Title: Exploring atomistic energy landscapes via bifurcation theory and numerical continuation techniques

Abstract: Potential energy landscapes associated with atomistic modelling of matter are typically severely nonconvex and reflect the nonlinear and many-body nature of interactions between atoms/molecules. Many problems in computational chemistry, structural biology, materials science, and engineering can be solved by exploring the energy landscape -- the preferred configurations of atoms typically correspond to local minima of the energy, whereas transitions between such configurations are often determined by the properties of the saddle points in the vicinity of the corresponding local minima.</p>In this talk I will present how bifurcation theory and numerical continuation techniques can be used to gain sophisticated insight into atomistic energy landscapes. In particular I will showcase the use of such techniques in the context of capturing (i) energy barriers to crack propagation in crystalline materials; (ii) dislocation emission in surface-step systems; (iii) phase transitions in two-species vacancy systems. I will also discuss on-going work on employing deflation techniques in this context and on implementing such algorithms as a wrapper around the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), the go-to high-performance computing software for atomistic simulations.