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Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries

  • Maher MoakherEmail author
  • Peter J. Basser
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

In this paper we give closed-form expressions of the orientation tensors up to the order four associated with some axially-symmetric orientation distribution functions (ODF), including the well-known von Mises-Fisher, Watson, and de la Vallée Poussin ODFs. Each is characterized by a mean direction and a concentration parameter. Then, we use these elementary ODFs as building blocks to construct new ones with a specified material symmetry and derive the corresponding orientation tensors. For a general ODF we present a systematic way of calculating the corresponding orientation tensors from certain coefficients of the expansion of the ODF in spherical harmonics.

Keywords

Orientation Distribution Function Concentration Parameter Modal Vector Fabric Tensor Orientation Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at TunisUniversity of Tunis El ManarTunis-BelvédèreTunisia
  2. 2.Section on Tissue Biophysics & Biomimetics, PPITS, NICHDNational Institutes of HealthBethesdaUSA

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