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DTSTART;TZID=America/Los_Angeles:20201109T150000
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SUMMARY:Applied Math Seminar: Multiscale analysis and high-order schemes for nonlinear multilevel Maxwell-Bloch equations given by Prof. Qing Xia (Rensselaer Polytechnic Institute)
DESCRIPTION:In this talk\, we will present a recent study of the\nMaxwell-Bloch equations that model the nonlinear interactions of light and\nmatter\, where the light is modeled classically by the Maxwell’s equations\nwith dispersions and the medium is modeled quantum-mechanically by the\nmultilevel rate equations. We will show the connection between rate\nequations and the density matrix\, where the former formulation is widely\nused in the engineering community and the latter in the Physics\nliterature. A multiscale analysis of the Maxwell-Bloch equations based on\nasymptotic expansions will also be discussed. The resulting reduced\nenvelope equations (or slow equations) capture amplitude dynamics of the\nunderlying solutions accurately and efficiently. In addition\, we will talk\nabout high-order accurate numerical schemes based on finite difference\napproximations in space and modified equation approach in time. The\nproposed schemes allow point-wise update of the solutions for both single\ndomains and domains with material interfaces\, thus enabling superb\nparallelism for arbitrary geometry. This is joint work with A. V.\nKildishev and L. J. Prokopeva from Purdue’s Birck Nanotechnology Center\,\nand J. W. Banks\, W. D. Henshaw\, G. Kovacic and D. W. Schwendeman from RPI.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-give-by-prof-qing-xia-rensselaer-polytechnic-institute/
LOCATION:Zoom
CATEGORIES:Applied Math Seminar
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