scholarly journals Optimized rectification of fiber orientation density function

2020 ◽  
Vol 85 (1) ◽  
pp. 444-455
Author(s):  
Hunter G. Moss ◽  
Jens H. Jensen
Keyword(s):  
Density Function ◽  
Fiber Orientation ◽  
Orientation Density

Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers

2007 ◽  
Vol 40 (3) ◽  
pp. 570-579 ◽  
Author(s):  
Helmut Schaeben ◽  
Ralf Hielscher ◽  
Jean-Jacques Fundenberger ◽  
Daniel Potts ◽  
Jürgen Prestin
Keyword(s):  
Mathematical Method ◽  
Adaptive Control ◽  
Probability Density Function ◽  
Density Function ◽  
Crystallographic Orientation ◽  
Uniform Grid ◽  
Successive Refinement ◽  
Orientation Density ◽  
Refined Grid ◽  
Fast Inversion

A novel control of a texture goniometer, which depends on the texture being measured itself, is suggested. In particular, it is suggested that the obsolete control with constant step sizes in both angles is replaced by an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid, where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. The prerequisites of this automated adaptive control is the fast inversion of pole intensities to orientation probabilities in the course of the measurements, and a mathematical method of inversion that does not require a raster of constant step sizes and applies to sharp textures.

scholarly journals The de la Vallée Poussin Standard Orientation Density Function

1999 ◽  
Vol 33 (1-4) ◽  
pp. 365-373 ◽  
Author(s):  
H. Schaeben
Keyword(s):  
Density Function ◽  
Series Expansion ◽  
Harmonic Series ◽  
Exact Representation ◽  
Standard Orientation ◽  
Orientation Density ◽  
De La Vallée Poussin

The de la Vallée Poussin standard orientation density function νκ(ω)=C(κ)cos⁡2κ(ω/2) is discussed with emphasis on the finiteness of its harmonic series expansion which, advantageously distinguishes it from other known standard functions. Given its halfwidth, the de la Vallée Poussin standard orientation density function allows, for example, to tabulate the degree of series expansion into harmonics required for its exact representation.

Orientation Analysis

2021 ◽  
Vol 1016 ◽  
pp. 605-610
Author(s):  
Janos Imhof
Keyword(s):  
Density Function ◽  
Initial Function ◽  
Minimum Principle ◽  
Density Functions ◽  
Pole Density ◽  
Orientation Analysis ◽  
Euler Space ◽  
Orientation Density ◽  
Basic Concepts ◽  
The Relationship

Simple figures illustrate the basic concepts: orientation, Euler angles, Euler space, orientation density function, pole density function. The iteration that decisively influenced the development of orientation analysis follows directly from the relationship between the two density functions. The minimum principle defines the initial function and the structure of the iteration. Using model orientation density function, we prove that this kind of orientation analysis is extremely effective.

Orientation Density Function of Ply yarn

2010 ◽  
Vol 80 (15) ◽  
pp. 1550-1556 ◽  
Author(s):  
Boong Soo Jeon ◽  
Young Jun Kim
Keyword(s):  
Density Function ◽  
Orientation Density
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