Lefschetz Center for Dynamical Systems Seminar
Abstract: We study linear functional differential equations of mixed type, and obtain a fundamental decomposition of the state space into forward and backward semiflows which satisfy the estimates of an exponential dichotomy. We obtain a corresponding factorization of the characteristic function analogous to a Wiener-Hopf factorization. The theory allows us to analyze boundary value problems on infinite intervals (heteroclinic orbits), and long finite intervals ("truncated" heteroclinic orbits).
Brown Analysis Seminar
Brown University, Joint Seminar,
Solid Mechanics/Hibbitt, Karlsson & Sorensen
James R. Rice Assistant Professor of Engineering, Brown University - Division of Engineering | |
Abstract: At the micron scale of a bacterial cell, viscous effects completely dominate inertial effects, and Brownian motion is important. These distinctive features of the small scale have led bacteria to adopt strategies for locomotion and sensing which are qualitatively different from macroscopic strategies. This talk will address the mechanical aspects of bacterial chemotaxis, the means by which E. coli moves towards higher concentrations of favorable chemicals. These cells swim using several slender helical propellers, or flagella, driven by rotary motors embedded at random points in the cell wall. In the presence of a chemical gradient, a bacterium drifts up the gradient by following a directed random walk. The random walk is not due to thermal fluctuations, but is part of the bacterial behavior. Near the beginning of each step of a walk, the rotating helical flagella form a bundle, and the cell moves in a directed manner. At the end of each step, the bundle flies apart, and the cell randomizes its direction for the next step. A clear understanding of the elements of the mechanics of the bundling and unbundling processes is only now emerging. These elements are (1) the interplay of elastic and viscous stresses in slender filaments, (2) the polymorphism of the flagella, and (3) the hydrodynamic interactions among the flagella. I will use slender-body theory to show that the counter-rotation of the cell body necessary for torque balance is sufficient to wrap the flagella into a bundle, even in the absence of the swirling flows produced by each individual flagellum. Then I will briefly review recent work by my collaborators on polymorphism and hydrodynamics. Finally, I will present results of our macroscopic experiments on rotating flexible helices in viscous fluids.
Scientific Computing Seminar
PDE Seminar
Department of Mathematics Colloquium
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