Skip to main content
Article thumbnail
Location of Repository

An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects

By Keith R. Daly, Giampaolo D'Alessandro and Malgosia Kaczmarek

Abstract

We develop a fast and accurate approximation of the normally stiff equations which minimize the Landau–de Gennes free energy of a nematic liquid crystal. The resulting equations are suitable for all configurations in which defects are not present, making them ideal for device simulation. Specifically they offer an increase in computational efficiency by a factor of 100 while maintaining an error of order $(10^{-4})$ when compared to the full stiff equations. As this approximation is based on a $\mathcal{Q}$-tensor formalism, the sign reversal symmetry of the liquid crystal is respected. In this paper we derive these equations for a simple two-dimensional case, where the director is restricted to a plane, and also for the full three-dimensional case. An approximation of the error in the perturbation scheme is derived in terms of the first order correction, and a comparison to the full stiff equations is give

Topics: QA, QC
Year: 2010
OAI identifier: oai:eprints.soton.ac.uk:164053
Provided by: e-Prints Soton

Suggested articles

Citations

  1. (1981). A discussion of symmetry and symmetry breaking,i n Singularities, doi
  2. (1995). Alignment tensor versus director: Description of defects in nematic liquid crystals, doi
  3. (1987). An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals, doi
  4. (2005). Control of topological defects in microstructured liquid crystal cells, doi
  5. (1994). Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator, doi
  6. (2010). Equilibrium order parameters of liquid crystals in the Landau-De Gennes theory, doi
  7. (2000). Fine structure of defects in radial nematic droplets,P h y s . doi
  8. (2006). Finite-element modeling of liquidcrystal hydrodynamics with a variable degree of order, doi
  9. (1986). Free energies in the Landau and molecular field approaches, doi
  10. Homepage of the Defect Free Q-Tensor Approximation Code,
  11. (2003). Hybrid organic-inorganic photorefractives, doi
  12. (1989). Integrity basis approach to the elastic free energy functional of liquid crystals, doi
  13. (2007). Liquid Crystals, Wiley Ser. Pure Appl. Optics, doi
  14. (1990). Liquid Crystals: Applications and Uses, World Scientific, doi
  15. (1962). Mathematical Theory of Elastic Equilibrium (Recent Results), doi
  16. (2007). Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau–de Gennes theory, doi
  17. (1999). Multidimensional director modeling using the Q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes, doi
  18. (1974). On Signorini’s perturbation method in finite elasticity, doi
  19. (1958). On the theory of liquid crystals, doi
  20. (2009). Regime independent coupled-wave equations in anisotropic photorefractive media, doi
  21. (2000). Spectral Methods in MATLAB, SIAM, doi
  22. (1930). Sulle deformazioni termoelastiche finite,
  23. (1983). Symmetry and bifurcation in three-dimensional elasticity. doi
  24. (1985). T h o m p s o n ,Z .U .A .W a r s i ,a n dC .W .M a s t i n , Numerical Grid Generation: Foundations and Applications, North–Holland,
  25. (1991). The Signorini perturbation scheme in an abstract setting,P r o c .R o y . doi
  26. (1933). The theory of liquid crystals, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.