@article{201031,
  author = {Priya Subramanian and I. G. Kevrekidis and P. G. Kevrekidis},
  title = {Exploring critical points of energy landscapes: From low-dimensional examples to phase field crystal PDEs},
  abstract = { In the present work we explore the application of a few root-finding methods to a series of prototypical examples. The methods we consider include: (a) the so-called continuous-time Nesterov (CTN) flow method; (b) a variant thereof referred to as the squared-operator method (SOM); and (c) the joint action of each of the above two methods with the so-called deflation method. More {\textquotedblleft}traditional{\textquotedblright} methods such as Newton{\textquoteright}s method (and its variant with deflation) are also brought to bear. Our toy examples start with a naive one degree-of-freedom (DOF) system to provide the lay of the land. Subsequently, we turn to a 2-DOF system that is motivated by the reduction of an infinite-dimensional, phase field crystal (PFC) model of soft matter crystallisation. Once the landscape of the 2-DOF system has been elucidated, we turn to the full PDE model and illustrate how the insights of the low-dimensional examples lead to novel solutions at the PDE level that are of relevance and interest to the full framework of soft matter crystallisation. },
  year = {2021},
  journal = {Communications in Nonlinear Science and Numerical Simulation },
  volume = {96},
  url = {http://dx.doi.org/10.1016/j.cnsns.2020.105679},
  language = {eng},
}