Seminars

Introduction to Homogenization Theory I, II

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Ying-Hong Liu

2008-09-26
12:30:00 - 14:30:00

Introduction to Homogenization Theory I, II

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

With the development of the modern technique, we have ability to construct the composite material needed in the environment. Usually, these devices are weaved in the micro- or nano-scales and they satisfy the inhomogeneous electromagnetic or elastic wave equations. However, for our human sensors, we always investigate them in the long wavelength or in the low frequency limit, mathematically, that means averaged governing equations describe the bulk behaviors of the composite system in the macro-scale. Therefore, how to carry out the transformation from the inhomogeneous to homogeneous governing equations is the main issue we want to address. In this talk, we start with one-dimensional elastodynamics and then introduce the typical procedure of homogenization analysis. In addition, several examples would be addressed: Darcy’s law, heat conduction in a composite and other applications.