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Tensor Visualization and Defect Detection in Nematic Liquid Crystals

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Tensor Visualization and Defect Detection in Nematic Liquid Crystals Mississippi State University Scholars Junction Theses and Dissertations Theses and Dissertations 1-1-2006 Nlcviz: Tensor Visualization And Defect Detection In Nematic Liquid Crystals Ketan Mehta Follow this and additional works at: https://scholarsjunction.msstate.edu/td Recommended Citation Mehta, Ketan, "Nlcviz: Tensor Visualization And Defect Detection In Nematic Liquid Crystals" (2006). Theses and Dissertations. 3292. https://scholarsjunction.msstate.edu/td/3292 This Graduate Thesis - Open Access is brought to you for free and open access by the Theses and Dissertations at Scholars Junction. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholars Junction. For more information, please contact [email protected]. NLCVIZ: TENSOR VISUALIZATION AND DEFECT DETECTION IN NEMATIC LIQUID CRYSTALS By Ketan Mehta A Thesis Submitted to the Faculty of Mississippi State University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Computer Science in the Department of Computer Science and Engineering Mississippi State, Mississippi August 2006 Copyright by Ketan Mehta 2006 NLCVIZ: TENSOR VISUALIZATION AND DEFECT DETECTION IN NEMATIC LIQUID CRYSTALS By Ketan Mehta Approved: T.J. Jankun-Kelly Robert James Moorhead II Assistant Professor of Computer Science Billie J. Ball Professor of and Engineering Electrical and Computer Engineering (Major Professor) (Committee Member) Rajendran Mohanraj Edward B. Allen Assistant Research Professor Associate Professor of Computer of Computational Engineering Science and Engineering, (Committee Member) and Graduate Coordinator, Department of Computer Science and Engineering Roger King Associate Dean for Research and Graduate Studies of the Bagley College of Engineering Name: Ketan Mehta Date of Degree: August 5, 2006 Institution: Mississippi State University Major Field: Computer Science Major Professor: Dr. T.J. Jankun-Kelly Title of Study: NLCVIZ: TENSOR VISUALIZATION AND DEFECT DETECTION IN NEMATIC LIQUID CRYSTALS Pages in Study: 93 Candidate for Degree of Master of Science Visualization and exploration of nematic liquid crystal (NLC) data is a challenging task due to the multidimensional and multivariate nature of the data. Traditionally, scientists have used a combination of different tools and techniques like 2D plots, histograms, cut views, etc. for data visualization and analysis. However, such an environment does not provide the required insight into NLC datasets. This thesis addresses two areas of the study of NLC data—understanding of the tensor order field (the Q-tensor) and defect detection in this field. Tensor field understanding is enhanced by using a new glyph (NLCGlyph) based on a new design metric which is closely related to the underlying physical properties of an NLC, described using the Q-tensor. A new defect detection algorithm for 3D unstructured grids based on the orientation change of the director is developed. This method has been used successfully in detecting defects for both structured and unstructured models with varying grid complexity. DEDICATION To my family and Swati. ii ACKNOWLEDGMENTS I would like to thank the many people who have played an important role in facilitating my thesis work and ultimately, my graduation at Mississippi State University. I acknowledge, appreciate, and return the love and support of my family, without whom this journey would not have been possible. My parents Kishor and Jasvanti Mehta have provided support and encouraged me to pursue my dreams. My brothers, Mitesh and Vijay have been constant sources of inspiration and kept me focused on my goal. My fiancee,´ Swati, has become the most important part of my life. Her love and companionship has encouraged me to take challenges and pursue my dreams as well. I would like to thank my committee members, Dr. T.J. Jankun-Kelly, Dr. Robert Moorhead and Dr. Rajendran Mohanraj for their advice and guidance throughout my research. I want to thank Dr. TJK for his encouragement and discussions, specifically his extensive help in writing papers and this thesis. The NLC glyph section would not have been possible without his ideas and inputs. I have been fortunate to have found a great mentor in Dr. Moorhead, whose professional advice and suggestions have helped me immensely. I want to thank him for convincing me to join MSU and making it one of the most exciting phase of my life. I want to acknowledge Dr. Ed Swan for his suggestions and teaching me how to plan and design a user study. I want to sincerely thank my previous iii manager, Ms. Sangeeta Gupta at Wipro for encouraging and helping me in going back to graduate school, without whom this journey would