University of Heidelberg, Applied Analysis Seminar
Thu 28.04.2016
14:15, posted in Applied Analysis
Laurent Bétermin (Institut für Angewandte Mathematik, Heidelberg)
Theta functions and minimization of interaction energies
INF 205, SR1
At the microscopic scale, most crystals are composed of atoms which are arranged on a periodic lattice, which can be viewed as a minimizer of a certain interaction energy. The goal of this talk is to explain how to minimize some energies per particle among Bravais lattices of R^2, when the interaction potential is long-range. By using a result of Montgomery about theta functions, we will show several properties of optimality and non-optimality of the triangular lattice for these energies, with or without a density constraint. This talk is partially based on a joint work with Peng Zhang (Shanghai Jiao Tong University).

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