echo sequence.
The continuum mechanical approach for deriving the generalized equations of multicomponent diffusion in fluids is described here in detail, which is based on application of the principle of linear momentum balance to a species in a mixture, resulting in the complete set of diffusion driving forces.
Prediction accuracy in all tests is estimated using standard N-fold cross-validation, in which the set of diffusion events of interest is randomly partitioned into N subsets of equal size, and the A-EDT algorithm is successively "trained" on N−1 of the subsets and "tested" on the held-out subset in such a way that each of the N subsets is used as the test set exactly once.
The sensitive radiotracer experiments and the subsequent diffusion profile analysis resulted in a consistent set of diffusion data in the whole investigated temperature range with Arrhenius behavior for both the Ag nano-GB diffusion (D0gb=4.7×10−4 m2/s, Hgb=173 kJ/mol) as well as for the much faster inter-agglomerate interface diffusion (D0a=8.1×10−5 m2/s, Ha=91 kJ/mol).
The forward problem defined by the set of diffusion Eqs.
An entity then contains a set of diffusion landscapes composed of the diffusion landscapes of all the entity's child particles.
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Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints.
For each set of diffusion-weighted data, 7 volumes with no diffusion weighting (b0) were acquired.
This analysis used an independent data set of diffusion-weighted images (DWIs).
Across the 10 sites and 12 scanners, a standardized multiple modality high-resolution structural MRI protocol was implemented, involving 3D T1- and T2-weighted volumes and a set of diffusion-weighted scans.
The Co-rich part of the Co-Al-X (X = W, Mo, Nb, Ni, Ta) ternary systems is especially important and was thus investigated using two sets of diffusion multiples (Ni-Co-CoAl-Cr-Mo-Nb-Ta-W and Ni-Co-NiAl-Si-Zr).
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