STABILITY PROPERTIES OF 1-DIMENSIONAL HAMILTONIAN LATTICES WITH NON-ANALYTIC POTENTIALS
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Date
2020
Authors
Bountis, Anastasios
Kaloudis, Konstantinos
Oikonomou, Thomas
Manda, Bertin Many
Skokos, Charalampos
Journal Title
Journal ISSN
Volume Title
Publisher
arxiv
Abstract
We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices
whose inter-particle forces are derived from non-analytic potentials. In particular, we study the
dynamics of a model governed by a “graphene-type” force law and one inspired by Hollomon’s
law describing “work-hardening” effects in certain elastic materials. Our main aim is to show
that, although similarities with the analytic case exist, some of the local and global stability
properties of non-analytic potentials are very different than those encountered in systems with
polynomial interactions, as in the case of 1D Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Our
approach is to study the motion in the neighborhood of simple periodic orbits representing
continuations of normal modes of the corresponding linear system, as the number of particles
N
and the total energy
E are increased. We find that the graphene-type model is remarkably stable
up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks,
yet is unstable at low energies and only attains stability at energies where the harmonic force
becomes dominant. We suggest that, since our results hold for larg
e
N, it would be interesting
to study analogous phenomena in the continuum limit where 1D lattices become strings.
Description
Keywords
Type of access: Open Access, Hamiltonian system, non-analytic potential, simple periodic orbits, stable and unstable dynamics, local and global
Citation
Bountis, A., Kaloudis, K., Oikonomou, T., Manda, B. M., & Skokos, C. (2020). Stability Properties of 1-Dimensional Hamiltonian Lattices with Nonanalytic Potentials. International Journal of Bifurcation and Chaos, 30(15), 2030047. https://doi.org/10.1142/s0218127420300475