Glimm has made outstanding contributions to shock wave theory, in which mathematical models are developed to explain natural phenomena that involve intense compression, such as air pressure in sonic booms, crust displacement in earthquakes, and density of material in volcanic eruptions and other explosions. He also has been a leading theorist in operator algebras, partial differential equations, mathematical physics, applied mathematics, and quantum statistical mechanics.
The changing status of knowledge from descriptive to analytic, from empirical to theoretical and from intuitive to mathematical has to be one of the most striking adventures of the human spirit. The changes often occur in small steps and can be lost from view. In this lecture we will review vignettes drawn from the speaker's personal knowledge that illustrate this transformation in thinking. Examples include not only the traditional areas of physics and engineering, but also newer topics, as in biology and medicine, in the social sciences, in commerce, and in the arts. We also review some of the forces driving these changes, which ultimately have a profound effect on the organization of human life.
New technologies have been introduced into the front tracking method to improve its performance in extreme applications, those dominated by a high density of interfacial area. New mathematical theories have been developed to understand the meaning of numerical convergence in this regime. In view of the scientific difficulties of such problems, careful verifaction, validation and uncertainty quantification studies have been conducted. A number of interface dominated flows occur within practical problems of high consequence, and in these cases, we are able to contribute to ongoing scientific studies. We include here turbulent mixing and combustion, chemical processing, design of high energy accelerators, nuclear fusion related studies, studies of nuclear power reactors and studies of flow in porous media. In this lecture, we will review some of the above topics.
During his visit, Dr. Glimm's schedule is open for meetings. All meetings with Dr. Glimm will be in Skiles 263 unless specified otherwise. You can schedule a meeting with him by locating "Glimm" as a resource in the campus Zimbra calendar system at my.gatech.edu. This may be slightly less convenient for Math users, but it allows others on campus to meet with him, too. Detailed instructions for School of Math users are available as an internal FAQ.
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