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Tournier, J. D., Calamante, F., Gadian, D. G. & Connelly, A. Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution.
The orientation, density, and alignment of collagen fibrils were mapped across six different valves.
In addition to axonal orientation, density and length distribution of the regenerated axons into the polymer scaffold have been measured.
Our spherical deconvolution approach completely parameterizes the fiber orientation density by a finite mixture of Bingham distributions.
Spherical deconvolution, in contrast, very economically produces a fiber orientation density function (fODF) without any explicit model assumptions.
However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed.
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After plane strain flange deformation during the early stages of deep drawing, the orientation densities increase around the P {011}〈111〉 and Goss {011}〈100〉 components.
In fact, the textures formed by deformations up to the desired strain of −1.0 have high orientation densities around {0 0 1}〈1 1 0〉 in accordance with the proposed mechanism.
Textures in route BC show orientation concentrations along fibers that consist of the {1 1 1}θ and 〈1 1 0〉θ partial fibers, yet the locations and orientation densities of the main texture components vary significantly with pass number.
They are quick and efficient and give reasonable orientation-density distribution functions for a relatively small number of the integration grid points.
The results from the CP-FEM simulations in the form of orientation-resolved dislocation densities and the orientation and density of recrystallization nuclei extracted from SEM/EBSD measurements were directly transferred into a 3D CA for the simulation of primary recrystallization.
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