Lefschetz Center for Dynamical Systems Seminar
Abstract: I will discuss the problem of speed selection for traveling wave solutions to a class of scalar second order reaction diffusion equations. One of the main problems is whether the minimal wave speed is determined by linear or nonlinear considerations. Another problem is the actual determination the minimal speed. I will present the geometric characterization of the minimal speed, as well as some recent work on its variational characterization.
Cognitive & Linguistic Sciences
Spring 2005 Colloquium and CG233 Speakers
Brown University --
Joint Materials/Solid Mechanics Seminar Series
Harvard University, Cambridge, MA | |
Abstract: We propose and experimentally verify a theory of persistent step-flow growth of strained films on vicinal substrates. For step flow to be stable against island formation, the deposition flux must be sufficiently low; when applied to pulsed laser deposition, this constraint requires that the time to evacuate adatoms deposited in one pulse be shorter than the period between pulses. For step flow to be stable against step bunching, the deposition flux must be sufficiently high, so that the effect of the adatom attachment barrier prevails over that of strain. These considerations lead to a morphological phase diagram that contains a step-flow regime, surrounded by regimes of three less desirable growth modes: step bunching, island formation, and concurrent island formation and step bunching. The theory rationalizes diverse growth modes observed in pulsed laser deposition of SrRuO_{3} on SrTiO_{3}, and is expected to be applicable to heteroepitaxial growth of other complex materials as well.
Center for Fluid Mechanics and
The Fluids, Thermal and Chemical Processes Group
of The Division of Engineering
Seminar Series
Columbia University, New York, New York | |
Abstract: Our research focuses on the behavior of dispersed particles in complex geometry and time-dependent flows. These flows are often encountered in such applications as materials processing or flow in the circulatory system. A well-known challenge in materials processing is that particles often end up nonuniformly distributed in space, while the quality of the product usually requires spatial uniformity. One relevant system involving a complex geometry is the flow of a concentrated suspension into an abrupt expansion. An example of a time-dependent flow is pressure-driven oscillatory flow of a concentrated suspension in a tube. Fundamental understanding of such systems is limited, mainly due to the small amount of available experimental data and modeling calculations.
In our study, suspensions of neutrally buoyant, noncolloidal spheres in Newtonian liquids undergo steady, pressure-driven flow in abrupt, axisymmetric 1:2 and 1:4 expansions, or oscillatory, pressure-driven flow in a straight tube. Particle concentration and velocity profiles are obtained by nuclear magnetic resonance imaging (NMRI). We aim to determine the particle properties and flow conditions (e.g. particle volume fraction, particle and flow Reynolds number, particle-tube radius ratio, expansion ratio) that lead to the observed concentration and flow fields. Recent results from oscillatory and expansion flow experiments will be presented, in addition to some recent efforts to scale down the systems into the microfluidic regime.
Special PDE & Lefschetz Center for Dynamical Systems Seminar
Brown Analysis Seminar
Scientific Computing Seminar
Abstract: The locally divergence-free discontinuous Galerkin method was originally developed for solving Maxwell equations by Cockburn, Li and Shu. In this method, the divergence-free property of the magnetic field was imposed locally by choosing piecewise divergence- free polynomials as the solution space. As a consequence, this method has a smaller computational cost than that of the discontinuous Galerkin method with standard piecewise polynomial spaces, meanwhile it produces an approximation of the same accuracy. The success of this "imposing-property-locally" idea in Maxwell equations leads to a broader application such as the one in magnetohydradynamics (MHD) equations and the one in Hamilton-Jacobi equations. In this presentation, we try to explore the ability of the method to solve the Laplace equation in mixed form.
PDE Seminar
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