Lefschetz Center for Dynamical Systems Seminar
Cognitive & Linguistic Sciences Presentations
BROWN UNIVERSITY -
Joint Materials/Solid Mechanics Seminar Series
University of Illinois at Urbana-Champaign | |
Abstract: Capillarity draws our curious attention from childhood. Our everyday experience tells us that small bodies floating on a liquid/air interface (e.g. cereal flakes on milk) attract each other and form clusters. In this talk, we will first consider the meniscus formed by a thin solid plate with a liquid in a uniform gravitational field. It is found that for a hydrophilic plate, the vertical force necessary to break the meniscus during removal of the plate from the liquid is larger than the force necessary to break the meniscus during submersion of the plate into the liquid. The reverse is true when the plate is hydrophobic. The study is then extended to investigate the interaction force between two plates, each forming a meniscus with the liquid. It is shown that the horizontal component of the interaction force between the plates is attractive for similar menisci (e.g., when the two plates are equally displaced in or out of the liquid), and repulsive when they form opposite menisci. If the two menisci are of the same type but not similar (e.g., one plate is pushed more into the liquid than the other) then the force is attractive at long distances and may be repulsive at shorter distances with a stable equilibrium at a finite distance between the plates depending on the elevations of the plates. Such interaction can be between two hydrophilic or two hydrophobic plates or between a hydrophilic and a hydrophobic plate. Thus, contrary to our everyday experience, floating bodies may not only attract each other, but also repel one another depending on the meniscus between them. This long range rich interaction between floating bodies may be exploited to form hierarchical self assembled 2D structures. Desktop experiments will be demonstrated to show the proof of concepts.
Center for Fluid Mechanics
And
The Fluids, Thermal And Chemical Processes Group
Of
The Division Of Engineering
Seminar Series
Massachusetts Institute of Technology, Cambridge, MA | |
Abstract: Microfluidics has become an important enabling technology for rapidly analyzing and separating biomolecules, synthesizing new materials, and performing fundamental studies on single molecules or colloids. Using fields and flows, these microfluidic devices can create unique environments to transport complex macromolecules and assemble field-responsive colloids. In this seminar, we will discuss how single molecule microscopy, scaling theory, and Brownian dynamics simulations can be combined to study the transport of large DNA molecules in microfluidic devices. We will concentrate on our studies of DNA electrophoresis in electric field gradients and arrays of posts. A formal analogy between DNA deformation in hydrodynamic flows and electric fields will be discussed, which allows us to develop theories to predict DNA deformation and also design a new method for stretching DNA. We will show how a fundamental understanding of these systems impacts DNA mapping technologies and pathogen detection systems.
Stochastic Systems Seminar
Abstract: We will discuss an asymptotic approximation of the slow dynamics of a singularly perturbed control system (SPCS) by the solutions of the averaged system in which the controls are measure-valued functions taking values in the set of limit occupational measures defined by the "fast" subsystem. For an important special class of SPCS, we will show that problems of optimal control are reduced to infinite dimension linear programming problems and we will discuss an approach to a numerical solution of such problems. Results will be illustrated by a numerical example.
Brown Univeristy - Graduate School Dissertation Defense
Special PDE Seminar
Please Note Special 2nd PDE Seminar For This Week Only |
Abstract: Thin, nearly uniform layers of some fluids can destabilize under the effects of intermolecular forces. After the initial phase, the fluid breaks into droplets connected by an ultra-thin layer of fluid. This structure coarsens on slow-time scale. The characteristic distance between droplets and their size grow, while their number is decreasing.
This physical process can be modeled in the lubrication approximation by a so called thin-film equation for the height of the fluid. I will discuss coarsening in thin-film equations with mobility equal to the height of the fluid. These equations are gradient flows in the Wasserstein metric. Using the gradient flow structure within the Kohn-Otto framework we obtain rigorous upper bound on the coarsening rate. The upper bound we obtain coincides with the coarsening rate that Glasner and Witelski conjectured for the 1-dimensional problem.
This is joint work with Felix Otto and Tobias Rump.
Brown Analysis Seminar
Brown University Graduate School Dissertation Defense Information
Scientific Computing Seminar
The main idea of scheme adaption is to apply different numerical methods to different parts of the computed solution. In the context of hyperbolic conservation laws, one may take advantage of this approach by applying expensive limiters near nonlinear shock waves only, while treating the rest of the computational domain by a high-order linearly stable method. Obviously, scheme adaption requires a certain mechanism for distinguishing between the smooth and nonsmooth regions. We have used an indicator based on a weak local residual, which not only measures the smoothness of the computed solution, but also verifies its quality.
Another important application of the scheme adaption technique is related to composite waves that have to be resolved with the help of limiters with relatively large built-in dissipation in order to guarantee convergence toward the unique entropy solution.
PDE Seminar
Abstract: Microchips often fail when the metallic interconnects between transistors and diodes on the chip degrade due to extremely high current densities. The physics of this process is quite interesting; it is a non-local moving interface problem involving elastic deformation and diffusion. Stress singularities can develop which make boundary conditions difficult to understand and numerical simulation difficult to implement reliably.
After describing the model, I will outline our recent proof of well-posedness, which uses techniques from semigroup theory and requires an analysis of a type of Dirichlet to Neumann map involving the equations of elasticity. I will also briefly describe my recent work on computing stable asymptotics for singularities of Agmon-Douglis-Nirenberg elliptic systems near corners and interface junctions, and show how to adjoin these singular functions to the finite element basis to accurately and efficiently resolve stress singularities without mesh refinement.
<--- 2005 Index