Constraints and vibrations in static packings of ellipsoidal particles.

We numerically investigate the mechanical properties of static packings of frictionless ellipsoidal particles in two and three dimensions over a range of aspect ratio and compression A0. While amorphous packings of spherical particles at jamming onset (A<¡> = 0) are isostatic and possess the minimum contact number ziso required for them to be collectively jammed, amorphous packings of ellipsoidal particles generally possess fewer contacts than expected for collective jamming (z < z¡s0) from naive counting arguments, which assume that all contacts give rise to linearly independent constraints on interparticle separations. To understand this behavior, we decompose the dynamical matrix M --H -- S for static packings of ellipsoidal particles into two important components: the stiffness H and stress 5 matrices. We find that the stiffness matrix possesses 2Ar(z¡S0 -- z) eigenmodes êo with zero eigenvalues even at finite compression, where N is the number of particles. In addition, these modes êo are nearly eigenvectors of the dynamical matrix with eigenvalues that scale as A0, and thus finite compression stabilizes packings of ellipsoidal particles. At jamming onset, the harmonic response of static packings of ellipsoidal particles vanishes, and the total potential energy scales as á4 for perturbations by amplitude S along these "quartic" modes, ê0. These findings illustrate the significant differences between static packings of spherical and ellipsoidal particles. [ABSTRACT FROM AUTHOR]