Seminar on Nonlinear Waves
Throughout the Term | |
Lefschetz Center for Dynamical Systems Seminar
Abstract: The Skyrme model (1961) was one of the first attempts to describe elementary particles as localized in space solutions of nonlinear PDEs. The fields take their values in $SU(2)=S^3$ and stabilize at spatial infinity. Thus, the configuration space splits into different sectors (homotopy classes) with a constant integer topological charge (the degree) in each sector. Faddeev's model (1975) was designed to provide additional internal structure (knottedness) to the localized solutions. The fields take their values in the two-dimensional sphere and the topological charge is the Hopf invariant. I will discuss some old and new results for these models.
Brown University Center for Statistical Sciences Seminar
Abstract: Over the last half century, randomized trials have been accepted as the most reliable means of measuring the efficacy of virtually all medical interventions. However, little research has been undertaken to verify that randomization is equally likely to be successful in promoting balance when large healthy populations are randomized, and the target event is cancer incidence or mortality. The objective of this presentation is to demonstrate that the probability of randomization failure is higher in such a randomized population trial (RPT) compared to the much more common randomized clinical trial (RCT), which is designed to study the effect of an intervention in a diseased population.
Joint Seminar, Division of Engineering, Microfluidics Laboratory and The Center for Fluid Mechanics
Abstract: The miniaturization and integration of multiple functionality for chemical analysis and synthesis into a handheld device requires efficient methods for transporting ultrasmall volumes of liquid through networked arrays. The majority of devices in development combine micromechanical and electrokinetic techniques for controlling flow in closed microchannels. We recently introduced a non-electronic means of flow control that could eventually lead to the construction of a chemical reactor on the surface of an integrated circuit. The design concept relies on thermocapillary transport of liquid streams or droplets on a surface of mixed wettability produced by micropatterning a self-asssembled monolayer. The chemical patterning confines the flowing liquid to selected pathways bearing a streamwise thermal gradient. Liquid flow is therefore controlled by simultaneously applying a shear stress at the air- liquid surface and a variable surface energy pattern at the liquid-solid interface. Advantages to this open architecture design include direct contact with the vapor phase, reduced friction and blockage, no electroactive additives, no moving parts and low power consumption. A distinct advantage of this approach is that micropatterned temperature fields can eventually be used in differential mode to route liquid along selected pathways and in absolute mode to induce chemical reactions at electronically addressable sites. The development and design of such an integrated microfluidic chip requires a fundamental understanding of thermocapillary flow on homogeneous and chemically micropatterned surfaces. We will survey modeling and experimental efforts describing the stability of thermocapillary driven flow on homogeneous surfaces and discuss extensions to chemically micropatterned ones. To downsize this technology further, we provide an estimate of the smallest liquid feature transportable by this technique.
Brown Analysis Seminar
Applied Mathematics Colloquium
Scientific Computing Seminar
Abstract: Radial basis functions (RBF) have been steadily growing in importance as a tool for scattered-data approximation. Their high accuracy and grid-free ease of use in any dimension make them an attractive foundation for difference methods for simulating PDEs. I will introduce RBFs and highlight some important theoretical properties (including recent results) as well as successful uses of RBFs in elliptic and diffusive equations. Then I will discuss challenging issues that remain unresolved, particularly stability for nondissipative propagation, and some early efforts to overcome them.
Special PDE/ALG GEOM Seminar
PDE Seminar
Beijing, China | |
Department of Mathematics Colloquium
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