Waves Seminar Series
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics
New Jersey Institute of Technology
Fall 2008
Talks in this series are held Wednesdays in Cullimore 611 at 2:45 pm unless noted otherwise. If you have any questions about a particular colloquium, please contact the person hosting the speaker. For general questions about the seminar schedule, please contact Roy Goodman.
Date |
Speaker and title |
Host |
9/24 |
Ehud Yariv, Technion, Electrokinetic flows about polarizable particles (abstract) |
Horacio Rotstein |
10/1 |
Leon Cohen, City University of New York, Why do Pulses Sometimes Contract?: A Phase Space Approach to Wave Propagation (abstract) |
Eliza Michalopoulou |
11/5 |
Jason Fleischer, Princeton University, Towards Optical Hydrodynamics (abstract) |
Roy Goodman |
September 24, Ehud Yariv, Technion, Electrokinetic flows about polarizable particles
Abstract: In traditional electrokinetic analyses it is common to postulate a prescribed surface charge density (or, alternatively, zeta potential). Implicit in that approach is the assumption of ideally non-polarizable surfaces, which are not affected by externally applied fields. Clearly, such an assumption is inappropriate to describe flows about electrically conducting surfaces, which are effectively infinitely polarizable. It may even be inappropriate for dielectric surfaces, which do possess a finite polarizability. Following recent experiments in flows about electrodes, there is now an increasing interest in electrokinetic flows about polarizable surfaces, where Debye-layer charge is induced by externally applied fields.
As in the more traditional fixed-charge electrokinetic analyses, prevailing models of induced -charge flows usually employ the thin-Debye-layer limit. The electrokinetic transport occurring within the Debye layer is then effectively lumped into respective no-flux and slip boundary conditions, governing the electric and flow fields. The archetypical problem in such flows entails an uncharged conducting spherical particle (say a metal sphere) which is suspended in an unbounded fluid domain. When placed under an externally imposed Faraday current, the particle becomes polarized and a quadrupolar flow structure is formed.
Because of the high symmetry in that problem, the ensuing electrokinetic flow does not result in particle motion. Unsurprisingly, then, current interest lies in asymmetric configurations, which can result in electrophoretic motion of zero-net-charge particles. In the first part of the talk I will describe how asymptotic methods and symmetry arguments help in understanding this phenomenon.
For sub-micron particles, the thin-layer model breaks down. In the second part of the talk I will present a general analysis for an arbitrary layer thickness. Many of the electrokinetic concepts (e.g. zeta potential) associated with the thin-layer limit lose their concrete meaning in that general case, where instead of slip-driven electro- osmosis one encounters force-driven electro-convection. Thus, a systematic investigation of the electro-kinetic flow requires a confrontation with the highly- coupled nonlinear electrokinetic equations. Fortunately, the small particle size allows linearization with respect to the external field intensity. Of special interest is the thick- Debye-layer limit, which applies to nano-particles. This limit is singular and requires a systematic use of inner-outer asymptotic expansions, in the spirit of Proudman & Pearson (1957).
October 1, 1pm, Leon Cohen, City University of New York, Why do Pulses Sometimes Contract?: A Phase Space Approach to Wave Propagation
Abstract: The fundamental nature of dispersive wave propagation is that different frequencies travel at different velocities and hence one would expect that a transformation into a joint position-wavenumber representation would be well suited to study dispersive propagation. Using phase space methods we derive an approximation method that is remarkably simple to apply and gives considerable insight into the nature of pulse propagation. The approximation shows that each point in phase-space evolves with constant velocity where the velocity is the group velocity at that point. Furthermore we define the concept of group acceleration and ask the question why it is that linear partial differential equations leads to the concept of group velocity but not to group acceleration. Indeed we show that there are partial differential equations that lead to wave like behavior and group acceleration exists. Also, we show that phase space considerations explains naturally why it is that pulses sometime contract before they expand.
November 5, Jason Fleischer, Princeton University, Towards Optical Hydrodynamics
Abstract: It is well-known that the basic equations of nonlinear optics can be mapped to equations from condensed matter physics. For example, in the paraxial approximation, a coherent light wave obeys the same SchrÃ¶dinger evolution as a coherent matter wave. Similarly, partially-condensed systems have much in common with partially-incoherent light. Here, we exploit these relations to develop an optical hydrodynamics. Using coherent laser light in a nonlinear crystal, we experimentally observe ideal (inviscid) fluid behavior, including dispersive shock waves, hydrodynamic instabilities, and vortex flow. Using spatially-incoherent light, we demonstrate all-optical plasma dynamics, including Landau damping, bump-on-tail instabilities, and weak and strong regimes of speckle turbulence. Theory is developed and shown to match very well with experiment. The results establish optical systems as an analog simulator for fluid behavior and hold potential for the design of new photonic devices.