157 research outputs found
Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic
We perform extensive computational studies of two-dimensional static
bidisperse disk packings using two distinct packing-generation protocols. The
first involves thermally quenching equilibrated liquid configurations to zero
temperature over a range of thermal quench rates and initial packing
fractions followed by compression and decompression in small steps to reach
packing fractions at jamming onset. For the second, we seed the system
with initial configurations that promote micro- and macrophase-separated
packings followed by compression and decompression to . We find that
amorphous, isostatic packings exist over a finite range of packing fractions
from in the large-system limit,
with . In agreement with previous calculations,
we obtain for , where is the rate
above which is insensitive to rate. We further compare the structural
and mechanical properties of isostatic versus hyperstatic packings. The
structural characterizations include the contact number, bond orientational
order, and mixing ratios of the large and small particles. We find that the
isostatic packings are positionally and compositionally disordered, whereas
bond-orientational and compositional order increase with contact number for
hyperstatic packings. In addition, we calculate the static shear modulus and
normal mode frequencies of the static packings to understand the extent to
which the mechanical properties of amorphous, isostatic packings are different
from partially ordered packings. We find that the mechanical properties of the
packings change continuously as the contact number increases from isostatic to
hyperstatic.Comment: 11 pages, 15 figure
Rods are less fragile than spheres: Structural relaxation in dense liquids composed of anisotropic particles
We perform extensive molecular dynamics simulations of dense liquids composed
of bidisperse dimer- and ellipse-shaped particles in 2D that interact via
repulsive contact forces. We measure the structural relaxation times obtained
from the long-time decay of the self-part of the intermediate scattering
function for the translational and rotational degrees of freedom (DOF) as a
function of packing fraction \phi, temperature T, and aspect ratio \alpha. We
are able to collapse the \phi and T-dependent structural relaxation times for
disks, and dimers and ellipses over a wide range of \alpha, onto a universal
scaling function {\cal F}_{\pm}(|\phi-\phi_0|,T,\alpha), which is similar to
that employed in previous studies of dense liquids composed of purely repulsive
spherical particles in 3D. {\cal F_{\pm}} for both the translational and
rotational DOF are characterized by the \alpha-dependent scaling exponents \mu
and \delta and packing fraction \phi_0(\alpha) that signals the crossover in
the scaling form {\cal F}_{\pm} from hard-particle dynamics to super-Arrhenius
behavior for each aspect ratio. We find that the fragility at \phi_0,
m(\phi_0), decreases monotonically with increasing aspect ratio for both
ellipses and dimers. Moreover, the results for the slow dynamics of dense
liquids composed of dimer- and ellipse-shaped particles are qualitatively the
same, despite the fact that zero-temperature static packings of dimers are
isostatic, while static packings of ellipses are hypostatic.Comment: 10 pages, 17 figures, and 1 tabl
Constraints and vibrations in static packings of ellipsoidal particles
We numerically investigate the mechanical properties of static packings of
ellipsoidal particles in 2D and 3D over a range of aspect ratio and compression
. While amorphous packings of spherical particles at jamming onset
() are isostatic and possess the minimum contact number required for them to be collectively jammed, amorphous packings of
ellipsoidal particles generally possess fewer contacts than expected for
collective jamming () 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 for static packings of ellipsoidal particles into two
important components: the stiffness and stress matrices. We find that
the stiffness matrix possesses eigenmodes
with zero eigenvalues even at finite compression, where is the number of
particles. In addition, these modes are nearly eigenvectors of the
dynamical matrix with eigenvalues that scale as , 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 for perturbations by amplitude
along these `quartic' modes, . These findings illustrate
the significant differences between static packings of spherical and
ellipsoidal particles.Comment: 18 pages, 21 figure
Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles
We study the structural and mechanical properties of jammed ellipse packings,
and find that the nature of the jamming transition in these systems is
fundamentally different from that for spherical particles. Ellipse packings are
generically hypostatic with more degrees of freedom than constraints. The
spectra of low energy excitations possess two gaps and three distinct branches
over a range of aspect ratios. In the zero compression limit, the energy of the
modes in the lowest branch increases {\it quartically} with deformation
amplitude, and the density of states possesses a -function at zero
frequency. We identify scaling relations that collapse the low-frequency part
of the spectra for different aspect ratios. Finally, we find that the degree of
hypostaticity is determined by the number of quartic modes of the packing.Comment: 4 pages, 4 figure
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