Elastic magnetic curves of ferromagnetic and superparamagnetic models

Abstract

In this paper, new energy functionals are described via the variational approach method. By doing this, a new class of elastic curves is described in the three-dimensional ordinary space. An alternative method is also investigated to compute critical points of the bending energy functionals acting on a class of magnetic curves. Then, classifications of these critical curves are presented as elastic magnetic curves of the Frenet-Serret vectors family. Moreover, the dynamics of the elastic magnetic curves of ferromagnetic and superparamagnetic models are discussed with their numerical and analytical analysis.