Some Problems in Simulation of the Thermodynamic Properties of Droplets

Modeling of a nanocylinder

“…The model kinetic energy in (1) is a classical analog of the exchange energy in the Heisenberg model for the two-dimensional space at the continuum approximation [21], which in our case corresponds to the infinite cylinder model [21,22]. In this case, the kinetic energy in (1) coincides in form with the kinetic energy of the particle (in cylindrical coordinates).…”

“…We consider a case of the application theory [21][22][23], where nanoparticles have the form of a long cylinder. We used a cylindrical coordinate system for which the characteristic spin function [21,22] is represented by angle function (r) about the cylinder axis z.…”

“…The free energy in this model can have the following form [21,22]: (1) where (r) is the angle between the cylinder axis and the magnetization vector; r is the radial coordinate, and k 1 is the second anisotropy constant.…”

“…In this case, the kinetic energy in (1) coincides in form with the kinetic energy of the particle (in cylindrical coordinates). This fact is not casual because the model under consideration permits exact analytical solutions in the form of quasi-particles (nonlinear waves), which are referred to as instantons (or skyrmions [21,22]). Note that, in our case, these quasi-particles are topological compositions, rather than dynamic particles.…”

“…Below, we will consider a new theory [21][22][23][24] that takes into account the cylindrical shape and the intermediate phase. Moreover, the size of the intermediate phase can be arbitrary.…”