Techniques for the Visualization of Topological Defect Behavior in Nematic Liquid Crystals

Abstract

Abstract-We present visualization tools for analyzing molecular simulations of liquid crystal (LC) behavior. The simulation data consists of terabytes of data describing the position and orientation of every molecule in the simulated system over time. Condensed matter physicists study the evolution of topological defects in these data, and our visualization tools focus on that goal. We first convert the discrete simulation data to a sampled version of a continuous second-order tensor field and then use combinations of visualization methods to simultaneously display combinations of contractions of the tensor data, providing an interactive environment for exploring these complicated data. The system, built using AVS, employs colored cutting planes, colored isosurfaces, and colored integral curves to display fields of tensor contractions including Westin's scalar cl, cp, and cs metrics and the principal eigenvector. Our approach has been in active use in the physics lab for over a year. It correctly displays structures already known; it displays the data in a spatially and temporally smoother way than earlier approaches, avoiding confusing grid effects and facilitating the study of multiple time steps; it extends the use of tools developed for visualizing diffusion tensor data, re-interpreting them in the context of molecular simulations; and it has answered long-standing questions regarding the orientation of molecules around defects and the conformational changes of the defects.

Superquadric Glyphs for Symmetric Second-Order Tensors

“…Faced with indefinite tensors, a frequent strategy is to map them to positive-definite tensors prior to visualization [34,22,21,52,33]. Even when bijective mappings are used (so mathematically, no information is lost), such mappings still visually obscure the difference between positive and negative eigenvalues, which is a fundamental qualitative aspect in various applications.…”

“…Alternatively, some authors enforce positivedefiniteness for visualization purposes, for example by taking the exponential of eigenvalues [34], by shifting them by the amount of the most negative eigenvalue [52], or other application-specific mappings [22,21,33]. An entirely different approach is to define symmetric tensor glyphs via algebraic equations, such as the quadratic surface of the tensor, known as the Cauchy stress quadric in geomechanics [18] and as the Dupin indicatrix in differential geometry [17], or the Reynolds glyph [18].…”

An Evaluation of Glyph Perception for Real Symmetric Traceless Tensor Properties

“…Cylindrical glyphs [AWB01] are naturally rotationally symmetric and strongly suggest orientation along the long axis of the shape. Ellipsoidal glyphs, described first for NLC physics by Allen [All89] and used subsequently elsewhere [FWZ01, SPL*06], can vary their different symmetries by changing the ratio of the major, medium, and minor axes. Finally, superellipsoids [JKM06] not only change their symmetry, but their underlying shape; the superellipsoid shape parameters vary between box‐, sphere‐, and cylinderlike appearance depending upon the NLC tensor.…”

“…Tensor visualization seeks to describe volumetric or other high‐dimensional properties of a system. One approach for depicting tensors is the use of glyphs: 3D shapes that act as icons encoding different parameters of the tensor [All89, AWB01, BH04, JKM06, KWH00, KW99, Kin04, SEHW02, SPL*06, SKH95, ZLK04]. An important issue in glyph visualization is the comprehensibility of such markers—how accurately do they communicate tensor characteristics?…”

Top Challenges in the Visualization of Engineering Tensor Fields

“…Visualization of engineering tensors fields is, however, a relatively new research topic [11,3,4]. Despite the potential advantages of tensor visualization in engineering, significant challenges make advances in the field difficult.…”