Wednesday, April 17, 2024
Time | Items |
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All day |
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3pm |
04/17/2024 - 3:00pm The dynamics of active and passive filaments in viscous fluids is frequently used as a model for many complex fluids in biological systems such as: microtubules which are involved in intracellular transport and cell division; flagella and cilia which aid in locomotion. The numerical simulation of such systems is generally based on slender-body theory which give asymptotic approximations of the solution. However, these methods are low-order and cannot enforce no-slip boundary conditions to high-accuracy, uniformly over the boundary. Boundary-integral equation methods which completely resolve the fiber surface have so far been impractical due to the prohibitive cost of current layer-potential quadratures for such high aspect-ratio geometries. In this talk, I will present new quadrature schemes which make such computations possible and new integral equation formulations which lead to well-conditioned linear systems upon discretization. I will present numerical results to show the efficiency of our methods. Location:
LOM 214
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4pm |
04/17/2024 - 4:00pm The moduli space of Anosov representations of a surface group in a semisimple group admits many more natural functions than the regular functions including length functions and correlation functions. We consider the Atiyah-Bott/Goldman Poisson bracket for length functions and correlation functions and give a formula that computes their Poisson bracket. This is done by introducing a new combinatorial framework including ghost polygons and a ghost bracket encoded in a formal algebra called the ghost algebra. As a consequence, we show that the set of length and correlation functions is stable under the Poisson bracket and give two applications: firstly in the presence of positivity we prove the convexity of length functions, generalising a result of Kerckhoff in Teichmüller space, secondly we exhibit subalgebras of commuting functions associated to laminations. This is joint with François Labourie. Location:
KT 207
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