Publications in Scientific Journals:

A. Iuorio, C. Kuehn, P. Szmolyan:
"Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem";
Discrete And Continuous Dynamical Systems-Series S, 13 (2020), 4; 1269 - 1290.

English abstract:
We investigate a singularly perturbed, non-convex variational problem arising in material science with a combination of geometrical and numerical methods. Our starting point is a work by Stefan Müller, where it is proven that the solutions of the variational problem are periodic and exhibit a complicated multi-scale structure. In order to get more insight into the rich solution structure, we transform the corresponding Euler-Lagrange equation into a Hamiltonian system of first order ODEs and then use geometric singular perturbation theory to study its periodic solutions. Based on the geometric analysis we construct an initial periodic orbit to start numerical continuation of periodic orbits with respect to the key parameters. This allows us to observe the influence of the parameters on the behavior of the orbits and to study their interplay in the minimization process. Our results confirm previous analytical results such as the asymptotics of the period of minimizers predicted by Müller. Furthermore, we find several new structures in the entire space of admissible periodic orbits.

Microstructure, Euler-Lagrange equation, singular perturbation, saddle-type slow manifolds, numerical continuation

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.