title: Communication: Newton homotopies for sampling stationary points of potential energy landscapes.
abstract: One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they all exhibit characteristic problems. Moreover, traditional methods can break down if the system contains singular solutions. Here, we propose an efficient implementation of Newton homotopies, which can sample a large number of the stationary points of complicated many-body potentials. We demonstrate how the procedure works by applying it to the nearest-neighbor ϕ(4) model and atomic clusters.
authors.affiliation: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556, USA.
authors.forename: Dhagash
authors.initials: D
authors.lastname: Mehta
authors.affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48823, USA.
authors.forename: Tianran
authors.initials: T
authors.lastname: Chen
authors.affiliation: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556, USA.
authors.forename: Jonathan D
authors.initials: JD
authors.lastname: Hauenstein
authors.affiliation: University Chemical Laboratory, The University of Cambridge, Cambridge CB2 1EW, United Kingdom.
authors.forename: David J
authors.initials: DJ
authors.lastname: Wales
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D015999:Multivariate Analysis; D017711:Nonlinear Dynamics