Investigation of symmetric non-spherical particle shapes by applying low-resolution spherical harmonics

Abstract

The issue of mathematical modelling of non-spherical shapes of particles is considered. Thus, application of the spherical harmonics (SH) technique in modelling the simplest symmetric star-shaped particles is demonstrated by applying low-resolution functions. The investigation was restricted to a circular cylinder and a rectangular parallelepiped, geometrically primitive, but widespread oblate industrial shapes. The modelling quality was studied by considering selected error norms and the most important integral characteristics of a particle geometry, including the surface area and volume. The presented results discovered new features of the spherical harmonic technique and enhanced understanding of their applicability to describe non-spherical shapes.

Keywords

• low-resolution spherical harmonics
• symmetric star-shaped particles
• circular cylinder
• rectangular parallelepiped