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 ϕ4 model and atomic clusters.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 28, 2014
- Source ID
- 10.1063/1.4896657
Entities
People
- David John Wales
- Dhagash Mehta
- Jonathan D Hauenstein
- Tianran Chen
Organizations
- Defense Advanced Research Projects Agency
- Michigan State University
- University of Cambridge
- University of Notre Dame