Fitting alignment tensor components to experimental RDCs, CSAs and RQCs

2015 ◽  
Vol 62 (1) ◽  
pp. 25-29 ◽  
Author(s):  
Lukas N. Wirz ◽  
Jane R. Allison
Keyword(s):  
Alignment Tensor

Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor

2014 ◽  
Vol 1651 ◽  
Author(s):  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Evolution Equations ◽  
Continuum Theory ◽  
Orientation Distribution ◽  
Line Length ◽  
Second Order ◽  
Dislocation Dynamics ◽  
Alignment Tensor ◽  
Length Changes ◽  
Edge Dislocations

ABSTRACTIn the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

scholarly journals Derivation and Application of an Algorithm for the Numerical Calculation of the Local Orientation of Nematic Liquid Crystals

1989 ◽  
Vol 44 (8) ◽  
pp. 693-703 ◽  
Author(s):  
A. Kilian ◽  
S. Hess
Keyword(s):  
Numerical Calculation ◽  
Liquid Crystals ◽  
Symmetry Property ◽  
Two Dimensional ◽  
Alignment Tensor ◽  
Dimensional Problem ◽  
Local Orientation ◽  
Static Behavior ◽  
Relaxation Equation ◽  
Director Field

Abstract Starting from a relaxation equation for the alignment tensor, an algorithm is derived which allows the numerical calculation of the dynamic and static behavior of the director field n with the correct nematic symmetry property, where n and - n are equivalent. As a first application, a two-dimensional problem is treated where the typical nematic defects with half-integer winding numbers only occur when the algorithm with the correct nematic symmetry property is used. Furthermore, the method is applied to the static and dynamic behavior of a Frederiks cell with strong and weak anchoring.

Determination of alignment tensor components for the H(2p) charge exchange excitation in proton-argon collisions

1982 ◽  
Vol 304 (1) ◽  
pp. 63-68 ◽  
Author(s):  
R. Hippler ◽  
G. Malunat ◽  
M. Faust ◽  
H. Kleinpoppen ◽  
H. O. Lutz
Keyword(s):  
Charge Exchange ◽  
Alignment Tensor

scholarly journals Characterization and Alignment of Carbon Nanofibers under Shear Force in Microchannel

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Jinshan Yang ◽  
Shaoming Dong ◽  
David Webster ◽  
John Gilmore ◽  
Chengying Xu
Keyword(s):  
Carbon Nanofibers ◽  
Shear Force ◽  
Major Axis ◽  
Second Order ◽  
Alignment Tensor ◽  
Shear Forces ◽  
Sem Images ◽  
Significant Alignment ◽  
Novel Method ◽  
High Degree

This work presents a novel method to align CNFs by using shear forces in microchannels. Effect of two different microchannel sizes (1 mm × 0.1 mm and 1 mm × 0.2 mm) on CNFs alignment is investigated. SEM images of CNFs preform display significant alignment by both microchannels, which can be interpreted using a second-order alignment tensor and a manual angle meter. In the second-order alignment tensor description, an elongated ellipse can signify high degree of alignment in the direction of the major axis. When the microchannel size is 1 mm × 0.2 mm, the lengths of major and minor axes of the ellipse are 0.982 to 0.018. An angle meter manually shows that 85% of the CNFs are aligned in the direction between 60° and 90° when the microchannel is 1 mm × 0.2 mm. Both methods can demonstrate that better alignment of CNFs can be obtained using the 1 mm × 0.2 mm microchannel.

scholarly journals Macroscopic Internal Variables and Mesoscopic Theory: A Comparison considering Liquid Crystals

2017 ◽  
Author(s):  
Christina Papenfuss ◽  
Wolfgang Muschik
Keyword(s):  
Distribution Function ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
State Space ◽  
Internal Variable ◽  
Internal Variables ◽  
Alignment Tensor ◽  
Balance Equations ◽  
Flexible Fibers ◽  
Mesoscopic Theory

Internal and mesoscopic variables differ from each other fundamentally: both are state space variables, but mesoscopic variables are additional equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers.

Sign in / Sign up

Export Citation Format

Share Document