| EPSRC Reference: |
EP/I028714/1 |
| Title: |
Analysis of liquid crystal models |
| Principal Investigator: |
Slastikov, Dr V |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
22 April 2011 |
Ends: |
21 October 2013 |
Value (£): |
102,726
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Modeling, simulation, analysis, and design of liquid crystal systems and devices raises many fundamental questions of physics and mathematics. The study of appropriate phase transitions, formation and evolution of singularities and defects in nematic liquid crystals leads to challenging mathematical problems. In order to understand these phenomena we rely on analysis of variational problems and nonlinear partial differential equations arising from corresponding physical models.There are several major theories to study nematic liquid crystals: Onsager theory, Maier-Saupe mean field theory, Oseen-Frank director theory, Ericksen theory, and Landau-de Gennes theory. These theories are based on investigation of the free energy of the liquid crystalline system. Minimizers of the free energy correspond to equilibrium states and in order to understand the liquid crystalline system behavior it is enough to study properties of these minimizers.The main goal of this project is to analytically investigate variational problems arising in Onsager-Maier-Saupe and Landau-de Gennes models. We would like to study the qualitative properties of the equilibrium states of liquid crystalline systems by investigating the minimizers of the corresponding energy functionals. In particular we plan to investigate formation and profiles of the singularities in liquid crystalline systems, phase transitions in biaxial nematics, and relation between different liquid crystal theories. We also would like to gain the insight about nonequilibrium phenomena in the liquid crystalline systems by studying the gradient flow (and related) dynamics generated by free energy.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bris.ac.uk |