Lefschetz Center for Dynamical Systems Seminar
Abstract: Semiconductor lasers are key components of a variety of modem photonic systems such as fiber, diode pumped solid state devices and Raman amplifiers. However when they are exposed to even small amounts of feedback or external injection from a distant reflector or another laser, then radiation emitted from these lasers exhibits a plethora of instabilities and irregular chaotic transitions. Recent experiments in semiconductor lasers subject to optical feedback as well as experiments with pairs of mutually coupled diode lasers have renewed the interest to dissect these experimetal findings with simple delay rate equations. We will review two novel cases. Diodes pumped close to threshold with long cavities and biased well above threshold with ultrashort cavities. When diode lasers are biased near threshold and subject to moderate optical feedback, low frequency fluctuations appear in their radio-frequency spectrum that are evident as dropout events in the intensity time traces. Traditionally these events were obseved to occur at sporadic time intervals. However, recent experimental measurements have shown that there are regions of the pumping current where these events appear at regular time intervals. The case of ultrashort cavities presents us with similar but ultimately more dramatic phenomena, such as periodic self pulsations and high speed oscillations. In addition, work on optical injection, for applications on bandwidth enhancement and optical generation of microwaves will be reviewed.
Special Joint Center for Fluid Mechanics and
Lefschetz Center for Dynamical Systems Seminar
University of Cincinnati | |
Abstract: Since instabilities in laminar shear channel flow can lead to transition to turbulence and the laminar flow is preferred in many applications, it is useful to design a control mechanism to suppress the instabilities to regulate the unstable or turbulent flow to or close to the laminar flow within a short time and then maintain it over time. Furthermore, the control should be designed in a way that its cost is minimized and it is robust with respect to time-delay, small changes of initial data and small perturbations, which are usually caused by sensors, actuators and processors.
The control of channel flow was previously considered by Speyer and coworkers, and Bewley and coworkers, who derived feedback laws based on linear optimal control, and implemented by wall--normal actuation. With an objective to achieve global Lyapunov stabilization, we arrive at a feedback law using tangential actuation (using teamed pairs of synthetic jets or rotating disks) and only local measurements of wall shear stress. This feedback is shown to guarantee global stability in at least $H^{2} $ norm, which by Sobolev's embedding theorem implies continuity in space and time of both the flow field and the control (as well as their convergence to the desired steady state). The theoretical results are limited to low values of Reynolds number, however, we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher. In addition, we present a time-delayed flow field and show how the delay affects the stability of the flow in the case of one space dimension.
Engineering Division Special Seminar
**Late Notice**
NASA Ames Center for Nanotechnology, Moffett Field, CA http://www.ipt.arc.nasa.gov | |
Abstract: Carbon nanotube (CNT) was discovered in the early 1990s and is an offspring of C60 (the fullerene or buckyball). CNT, depending on chirality and diameter, can be metallic or semiconductor and thus allows formation of metal-semiconductor and semiconductor-semiconductor junctions. CNT exhibits extraordinary electrical and mechanical properties and offers remarkable potential for revolutionary applications in electronics devices, computing and data storage technology, sensors, composites, storage of hydrogen or lithium for battery development, nanoelectromechanical systems (NEMS), and as tip in scanning probe microscopy (SPM) for imaging and nanolithography. Thus the CNT synthesis, characterization and applications touch upon all disciplines of science and engineering. We have significant work in progress in some of the above areas, particularly in growth, characterization, SPM applications, sensor development, molecular electronics and also, a strong computational nanotechnology program. This talk will discuss some recent results from the above efforts, NASA's needs and applications, and research challenges and opportunities ahead.
Brown University Center for Statistical Sciences Seminar
NIEHS, National Institute of Health | |
Abstract: Technologies are available for large scale analysis of DNA, mRNA, and protein. Such technologies offer new windows through which epidemiologists can examine susceptibility, exposure, and disease. The use of DNA for genotyping studies has increasingly become a mainstream activity in epidemiology. Current bottlenecks in both polymorphism discovery and in mass genotyping will be discussed, along with implications for epidemiology studies. Array technology for examining expression using mRNA appears to offer an important tool to molecular biology, and enthusiasm for this technique has drawn considerable speculation from epidemiologists on use in population-based studies. Such epidemiologic applications may be quite restricted because of cost, experimental limitations, and requirements for mRNA. The examination of proteins on a large scale basis has been problematic because of cumbersome techniques and has attracted little interest from epidemiologists. Emerging technologies in proteomics promise rapid inexpensive analysis of very small samples from population-based studies. Proteomics offers a number of advantages over mRNA expression and perhaps over genomic analyses. While the applications of proteomic approaches has yet to be widely tested and tempered by field studies, these approaches may provide the epidemiologist with a powerful new tool.
*Sponsored by the Brown University Faculty Lectures as part of the Statistical Methodology for Genetics: Recent Advances lecture series.
* This is a joint seminar with the Department of Community Health.
*Refreshments following seminar.
Brown Analysis Seminar
Applied Mathematics Colloquium
Scientific Computing Seminar
University of Delaware and INRIA. France | |
Abstract: The study of thin coatings is of special interest in many applications related to antennas or stealth technology (where these coatings are used, for example, as absorbants). We discuss in this talk the use of thin layer approximation, called effective boundary conditions, in electromagnetic (time dependent) scattering problems, to take into account the effect of these thin coatings.
The main motivation behind using these effective boundary conditions comes from numerical considerations. Roughly speaking, as the obtained approximate model is posed on the exterior domain (i.e. not including the thin layer), we eliminate the geometrical constraints for meshing. This reduces (especially for layers that are very thin compared with the wavelength of the incident wave) the size of the discrete model, and thus the time of computations.
We first consider the case where the coatings are formed by linear materials. We describe, through an asymptotic study, the formal derivation of the effective boundary conditions. We then discuss the stability in time of the new initial boundary value problems (we show for instance how high order conditions may be unstable and not efficient). The stability plays then a fundamental role in both the convergence study for the continuous model and the design of stable numerical schemes. We give in the last part a generalization to non linear coatings of ferromagnetic type, and some numerical examples in this case.
PDE Seminar
Department of Mathematics Colloquium
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