Skip to main content
SpringerLink
Log in

Tensor Visualization and Defect Detection for Nematic Liquid Crystals using Shape Characteristics

  • Chapter
Book cover Visualization and Processing of Tensor Fields

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Summary

Two alternate sets of tensor shape characteristics are introduced for the study of nematic liquid crystals, a little studied problem in tensor visualization. One set of characteristics are based on the physics of the liquid crystal system (a real, symmetric, traceless tensor); the other set is an application of the well known Westin DT-MRI shape characteristics. These shape metrics are used both for direct tensor visualization and for detection of defects within the liquid crystal matrix.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. J. Collings. Liquid Crystals: Nature’s Delicate Phase of Matter, 2nd. edition. Priceton University Press, Princeton, NJ, 2002.

    Google Scholar 

  2. P. K. Mukherjee. Critical behavior of uniaxial-biaxial nematic phase transition. The Journal of Chemical Physics, 109(7):2941–2946, 1998.

    Article  Google Scholar 

  3. I. Dierking. Textures of Liquid Crystals. Wiley, New York, 2003.

    Book  Google Scholar 

  4. N. Morrtram and C. Newton. Introduction to Q-tensor theory. Technical Report, Department of Mathematics, University of Strathclyde, 2004.

    Google Scholar 

  5. P. G. de Gennes. The Physics of Liquid Crystals. Clarendon, Oxford, 1974.

    Google Scholar 

  6. R. J. Low. Measuring order and biaxiality. European Journal of Physics, 23:111–117, 2002.

    Article  MATH  Google Scholar 

  7. C. Zannoni. Distribution functions and order parameters. In G.R. Luckhurst and G.W. Gray, editors, The Molecular Physics of Liquid Crystals, chapter 3, Academic Press, London, pp. 51–83, 1979.

    Google Scholar 

  8. C.F. Westin, S. Peled, H. Gudbjartsson, R. Kikinis, and F. A. Jolesz. Geometrical diffusion measures for MRI from tensor basis analysis. In Proceedings of the Fifth Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM ’97) , Vancouver Canada, p. 1742, 1997.

    Google Scholar 

  9. G. Kindlmann. Visualization and Analysis of Diffusion Tensor Fields. PhD thesis, University of Utah, 2004.

    Google Scholar 

  10. T.J. Jankun-Kelly and K. Mehta. Superellipsoid-based, real symmetric traceless tensor glyphs motivated by nematic liquid crystal alignment visualization. IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization/Information Visualization 2006) , 12(5):1197–1204, 2006.

    Article  Google Scholar 

  11. V. A. Slavin, R. A. Pelcovits, G. Loriot, A. Callan-Jones, and D. H. Laidlaw. Techniques for the visualization of topological defect behavior in nematic liquid crystals. IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization/Information Visualization 2006) , 12(5):1323–1328, 2006.

    Article  Google Scholar 

  12. A. C. Callan-Jones, R. A. Pelcovits, V. Slavin, S. Zhang, D. H. Laidlaw, and G. B. Loriot. Simulation and visualization of topological defects in nematic liquid crystals. Physical Review E, 74(6), 2006.

    Google Scholar 

  13. S. Zhang, D. H. Laidlaw, and G. L. Kindlmann. Diffusion tensor MRI visualization. In C. D. Hansen and C. R. Johnson, editors, The Visualization Handbook, chapter 16, Elsevier Academic Press, Amsterdam, pp. 327–340, 2004.

    Google Scholar 

  14. J. E. Anderson, P. Watson, and P. J. Bos. Comparisons of the vector method and tensor method for simulating liquid crystal devices. Liquid Crystals, 28:109–115, 2001.

    Article  Google Scholar 

  15. A. Sonnet, A. Kilian, and S. Hess. Alignment tensor versus director: Description of defects in nematic liquid crystals. Physical Review E, 52:718–722, 1995.

    Article  Google Scholar 

  16. M. Gregory Forest, Q. Wang, and H. Zhou. Methods for the exact construction of mesoscale spatial structures in liquid crystal polymers. Physica D, 152–153:288–309, 2001.

    Article  Google Scholar 

  17. G. L. Kindlmann. Superquadric tensor glyphs. In O. Deussen, C. Hansen, D. A. Keim, and D. Saupe, editors, Proceedings of the Eurographics/IEEE VGTC Symposium on Visualization (VisSym ’04) , pp. 147–154, 2004.

    Google Scholar 

  18. A. H. Barr. Superquadrics and angle-preserving transformations. IEEE Computer Graphics and Applications, 1(1):11–22, 1981.

    Article  Google Scholar 

  19. C. D. Shaw, D. S. Ebert, J. M. Kukla, A. Zwa, I. Soboroff, and D. Aaron Roberts. Data visualization using automatic, perceptually-motivated shapes. In Proceedings of Visual Data Exploration and Analysis. SPIE, 11 April 1998.

