Table 1.

Definitions of Shape Functions in Terms of Eigenvalues of the Gyration Tensor G

Shape Function	Definition
Asphericity (55,65)	B = $\langle {\lambda }_3^2\rangle -\frac{1}{2}\left[\langle {\lambda }_1^2\rangle +\langle {\lambda }_2^2\rangle \right]$ (7)
Acylindricity (55,65)	C = $\langle {\lambda }_2^2\rangle -\langle {\lambda }_1^2\rangle$ (8)
Degree of prolateness (52,56,65)	S = $\frac{\langle \left(3{\lambda }_1^2-I_1\right)\left(3{\lambda }_2^2-I_1\right)\left(3{\lambda }_3^2-I_1\right)\rangle }{\langle {\left(I_1\right)}^3\rangle }$ (9)
Relative shape anisotropy (52,55,56,65)	κ2 = 1 − 3$\frac{\langle I_2\rangle }{\langle I_1^2\rangle }$ (10)

Note that I₁ = ${\lambda }_1^2+{\lambda }_2^2+{\lambda }_3^2$ and I₂ = ${\lambda }_1^2{\lambda }_2^2+{\lambda }_2^2{\lambda }_3^2+{\lambda }_3^2{\lambda }_1^2$ are invariants of G.