Details:
Speaker: Joseph C. (Joe) Majdalani, Auburn Alumni Professor & Chair Department of Aerospace Engineering
Title: On the Power of Perturbations
Abstract: This presentation explores the use of perturbation methods (or asymptotic approximation methods) as a powerful tool in mathematics, science, and engineering. The talk will introduce two new courses that have been cross-listed as MATH/AERO 5460/6460 (Perturbations I) and MATH/AERO 7460 (Perturbations II). The motivation for introducing these two courses is as follows. Many of the problems facing mathematicians, physicists, and engineers involve difficulties in solving nonlinear equations, transcendental equations, differential equations with variable coefficients, and nonlinear integral equations. Solutions to such problems are usually approximated using numerical techniques, analytical techniques, or combinations thereof. Foremost among analytical techniques are the systematic methods of perturbation theory, where a problem is linearized and solved approximately in terms of a small or a large parameter or coordinate. These mathematical techniques constitute an essential component of a student’s “toolbox” for reducing the complexity of mathematical problems before solving them. Some of the methods that will be surveyed include regular and singular perturbation techniques, method of ansatz, Lindstedt, PLK, and Pritulo, Matched-Asymptotic Expansions, Multiple Scales, WKB, Rayleigh-Janzen, Latta, van der Pol, Adomian Decomposition, and Homotopy Analysis Methods. At the end of this seminar, participants will gain a deeper appreciation of what perturbation methods are all about.
Biography: Dr. Majdalani serves as Professor and Chair of Aerospace Engineering at Auburn University. His research devotes itself to the theoretical and computational modeling of internal flow fields associated with injection and swirl-driven rocket systems. His interests include unsteady fluid mechanics, swirl combustion, high speed gas dynamics, instability, advanced rocket concepts, engine internal ballistics, and singular perturbation theory. His research activities since 1997 have materialized in over 235 publications. His work on helical flow modeling has led to the discovery of new Trkalian and Beltramian families of solutions to describe cyclonic motions in self-cooled liquid and hybrid rocket engines. His work on wave propagation has resulted in the development of a generalized-scaling technique in perturbation theory, and of a fully compressible framework for capturing both vorticoacoustic and biglobal stability waves in simulated rocket chambers. Recently, his work on compressible gas motions has required the development of a systematic procedure for modeling high speed flow problems. A total of eighteen thermofluid-related dimensionless parameters have been identified in the course of his research investigations.
Everyone is invited and encouraged to attend.
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