ITLApplied  Computational Mathematics Division
ACMD Seminar Series
Attractive Image NIST

Beyond the Spherical Cow: A New Approach to Modeling Physical Quantities for Objects of Arbitrary Shape

Marc De Graef
Carnegie Mellon University, Department of Materials Science and Engineering

Wednesday, April 27, 2005 15:00-16:00,
NIST North (820), Room 145
Wednesday, April 27, 2005 13:00-14:00,
Room 4550

Abstract: Many physical properties depend on the details of the shape of an object. Such shape functionals include the moment-of-inertia tensor, the demagnetization tensor, gravitational and electrostatic fields, and so on. Often, the shape of an object is taken into account in the form of integration boundaries, and this severely limits the range of object shapes that can be explicitly considered. Often, the sphere is the only shape for which an analytical expression can be obtained. In this presentation we will introduce a new theoretical tool for the computation of shape-dependent physical quantities: the shape function. After describing some of the intrinsic properties of this function, we will illustrate its use with examples taken mostly from magnetism. We will derive the demagnetization tensor field for a particle of arbitrary shape, and derive from it an expression for the interaction energy between two particles of arbitrary shape. Other examples covered will include the gravitational field and the moment-of-inertia tensor. We will conclude this talk with more general considerations on the applicability range of the shape function concept.

Speaker Bio: Professor De Graef received his PhD in Physics from the Catholic University of Leuven, Belgium, in 1989, with a thesis on copper-based shape memory alloys. He subsequently joined Carnegie Mellon University in 1993. Professor De Graef's research interests lie in the area of microstructural characterization of structural intermetallics and magnetic materials. His current focus is on the development of experimental and modeling techniques for the quantitative study of magnetic domain configurations in a variety of materials, including ferromagnetic shape memory alloys, magnetic thin films, and patterned structures. This study includes a theoretical analysis of the use of shape functions in the computation of shape-dependent material properties.

Presentation Slides: PDF

Contact: P. M. Ketcham

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

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