On the Stability of Objective Structures

Abstract: We discuss the stability of objective structures of interacting atoms that form a far reaching generalization of crystal lattices. To this end, we use methods from harmonic analysis to set up a second derivative test of the configurational energy at equilibria, a key point being the identification of a carefully chosen seminorm with respect to which coercivity is estimated. In particular, a novel discrete Korn type inequality is established in the setting of objective structures. We also provide an efficient algorithm to check for atomistic stability which we illustrate numerically for a general carbon nanotube. (This is joint work with M. Steinbach, Augsburg)

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)