5 research outputs found
Localization behavior of vibrational modes in granular packings
We study the localization of vibrational modes of frictionless granular
media. We introduce a new method, motivated by earlier work on non-Hermitian
quantum problems, which works well both in the localized regime where the
localization length is much less than the linear size and in the
regime grater or of order when modes are extended throughout our
finite system. Our very lowest frequency modes show "quasi-localized"
resonances away from the jamming point; the spatial extent of these regions
increases as the jamming point is approached, as expected theoretically.
Throughout the remaining frequency range, our data show no signature of the
nearness of the jamming point and collapse well when properly rescaled with the
system size. Using Random Matrix Theory we derive the scaling relation ~
for the regime >> in dimensions.Comment: 6 pages, 7 figure
Heat transport in model jammed solids
We calculate numerically the normal modes of vibrations in 3D jammed packings
of soft spheres as a function of the packing fraction and obtain the energy
diffusivity, a spectral measure of transport that controls sound propagation
and thermal conductivity. The crossover frequency between weak and strong
phonon scattering is controlled by the coordination and shifts to zero as the
system is decompressed towards the critical packing fraction at which rigidity
is lost. Below the crossover, the diffusivity displays a power-law divergence
with inverse frequency, which suggests that the vibrational modes are primarily
transverse waves, weakly scattered by disorder. Above it, a large number of
modes appear whose diffusivity plateaus at a nearly constant value independent
of the inter-particle potential, before dropping to zero above the Anderson
localization frequency. The thermal conductivity of a marginally jammed solid
just above the rigidity threshold is calculated and related to the one measured
experimentally at room temperature for most glasses.Comment: 15 pages, 7 figure
Critical jamming of frictional grains in the generalized isostaticity picture
While frictionless spheres at jamming are isostatic, frictional spheres at
jamming are not. As a result, frictional spheres near jamming do not
necessarily exhibit an excess of soft modes. However, a generalized form of
isostaticity can be introduced if fully mobilized contacts at the Coulomb
friction threshold are considered as slipping contacts. We show here that, in
this framework, the vibrational density of states (DOS) of frictional discs
exhibits a plateau when the generalized isostaticity line is approached. The
crossover frequency to elastic behavior scales linearly with the distance from
this line. Moreover, we show that the frictionless limit, which appears
singular when fully mobilized contacts are treated elastically, becomes smooth
when fully mobilized contacts are allowed to slip.Comment: 4 pages, 4 figures, submitted to PR