School Seminars and Colloquia

Discrete Minimal Energy Problems


by Professor Edward B. Saff

Institution: Vanderbilt University
Date: Tue 15th March 2011
Time: 12:00 PM
Location: Russell Love Theatre

Abstract: For a closed and bounded surface A in 3-space (or higher dimensional
space), such as a sphere or torus, we analyze the behavior (for large N)
of N-point equilibrium configurations on A for the potential (1/r)^s,
where s>0 is a parameter and r denotes Euclidean distance between points.
(The case s=1 corresponds to the familiar Coulomb potential, while large s
corresponds (in the limit) to best-packing.) If d=dim(A) and s of long range interactions), the analysis of such points falls under the
umbrella of classical potential theory and is a consequence of the
continuous theory.
But what if s>d or s=d ? In such cases, the classical theory does not
apply and new techniques are needed to analyze the behavior of minimal
energy configurations. We shall describe these techniques, which also
yield information about "best-packing points" on A. The research
has relevance to the study of self-assembling materials and has
extensions to higher dimensions. Many graphical illustrations
help to make this introductory talk accessible to students as well as to
the general science faculty.

Colloquium Website