Micromorphology characterization and reconstruction of sand particles using micro X-ray tomography and spherical harmonics

Determining the shape of agricultural materials using spherical harmonics

“…Therefore, a mathematically consistent description involves not only surface values, but also their derivatives. Expressions for the curvature, surface constants, and required derivatives in spherical coordinates are given in (Poelaert et al, 2011 andZhou et al, 2015). Furthermore, description of the sequence of an entire process using SHM is given in Garboczi (2002) and Feinauer et al (2015).…”

“…As the development of SHM for its application in DEM is still in progress, the number of direct contributions that use SHM in DEM is limited (Garboczi, 2011;Garboczi and Bullard, 2013;Zhou et al, 2015). In this regard, two strategies can be followed to incorporate SHM into DEM codes: (1) development of shape-independent universal models with the use of continuous function representations (CFR) to analytically describe real shapes (Lu et al, 2012), or (2) development of shape-specific DEM models such as a sphero-polyhedrals or MS using approximated SH expressions.…”

“…The earliest studies using spherical harmonics focused on concrete (Garboczi, 2002), with successful 3D applications of sophisticated spherical harmonics to represent lunar regolith (Garboczi, 2011) and sand (Liu et al, 2011;Zhou et al, 2015) particles. There have been several studies using spherical harmonics, although none, to the best of our knowledge, have considered the field of agriculture.…”

Structural characterization of particle systems using spherical harmonics

“…Spherical harmonics have proven to be a valuable tool for the representation of particles [20,21]. The exact shape of a particle is represented as a combination of objects with growing roughness, the spherical harmonic functions.…”

Application of spherical harmonics analysis on LBS particles and LBS fragments

“…The second objective is to randomly generate shapes for numerical simulation models. Fourier transformation and spherical harmonics method could mathematically reconstruct and randomly generate particle shapes in two-dimension and three-dimension, respectively [5,6].…”