Elastic magnetic curves of ferromagnetic and superparamagnetic models

We are interested in defining new energy functionals and solving them by using the variational approach method. That is, we aim to define a new class of elastic curves in the three-dimensional ordinary space. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves. Then, we classify these critical curves as elastic magnetic curves of the Frenet-Serret vector family. Moreover, we investigate the dynamics of the elastic magnetic curves of ferromagnetic and superparamagnetic models and discuss their numerical and analytical analysis.