Variational methods in Material Science
timetable:
Tue 10 Oct, 17:30 - 18:25, Aula Dini
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seminar: Minimum energy configurations of classical charges
speaker: Gero Friesecke (University of Warwick)abstract: We study minimum energy configurations of $N$ particles in $\R3$ of charge $-1$ (`electrons') in the potential of $M$ particles of charges $Z\alpha>0$ ('atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron distribution explicitly, showing in particular that the number of electrons surrounding each nucleus is asymptotic to the nuclear charge ("screening''). The proof proceeds by establishing, via Gamma-convergence, a coarse-grained variational principle for the limit distribution, which can be solved explicitly. (Joint work with Stephane Capet.) As an application, we give a simple proof of the celebrated Dyson-Lenard theorem in quantum mechanics
timetable:
Tue 10 Oct, 17:30 - 18:25, Aula Dini
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