Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Analysis-Seminar Augsburg-München

 

Dr. Leonard Kreutz
Universität Wien

 
spricht am
 
Donnerstag, 13. Dezember 2018
 
um
 
17:30 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Finite crystallization for ionic dimers«

Abstract:
In this talk we will present some crystallization results of ionic dimers. In partic- ular we consider nite discrete systems consisting of two di erent atomic types and investigate ground-state con gurations for con gurational energies featuring two- body short-ranged particle interactions. The atomic potentials favor some reference distance between di erent atomic types and include repulsive terms for atoms of the same type, which are typical assumptions in models for ionic dimers. Our goal is to show a two-dimensional crystallization result. More precisely, we give conditions in order to prove that energy minimizers are connected subsets of the hexagonal lattice where the two atomic types are alternately arranged in the crystal lattice. We also provide explicit formulas for the ground-state energy. Finally, we charac- terize the net charge, that means, the di erence of the number of the two atomic types. Analyzing the deviation of con gurations from the hexagonal Wul shape, we prove that for ground states consisting of n particles the net charge is at most of order O(n 1/4) where the scaling is sharp.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Bernd Schmidt
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



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