not have been made. I also want to to thank my collaborators, Dr. Rajendran Mohanraj and Ms. Huangli Li of the SimCenter, High Performance Computing Collaboratory, for their helpful support, discussions, and thoughtful feedback. I have learned a lot about liquid crystals and simula- tions during our interactions. I want to acknowledge their collaboration and extensive help in generating the required datasets without which this thesis would not have been possi- ble. I appreciate their time and effort invested in using my tools and providing feedback on comparison analysis for verification. I want to acknowledge and thank my fellow colleagues– Adam, Chris, Eric and Matt– for creating a stimulating and exciting environment at the VizLab. We have spent countless hours discussing and talking about visualization and various topics. I have been fourtunate to learn a lot about American life and culture in their company. I want to thank and acknowledge Matt for our daily “coffee-rounds” and for listening to my weird talk, and Eric for our long late-night discussions. Lastly, I want to thank and acknowledge the different research programs that funded my graduation and research. A major part of the research was funded through the National Science Foundation EPSCoR program (via award #0132618) and the remaining funding came from the Department of Computer Science and Engineering, Mississippi State Uni- versity. iv TABLE OF CONTENTS Page DEDICATION .................................... ii ACKNOWLEDGMENTS ............................... iii LIST OF TABLES .................................. vii LIST OF FIGURES .................................. viii LIST OF NOMENCLATURE ............................ xi CHAPTER I. INTRODUCTION ................................ 1 1.1 Nematic Liquid Crystal Basics ...................... 1 1.2 NLC Application: Biosensor ....................... 3 1.3 Hypothesis ................................. 4 1.4 Motivation ................................. 5 1.5 Objective ................................. 6 1.6 Simulation Data .............................. 7 II. SURVEY OF CURRENT LITERATURE ................... 8 2.1 Tensor Visualization ............................ 9 2.1.1 Discrete Visualization Techniques . 12 2.1.2 Topology Visualization Techniques . 15 2.2 Defect Detection in Nematic Liquid Crystals . 18 2.2.1 Disclination Basics ........................ 19 2.2.2 Scalar Order Parameter (S) Based Analysis ........... 21 2.2.3 Director (n) Based Analysis .................... 23 2.3 Unstructured Grid Visualization ..................... 28 III. NLC TENSOR GLYPH ............................. 30 3.1 Introduction ................................ 30 v CHAPTER Page 3.2 Nematic Liquid Crystal Alignment .................... 32 3.3 NLC Tensor Glyphs ............................ 34 3.3.1 NLC Tensor Glyph Generation .................. 38 3.4 Examples and Discussion ......................... 44 3.5 User Feedback ............................... 49 3.6 Conclusions ................................ 51 IV. AUTOMATIC DEFECT DETECTION ..................... 52 4.1 Introduction ................................ 53 4.2 NLC Defect Detection on Unstructured Grid . 54 4.3 Results and Verification .......................... 59 4.4 Case Studies ................................ 61 4.4.1 Structured Case: Cube ....................... 61 4.4.2 Unstructured Case: Disclination Annihilation . 64 4.4.3 Unstructured Case: A Protein Molecule . 67 4.5 User Feedback ............................... 70 4.6 Conclusions ................................ 70 V. CONCLUSIONS ................................ 71 5.1 Future Work ................................ 74 REFERENCES .................................... 75 APPENDIX A. CONSTRUCTION OF THE BARYCENTRIC TENSOR GLYPH SPACES . 82 B. DEFECT DETECTION ALGORITHM .................... 86 C. TENSOR MATH BASICS ........................... 89 C.1 Eigenvalue Computation ......................... 90 C.2 Eigenvector Calculation .......................... 92 vi LIST OF TABLES TABLE Page 2.1 Existing tensor glyph techniques . 11 vii LIST OF FIGURES FIGURE Page 1.1 Uniaxial (left) and Biaxial (right) macro-molecules. 2 1.2 Schematic illustration of solid, liquid crystal and liquid phases. 3 2.1 Order parameter variation with transition temperature (Tc) in NLC . 22 2.2 Validation method: S-based analysis using FieldView . 22 2.3 Contractible and Uncontractible defect loop . 25 2.4 Disclination detection algorithm by Zapotocky et al. 25 3.1 Major alignments of NLC molecules. ...................... 31 3.2 Superellipses: Shaded region represents the NLC alignment tensor space. 37 3.3 Visual Ambiguity: NLC Glyphs using offset (left three) and our method (right). 38 3.4 Glyph shapes at extremes of metric ....................... 41 3.5 Effect of shape control parameters – γb and γu
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