scholarly journals Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials

1993 ◽  
Vol 21 (4) ◽  
pp. 233-250 ◽  
Author(s):  
David D. Sam ◽  
E. Turan Onat ◽  
Pavel I. Etingof ◽  
Brent L. Adams
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Measurement Data ◽  
Orientation Distribution ◽  
Harmonic Polynomials ◽  
Crystallite Orientation ◽  
Orientation Measurement ◽  
Three Dimensional Space

The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three-dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty-first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.

A software for diffraction stress factor calculations for textured materials

2012 ◽  
Vol 27 (2) ◽  
pp. 114-116 ◽  
Author(s):  
Thomas Gnäupel-Herold
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Elastic Constants ◽  
Orientation Distribution Function ◽  
Lattice Strain ◽  
Orientation Distribution ◽  
Crystallite Orientation ◽  
Interaction Models ◽  
Grain Interaction ◽  
Textured Materials

A software for the calculation of diffraction elastic constants (DEC) for materials both with and without preferred orientation was developed. All grain-interaction models that can use the crystallite orientation distribution function (ODF) are incorporated, including Kröner, Hill, inverse Kröner, and Reuss. The functions of the software include: reading the ODF in common textual formats, pole figure calculation, calculation of DEC for different (hkl,φ,ψ), calculation of anisotropic bulk constants from the ODF, calculation of macro-stress from lattice strain and vice versa, as well as mixture ratios of (hkl) of overlapped reflections in textured materials.

Orientation Distribution of Fiber Suspensions in Extensional Flow

2013 ◽  
Vol 785-786 ◽  
pp. 981-984 ◽  
Author(s):  
Zan Huang ◽  
Jin Ping Qu ◽  
Ji Wei Geng ◽  
Shu Feng Zhai ◽  
Shi Kui Jia
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Fiber Suspensions ◽  
Short Fibers ◽  
Fiber Orientation Distribution

An orientation distribution function is adopted to describe three-dimensional orientation distribution of short fibers suspensions in extensional flow. A mathematical model of evolution process on fiber orientation distribution function is established by analytical method. Numerical simulation is also used to describe two and three dimensional orientation distribution of fibers. Therefore, analytical solution of differential equation on forecast fiber orientation distribution is deduced.

ON THE DOI MODEL FOR THE SUSPENSIONS OF ROD-LIKE MOLECULES IN COMPRESSIBLE FLUIDS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250027 ◽  
Author(s):  
HANTAEK BAE ◽  
KONSTANTINA TRIVISA
Keyword(s):  
Dimensional Space ◽  
Initial Density ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Polymeric Fluids ◽  
Atmospheric Sciences ◽  
Practical Applications ◽  
Doi Model ◽  
Time Existence ◽  
Three Dimensional Space

Polymeric fluids arise in many practical applications in biotechnology, medicine, chemistry, industrial processes, and atmospheric sciences. In this paper, the Doi model for the suspensions of rod-like molecules in a compressible fluid is investigated. The model under consideration describes the interaction between the orientation of rod-like polymer molecules on the microscopic scale and the macroscopic properties of the fluid in which these molecules are contained. Prescribing arbitrarily the initial density of the fluid, the initial velocity, and the initial orientation distribution in suitable spaces, we establish the global-in-time existence of a weak solution to our model defined on a bounded domain in the three-dimensional space. The proof relies on the construction of an approximate sequence of solutions by introducing appropriate regularization and the establishment of compactness.

scholarly journals A Test of the Refinement Procedure for Determining the Crystallite Orientation Distribution: Polyethylene Terephthalate

Texture ◽  
1972 ◽  
Vol 1 (1) ◽  
pp. 9-16 ◽  
Author(s):  
W. R. Krigbaum ◽  
Anna Marie Harkins Vasek
Keyword(s):  
Distribution Function ◽  
Polyethylene Terephthalate ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Fiber Texture ◽  
Fiber Axis ◽  
Crystallite Orientation ◽  
Plane Normal ◽  
Pole Figures ◽  
Refinement Procedure

A test of the refinement procedure for improving the crystallite orientation distribution function is presented for a fiber texture sample of polyethylene terephthalate. This is a particularly difficult example because the triclinic unit cell offers no simplification due to symmetry, and the pole figures are sharply peaked. The analysis employed 17 observed pole figures and an additional 29 unobserved pole figures reconstructed from the crystallite orientation distribution function. After three cycles of refinement, in which the maximum value of the coefficient was increased from 6 to 16, the standard deviations, σq and σw, of the plane-normal and crystallite orientation distributions were reduced by about a factor of 3. The refined crystallite orientation distribution function indicates that the c-axis tends to align along the fiber axis for this polyethylene terephthalate sample.

On the Geometry of 3D Orientation Measurement Using a New Class of Wireless Angular Position Sensors

2003 ◽  
Author(s):  
Q. J. Ge ◽  
J. Rastegar ◽  
Carlos Pereira
Keyword(s):  
Energy Level ◽  
Wireless Sensors ◽  
Dimensional Space ◽  
Angular Position ◽  
Three Dimensional ◽  
Electromagnetic Energy ◽  
Orientation Measurement ◽  
New Class ◽  
Orientation Sensor ◽  
Three Dimensional Space

This paper deals with the geometric issues that arise in designing a system for measuring the orientation of an object in three dimensional space using a new class of wireless angular position sensors. The wireless sensors are waveguides that receive and record the electromagnetic energy emitted by a polarized RF source. The angular position of the waveguide relative to the source is indicated by the energy level. A system equipped with multiple waveguides is used as a 3D orientation sensor. This paper explores the geometry for orientation measurement using the system and provides the guidelines for sensor design.

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