Center for Fluid Mechanics, Division of Applied Mathematics Fluids, Thermal and Chemical Processes Group, School of Engineering Joint Seminar Series
Abstract: We developed three-level multiscale models of red blood cells (RBCs) from the individual proteins to the whole cell, and coupled these models with a Boundary Element Method of Stokes flow to study healthy and diseased RBCs in various in-vitro and in-vivo conditions. First, we predicted the RBC resting shapes, and simulated the detachment of the lipid bilayer from the cytoskeleton in micropipette aspiration and studied the effect of protein unfolding. Then we investigated the different mechanical responses of healthy RBCs and spherocytes of anemia undergoing tank-treading motion in shear flow, and focused on the bilayer-skeleton interaction force in the molecular level. Finally we built models based on the 3D confocal images of malaria-infected RBCs and parasites, and explored the critical conditions for malaria-infected RBCs being filtered by the narrow endothelial slits in the spleen.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: We propose a non-parametric probabilistic model for prior knowledge in segmentation of medical images. The resulting inference algorithms register individual training images to the new image, transfer the segmentation labels and fuse them to obtain the final segmentation of the test subject. Our generative model yields previously proposed label fusion algorithms as special cases, and also leads to a new variant that aggregates evidence for the segmentation label locally. We demonstrate the advantages of our approach in two clinical applications: segmentation of neuroanatomical structures and segmentation of the left heart atrium whose shape varies significantly across the population.
Applied Mathematics Colloquium
Abstract: Landau damping is a collisionless stability phenomenon of considerable importance in plasma physics, as well as in galactic dynamics. Roughly speaking, it says that spatial waves are damped in time (very rapidly) by purely conservative mechanisms, on a time scale much lower than the effect of collisions. These evolution systems are described mathematically by nonlinear Hamiltonian partial differential equations describing transports of particles called Vlasov-Poisson equations. We shall in this talk give a general mathematical overview and history of this question together with a presentation of a joint work with C. Villani which provides the first positive mathematical result for this damping effect in the nonlinear regime. We shall also discuss the questions of microscopic irreversibility, macroscopic irreversibility, Boltzmann's conception of entropy, and their link with Landau damping.
Scientific Computing Seminar
The Korteweg-de Vries (KdV) equation is a nonlinear mathematical model for the unidirectional propagation of waves in a
variety of nonlinear, dispersive media. Recently it has attracted increasing attention as test-bed for the competition
between nonlinear and dispersive effects leading to a host of analytical issues such global existence and finite time
In this presentation, we construct, analyze, and numerically validate a class of conservative discontinuous Galerkin schemes for the generalized KdV equation. The schemes preserve the first two invariants (the integral and L2 norm) of the numerical approximations. We provide numerical evidence that this property imparts the approximations with beneficial attributes such as more faithful reproduction of the amplitude and phase of traveling wave solutions.
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