Reciprocal and related theorems for nematic liquid crystals |
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| Affiliation: | 1. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK;2. Área Cientı́fica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emı́dio Navarro, 1949-014 Lisboa, Portugal;1. GREA Innovació Concurrent, Universitat de Lleida, Edifici CREA, Pere de Cabrera s/n, 25001, Lleida, Spain;2. Department of Chemical & Materials Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand;1. Department of Construction Engineering, École de technologie supérieure, 1100 rue Notre-Dame Ouest H3C 1K3, Montréal, Quebec, Canada;2. CanmetENERGY, Natural Resources Canada, Varennes, Canada;1. Division of Technology for Energy Systems and Renewable Energy, Bavarian Center for Applied Energy Research, 85748 Garching, Germany;2. Institute for Energy Systems, Faculty of Mechanical Engineering, Technical University Munich, 85748 Garching, Germany;3. School of Power and Mechanical Engineering, Wuhan University, 430072 Wuhan, China;4. School of Civil Engineering, Hunan University of Technology, 412007 Zhuzhou, China;1. Building Works Design Group, Hyundai E&C Co. Ltd., Seoul 110-920, Republic of Korea;2. Department of Architecture, Inha University, Incheon 402-751, Republic of Korea;3. Department of Civil and Environmental Engineering, KAIST, Daejeon 305-701, Republic of Korea;1. Graduate School, Sungkyunkwan University, 2066 Seoburo, Suwon, Gyeonggi 440-746, South Korea;2. Department of Architectural Engineering, Sungkyunkwan University, 2066 Seoburo, Suwon, Gyeonggi 440-746, South Korea;3. Department of Architectural Engineering, Hanbat National University, 125 Dongseodaero, Daejeon 305-719, South Korea |
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| Abstract: | Reciprocal and related theorems are considered for uniaxial and biaxial nematic liquid crystals. In the general case, where the directors of real and reciprocal materials are assumed to coincide, integral relations between velocity and stress fields of the real and reciprocal materials are obtained. Simplified expressions are also obtained for the high viscosity and elasticity limits. |
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