    Google Scholar 

  20. C. D. Shaw, J. Hall, C. Blahut, D. S. Ebert, and D. Aaron Roberts. Using shape to visualize multivariate data. In Proceedings of the Workshop on New Paradigms in Information Visualization and Manipulation (NPIVM-99) , ACM Press, New York, pp. 17–20, 1999.

    Google Scholar 

  21. R. L. Burden and J. Douglas Faires. Numerical Analysis, chapter 1, PWS Publishing Co., pp. 17–18, 1994.

    Google Scholar 

  22. H.Wu and R. Mohanraj. Computational simulations for study of a liquidcrystal- based sensor system. In J. Graef, H. Lim, R. Shivaji, B. Soni, and J. Zhu, editors, Proceedings of the Sixth Mississippi State-UAB Conference on Differential Equations and Compuational Simulations, May 2005.

    Google Scholar 

  23. T. Tsuji and A. D. Rey. Orientation mode selection mechanisms for sheared nematic liquid crystalline materials. Physical Review E, 57(5):5609–5625, 1998.

    Article  Google Scholar 

  24. J. L. Billeter, A. M. Smondyrev, G. B. Loriot, and R. A. Pelcovits. Phaseordering dynamics of the Gay-Berne nematic liquid crystal. Physical Review E, 60, 1999.

    Google Scholar 

  25. J. G. Gay and B. J. Berne. Modification of the overlap potential to mimic a linear site-site potential. Journal of Chemical Physics, 74(6):3316–3319, 1981.

    Article  Google Scholar 

  26. M. Zapotocky, P. M. Goldbart, and N. Goldenfeld. Kinetics of phase ordering in uniaxial and biaxial nematic films. Physical Review E, 51(2):1216–1235, 1995.

    Article  Google Scholar 

  27. C. Chiccoli, O. D. Lavrentovich, P. Pasini1, and C. Zannoni. Monte carlo simulations of stable point defects in hybrid nematic films. Physical Review Letters, 79(22):4401–4404, 1997.

    Article  Google Scholar 

  28. K. Mehta and T. J. Jankun-Kelly. Detection and visualization of defects in 3d unstructed models of nematic liquid crystals. IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization/ Information Visualization 2006) , 12(5):1045–1052, 2006.

    Article  Google Scholar 

  29. S. Zhang, C. Demiralp, and D. H. Laidlaw. Visualizing diffusion tensor MR images using streamtubes and streamsurfaces. IEEE Transactions on Visualization and Computer Graphics, 9(4):454–462, 2003.

    Article  Google Scholar 

  30. C. Upson, T. Faulhaber Jr., D. Kamins, D. H. Laidlaw, D. Schlegel, J. Vroom, R. Gurwitz, and A. van Dam. The application visualization system: A computational e nvironment for scientific visualization. Computer Graphics and Applications, 9(4):30–42, 1989.

    Article  Google Scholar 

  31. N. Schopohl and T. J. Sluckin. Erratum: Defect core structure in nematic liquid crystals [Physical Review Letters 59, 2582 (1987)]. Physical Review Letters, 60:755, 1988.

    Article  Google Scholar 

  32. M. P. Allen, M. A. Warren, M. R. Wilson, A. Sauron, and W. Smith. Molecular dynamics calculation of elastic constants in Gay-Berne nematic liquid crystals. Journal of Chemical Physics, 105:2850–2858, 1996.

    Article  Google Scholar 

Download references

Acknowledgments

We thank Ketan Mehta for his work on unstructured grid-based disclination detection and Gordon Kindlmann for our in-depth discussions. Rajendran Mohanraj and Huangli Wu, formerly of the Mississippi State SimCenter, provided the human Ig anitibody simulation data. This work was partially funded through the National Science Foundation EPSCoR program via award No. 0132618.

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Bagley College of Engineering, Mississippi State University, Mississippi State, MS, USA

    T. J. Jankun-Kelly & Song Zhang

  2. Institut Curie, UMR CNRS 168, 26rue dUlm, 75248, Paris Cedex 05, France

    A. C. Callan-Jones

  3. Department of Physics, Brown University, Providence, RI, USA

    Robert A. Pelcovits

  4. Department of Computer Science, Brown University, Providence, RI, USA

    V. A. Slavin & David H. Laidlaw

Authors
  1. T. J. Jankun-Kelly
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Song Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. C. Callan-Jones
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Robert A. Pelcovits
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. V. A. Slavin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. David H. Laidlaw
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Brown University, Box 1910, 02912, Providence, RI, USA

    David Laidlaw

  2. Faculty of Mathematics and Computer Science Mathematical Image Analysis Group, Saarland University, 66041, Saarbrücken, Germany

    Joachim Weickert

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Jankun-Kelly, T.J., Zhang, S., Callan-Jones, A.C., Pelcovits, R.A., Slavin, V.A., Laidlaw, D.H. (2009). Tensor Visualization and Defect Detection for Nematic Liquid Crystals using Shape Characteristics. In: Laidlaw, D., Weickert, J. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88378-4_11

Download citation

Publish with us

Policies and ethics

Search

Navigation