Calculus of Variations and Geometric Measure Theory

G. Lazzaroni - U. Stefanelli

Chain-like ground states in three dimensions

created by lazzaroni on 04 May 2017
modified on 22 Nov 2018


Published Paper

Inserted: 4 may 2017
Last Updated: 22 nov 2018

Journal: Transactions of Mathematics and Its Applications
Volume: 2
Pages: 1-22
Year: 2018
Links: Journal website


We investigate the minimization of configurational energies of Brenner type. These include two- and three-body interaction terms which favor the alignment of first neighbors. In particular, such configurational energies arise in connection with the molecular-mechanical modeling of covalent $sp$-bonding in carbon.

Ground states in three dimensions are characterized and the stability of chains and rings is discussed. The interaction energy is then augmented with terms corresponding to weaker interactions favoring the stratification of configurations. This gives rise to stratified structures which are reminiscent of nanoscrolls and multi-wall nanotubes. Optimal stratified configurations are identified and their geometry is discussed.