Energy simulations for some optic systems: the Heisenberg ferromagnetic and the recursive vortex filament approximations

Abstract

In this study, we obtain the energy equations for some optical systems with q-frame in 3D Euclidean space. Here, first of all, we create the theoretical background for the energy equations defined with the help of biharmonic maps. In this way, we obtain the energy equation of a vector field on a surface represented by the arc-length and time parameters. Next, we geometrically express the energy equation of a magnetic flux in a ferromagnetic media and the energy equation of a recursive flow making a vortex filament flow. For this, we make use of the vortex filament (Da Rios) equation and Heisenberg ferromagnetic (f-magnetic) spin chain equation. These equations are important equations of non-linear optic systems and have significant contributions to field such as ferromagnetism, spin wave theory, fluid dynamics, magnetic flows. Finally, we plot the energy simulations we obtained for the ferromagnetic Heisenberg model and the recursive vortex filament model.