| FOREWORD | 6 |
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| PREFACE | 7 |
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| CONTENTS | 9 |
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| AN ENERGETIC VARIATIONAL FORMULATION WITH PHASE FIELD METHODS FOR INTERFACIAL DYNAMICS OF COMPLEX FLUIDS: ADVANTAGES AND CHALLENGES | 11 |
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| 1. Introduction | 11 |
| 2. An energy-based phsuse-field theory. | 13 |
| 3. Numerical scheme. | 16 |
| 4. Advantages of the diffuse-interface model. | 18 |
| 5. Physical and numerical subtleties. | 22 |
| 6. Concluding remarks. | 31 |
| 7. Acknowledgments. | 32 |
| REFERENCES | 32 |
| NON-EQUILIBRIUM STATISTICAL MECHANICS OF NEMATIC LIQUIDS | 37 |
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| 1. Introduction. | 37 |
| 2. Kinetic equation. | 40 |
| 3. Viscous stress tensor. | 51 |
| 4. Microscopic viscosity coefficients. | 58 |
| 5. Rotational friction constant. | 72 |
| 6. Spatial inhomogeneities and domain structure. | 85 |
| REFERENCES | 92 |
| ANISOTROPY AND HETEROGENEITY OF NEMATIC POLYMER NANO-COMPOSITE FILM PROPERTIES | 95 |
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| 1. Introduction. | 95 |
| 2. Plane Couette film flow of nematic polymers. | 96 |
| 3. Conductivity properties across the phase diagram of flowinduced film structures. | 99 |
| REFERENCES | 107 |
| NON-NEWTONIAN CONSTITUTIVE EQUATIONS USING THE ORIENTATIONAL ORDER PARAMETER | 108 |
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| 1. Introduction. | 108 |
| 2. Dynamics of the orientational order parameter tensor. | 109 |
| 3. Stress tensor. | 111 |
| 4. Dynamic stress tensor equation. | 112 |
| 6. Summary. | 116 |
| REFERENCES | 116 |
| SURFACE ORDER FORCES IN NEMATIC LIQUID CRYSTALS | 119 |
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| 1. Introduction. | 119 |
| 2. Energy and stresses. | 122 |
| 3. Twist cell | 125 |
| 4. Torque and force. | 129 |
| 5. Surface biaxial force. | 135 |
| 6. Conclusion. | 137 |
| REFERENCES | 139 |
| MODELLING LINE TENSION IN WETTING | 141 |
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| 1. Introduction. | 141 |
| 2. Line tension effects on equilibria. | 144 |
| 3. Modelling surface tension. | 147 |
| 4. Modelling line tension. | 153 |
| 5. Line tension elSects on stability. | 157 |
| 6. Wetting transition. | 166 |
| 7. Dewetting Transition. | 170 |
| 8. Conclusions. | 172 |
| REFERENCES | 173 |
| VARIATIONAL PROBLEMS AND MODELING OF FERROELECTRICITY IN CHIRAL SMECTIC C LIQUID CRYSTALS | 177 |
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| 1. Introduction. | 177 |
| 2. Free energy functions of smectic materials. | 179 |
| 4. Asymptotic form of the energy minimizers. | 186 |
| 5. Applied constant electric fields and boundary conditions. | 190 |
| 6. Variable electric fields. | 193 |
| 7. Conclusions. | 194 |
| REFERENCES | 195 |
| STRIPE-DOMAINS IN NEMATIC ELASTOMERS: OLD AND NEW | 197 |
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| 1. Introduction. | 197 |
| 2. A minimalist model. | 198 |
| 3. Stripe - domain patterns: the classics. | 203 |
| 4. Stripe-domain patterns: recent observations. | 205 |
| 5. Conclusions and Outlook. | 209 |
| REFERENCES | 210 |
| NUMERICAL SIMULATION FOR THE MESOSCALE DEFORMATION OF DISORDERED REINFORCED ELASTOMERS | 212 |
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| 1. Introduction. | 212 |
| 2. Description of the model. | 214 |
| 4. Results. | 222 |
| 5. Conclusion. | 232 |
| 6. Acknowledgments. | 235 |
| APPENDIX | 235 |
| REFERENCES | 238 |
| STRESS TRANSMISSION AND ISOSTATIC STATES OF NON-RIGID PARTICULATE SYSTEMS | 241 |
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| 1. Introduction. | 241 |
| LIST OF WORKSHOP PARTICIPANTS | 253 |
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| IMA SUMMER PROGRAMS | 257 |
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| IMA | 257 |
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| IMA | 257 |
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| 258 | 257 |