Apala Majumdar - Pattern Formation in Confined Nematic Systems
| Dates: | 12 February 2020 |
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| Times: | 14:00 - 14:50 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Apala Majumdar |
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Apala Majumdar (University of Strathclyde) joins us for this event in the Physical Applied Mathematics Series (rescheduled from November 2019).
Abstract: Nematic liquid crystals are classical examples of partially ordered materials intermediate between isotropic liquids and crystalline solids. We study spatio-temporal pattern formation for nematic liquid crystals in two-dimensional regular polygons, subject to physically relevant non-trivial tangent boundary conditions, in the powerful continuum Landau-de Gennes framework. We study two asymptotic limits, relevant for "small" nano-scale domains and macroscopic domains respectively, and analytically study how the solution landscape changes with the domain size, including the admissible singularities. Notably, in the small domain limit, we always have an isolated degree +1 vortex at the centre of the regular polygon, which splits into fractional defects at the polygon vertices, as the domain size increases. We numerically compute bifurcation diagrams using arc continuation methods and deflation techniques, tracking stable and unstable nematic equilibria as a function of domain size. In the last part of the talk, we discuss two-dimensional ferronematic systems, as a generalization of our work on nematic equilibria in regular polygons, and the coupling between the nematic order parameter and the spontaneous magnetization induced by the suspended nanoparticles. Our most striking numerical observations concern the stabilization of interior fractional nematic point defects and magnetic domain walls, purely induced by geometric effects and the ferronematic coupling, without any external magnetic fields. All collaborations will be acknowledged during the talk.
Speaker
Apala Majumdar
Organisation: University of Bath
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Frank Adams 1
Alan Turing Building
Manchester
