Using Cylindrical and Spherical Symmetries in Numerical Simulations of Quasi-Infinite Mechanical Systems

The application of cylindrical and spherical symmetries for numerical studies of many-body problems is presented. It is shown that periodic boundary conditions corresponding to formally cylindrical symmetry allow for reducing the problem of a huge number of interacting particles, minimizing the effect of boundary conditions, and obtaining reasonably correct results from a practical point of view. A physically realizable cylindrical configuration is also studied. The advantages and disadvantages of symmetric realizations are discussed. Finally, spherical symmetry, which naturally realizes a three-dimensional system without boundaries on its two-dimensional surface, is studied. As an example, tectonic dynamics are considered, and interesting patterns resembling real ones are found. It is stressed that perturbations of the axis of planet rotation may be responsible for the formation of such patterns.

Automated summary

This article presents the application of cylindrical and spherical symmetries in numerical studies of many-body problems. The use of periodic boundary conditions with cylindrical symmetry is shown to effectively reduce the influence of boundary conditions and obtain reasonably accurate results. A physically realizable cylindrical configuration is also explored. The advantages and disadvantages of symmetric realizations are discussed. Furthermore, the article investigates the use of spherical symmetry, which eliminates boundaries in a three-dimensional system. Using tectonic dynamics as an example, interesting patterns resembling real structures are found, emphasizing the potential role of perturbations in the planet's axis of rotation in their formation.