Exploring defects in nematic liquid crystal

1
Exploring Topological Defects in Nematic Liquid
Crystal KETAN MEHTA, Dr. T. J. JANKUN-KELLY Depart
ment of Computer Science and Engineering,
Mississippi State University
Motivation The study of topological defects in
nematic Liquid Crystal (LC) enables scientists to
predict the impurities or external contamination.
LC data consists of a complex time varying
tensor, vector and scalar data generated over
unstructured grid. Visualization (viz) research
is focused on finding novel techniques that will
enable scientists to explore massive data
interactively. LC simulation generates a huge
quantity of data and currently requires a lot of
preprocessing and filtering effort understand
data.
Visualization Current research focuses on
multiple level viz with FocusContext and various
filtering techniques. Research effort is
concentrated in finding efficient exploration and
visualization techniques for enabling real-time
interactive exploration and visualization of
tensor data sets.
Background Tensor visualization is an active
area of research due to the complexity of
handling and representing tensor data effectively
and efficiently. Different techniques like
stream-tubes, hyper-streamlines and
stream-surface have been developed to visualize
the tensor data. Glyph based rendering uses
super-quadrics and super-ellipsoids to capture
the scalar and tensor properties for a tensor
data point. Kindlmann 1 has recently introduced
techniques for generation of efficient
super-quadric shapes, but the described
techniques are too computationally expensive to
be implemented for real-time interaction. The
liquid crystal research community uses graphs, 2D
color plots and offline 3D rendering for
visualization 3. Existing commercial tools are
not capable of efficient exploration of tensor
data sets, due to the multivariate nature of
data. Recent research used stream-lines and
ellipsoids with pre-processing to render tensor
data in CAVE 4. Our research focuses on finding
efficient and scalable techniques for exploring
liquid crystal simulation data sets in an
interactive manner.
Fig 1 Timeline visualization Visualization
shows the scalar order density (nS) distribution
as directed sticks and scalar value distribution
along grid axis. Initial state (time step 0 )
shows all nS with constant value (solid state)
which distorts over time. Using distribution plot
it is easy to visualize and select appropriate
the time step for further study where there is
sharp change in the scalar order orientation.
Fig 2 Parallel coordinate viz Parallel
coordinate visualization brings out the
clustering among the multi-dimensional data
points. Above is testing visualization showing
scalar order value distribution along with grid
position.

• Approach
• Current research is focused
• on identifying parameter of
• interest and efficient clustering
• techniques
• Visualization approach involves
• Level 0 Analyze various time steps using
  time-scale visualization. Visualize distribution
  of the specific parameter for a time step Fig.
  1.
• Level 1 Select multiple (filtered) time steps
  for identified parameter over all tensor data
  points Fig. 2.
• Level 2 In-depth study of selected set of tensor
  points using glyphs Fig 3.

• Future Work
• Optimized glyph rendering.
• Refine parallel coordinate design.
• More linkage and filtering capabilities.2

Acknowledgements This research is funded by NSF
Mississippi EPSCoR program.

• References
• G Kindlmann. Superquadric Tensor Glyphs, IEEE
  TCVG Sym. on Viz., May, 2004, pp. 147--154.
• H. Doleisch and H. Hauser. Smooth Brushing for
  FocusContext Visualization of Simulation Data in
  3D, 10th Intl. Conf. on Computer Graphics,
  Plzen, 2002, vol. 10, pp. 147154.
• N. Mottram and C. Newton, Introduction to
  Q-tensor theory.
• V. Slavin, D.H. Laidlaw, et al. Visualization of
  Topological Defects in Nematic Liquid Crystals
  using Streamtubes, Streamsurfaces and
  Ellipsoids, IEEE Viz 04 Poster Compendium.

Fig 3 Tensor viz Tensor visualization is a
challenging problem due to the multi-variate and
complex data. Various glyph-based techniques are
applied for studying all information at each
point. Here single tensor point has been
explained and visualized using super-quadric and
super-ellipsoidal glyphs.