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Thomas Stelson Lecture Series

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Now showing 1 - 4 of 4
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    How Quantum Theory and Statistical Mechanics Gave a Polynomial of Knots
    (Georgia Institute of Technology, 2014-09-25) Jones, Vaughan
    We will see how a result in von Neumann algebras (a theory developed by von Neumann to give the mathematical framework for quantum physics) gave rise, rather serendipitously, to an elementary but very useful invariant in the theory of ordinary knots in three dimensional space. Then we'll look at some subsequent developments of the theory, and talk about a thorny problem which remains open.
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    Riemann, Boltzmann and Kantorovich Go to a Party
    (Georgia Institute of Technology, 2013-04-19) Villani, Cedric
    This talk is the story of an encounter of three distinct fields: non-Euclidean geometry, gas dynamics and economics. Some of the most fundamental mathematical tools behind these theories appear to have a close connection, which was revealed around the turn of the 21st century, and has developed strikingly since then.
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    Role of Mathematics Across Science and Beyond
    (Georgia Institute of Technology, 2010-11-22) Glimm, James
    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.
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    Multiscale Modeling and Simulation: The Interplay Beween Mathematics and Engineering Applications
    (Georgia Institute of Technology, 2009-10-26) Hou, Thomas Y.
    Many problems of fundamental and practical importance contain multiple scale solutions. Composite and nano materials, flow and transport in heterogeneous porous media, and turbulent flow are examples of this type. Direct numerical simulations of these multiscale problems are extremely difficult due to the wide range of length scales in the underlying physical problems. Direct numerical simulations using a fine grid are very expensive. Developing effective multiscale methods that can capture accurately the large scale solution on a coarse grid has become essential in many engineering applications. In this talk, I will use two examples to illustrate how multiscale mathematics analysis can impact engineering applications. The first example is to develop multiscale computational methods to upscale multi-phase flows in strongly heterogeneous porous media. Multi-phase flows arise in many applications, ranging from petroleum engineering, contaminant transport, and fluid dynamics applications. Multiscale computational methods guided by multiscale analysis have already been adopted by the industry in their flow simulators. In the second example, we will show how to develop a systematic multiscale analysis for incompressible flows in three space dimensions. Deriving a reliable turbulent model has a significant impact in many engineering applications, including the aircraft design. This is known to be an extremely challenging problem. So far, most of the existing turbulent models are based on heuristic closure assumption and involve unknown parameters which need to be fitted by experimental data. We will show that how multiscale analysis can be used to develop a systematic multiscale method that does not involve any closure assumption and there are no adjustable parameters.