Mathematics Home / Research Seminars: Applied and Computational Mathematics
Time & Location: Typically talks will be in Gibson Hall 310 at 3:30 PM.
Organizers: Nathan Glatt-Holtz and Kun Zhao
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Title: A minimal model of the hydrodynamical coupling of flagella on a spherical body
Karin Leiderman | Colorado school of Mines
Abstract:
Flagella are hair-like appendages attached to microorganisms that allow the organisms to traverse their fluid environment. The algae Volvox are spherical swimmers with thousands of individual flagella on their surface that coordinate in a way that is not fully understood. In this work, we have extended a previously developed minimal model of flagella synchronization on a plane to examine synchronization on the outer surface of a sphere. Each beating flagella tip is modelled as a small rotating sphere, elastically attached to a point just above the spherical surface and a regularized image system for Stokes flow outside of a sphere is used to enforce the no-slip condition. Biologically relevant distributions of rotors results in a rapidly developing and robust symplectic metachronal wave traveling from the anterior to the posterior of the spherical Volvox body.
Title: Mapping TASEP back in time
Leonid Petrov | University of Virginia
Abstract:
We obtain a new relation between the distributions μ_t at different times t ≥ 0 of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions μ_t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a ver- sion of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving μ_t which in turn brings new identities for expectations with respect to μ_t. Based on a joint work with Axel Saenz.
Title: Probabilistic global flow for energy-supercritical PDE
Mouhamadou Sy | University of Virginia
Abstract:
Global wellposedness for energy-supercritical Schrödinger (and Wave) equations is an important open problem in the dispersive PDE field. The well-known probabilistic alternatives (Gibbs measures theory or Fluctuation-dissipation) come across hight difficulties when applied to these equations. In this talk, I will present a combination of these two probabilistic methods in order to construct a global probabilistic flow for the energy-supercritical NLS. If the time permits, I will sketch the application of that approach to the 3D Euler equations.
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Le Chen | Emery University
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Guangyu Xi | University of Maryland - College Park
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Leonid Berlyand | Penn State
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Thanksgiving
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William Cuello | Rutgers
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