3,290 research outputs found
Effects of compression on the vibrational modes of marginally jammed solids
Glasses have a large excess of low-frequency vibrational modes in comparison
with most crystalline solids. We show that such a feature is a necessary
consequence of the weak connectivity of the solid, and that the frequency of
modes in excess is very sensitive to the pressure. We analyze in particular two
systems whose density D(w) of vibrational modes of angular frequency w display
scaling behaviors with the packing fraction: (i) simulations of jammed packings
of particles interacting through finite-range, purely repulsive potentials,
comprised of weakly compressed spheres at zero temperature and (ii) a system
with the same network of contacts, but where the force between any particles in
contact (and therefore the total pressure) is set to zero. We account in the
two cases for the observed a) convergence of D(w) toward a non-zero constant as
w goes to 0, b) appearance of a low-frequency cutoff w*, and c) power-law
increase of w* with compression. Differences between these two systems occur at
lower frequency. The density of states of the modified system displays an
abrupt plateau that appears at w*, below which we expect the system to behave
as a normal, continuous, elastic body. In the unmodified system, the pressure
lowers the frequency of the modes in excess. The requirement of stability
despite the destabilizing effect of pressure yields a lower bound on the number
of extra contact per particle dz: dz > p^(1/2), which generalizes the Maxwell
criterion for rigidity when pressure is present. This scaling behavior is
observed in the simulations. We finally discuss how the cooling procedure can
affect the microscopic structure and the density of normal modes.Comment: 13 pages, 8 figure
Inhomogeneous elastic response of silica glass
Using large scale molecular dynamics simulations we investigate the
properties of the {\em non-affine} displacement field induced by macroscopic
uniaxial deformation of amorphous silica,a strong glass according to Angell's
classification. We demonstrate the existence of a length scale
characterizing the correlations of this field (corresponding to a volume of
about 1000 atoms), and compare its structure to the one observed in a standard
fragile model glass. The "Boson-peak'' anomaly of the density of states can be
traced back in both cases to elastic inhomogeneities on wavelengths smaller
than , where classical continuum elasticity becomes simply unapplicable
A Ball in a Groove
We study the static equilibrium of an elastic sphere held in a rigid groove
by gravity and frictional contacts, as determined by contact mechanics. As a
function of the opening angle of the groove and the tilt of the groove with
respect to the vertical, we identify two regimes of static equilibrium for the
ball. In the first of these, at large opening angle or low tilt, the ball rolls
at both contacts as it is loaded. This is an analog of the "elastic" regime in
the mechanics of granular media. At smaller opening angles or larger tilts, the
ball rolls at one contact and slides at the other as it is loaded, analogously
with the "plastic" regime in the mechanics of granular media. In the elastic
regime, the stress indeterminacy is resolved by the underlying kinetics of the
ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps
Models of stress fluctuations in granular media
We investigate in detail two models describing how stresses propagate and
fluctuate in granular media. The first one is a scalar model where only the
vertical component of the stress tensor is considered. In the continuum limit,
this model is equivalent to a diffusion equation (where the r\^ole of time is
played by the vertical coordinate) plus a randomly varying convection term. We
calculate the response and correlation function of this model, and discuss
several properties, in particular related to the stress distribution function.
We then turn to the tensorial model, where the basic starting point is a wave
equation which, in the absence of disorder, leads to a ray-like propagation of
stress. In the presence of disorder, the rays acquire a diffusive width and the
angle of propagation is shifted. A striking feature is that the response
function becomes negative, which suggests that the contact network is
mechanically unstable to very weak perturbations. The stress correlation
function reveals characteristic features related to the ray-like propagation,
which are absent in the scalar description. Our analytical calculations are
confirmed and extended by a numerical analysis of the stochastic wave equation.Comment: 32 pages, latex, 18 figures and 6 diagram
Stress in frictionless granular material: Adaptive Network Simulations
We present a minimalistic approach to simulations of force transmission
through granular systems. We start from a configuration containing cohesive
(tensile) contact forces and use an adaptive procedure to find the stable
configuration with no tensile contact forces. The procedure works by
sequentially removing and adding individual contacts between adjacent beads,
while the bead positions are not modified. In a series of two-dimensional
realizations, the resulting force networks are shown to satisfy a linear
constraint among the three components of average stress, as anticipated by
recent theories. The coefficients in the linear constraint remain nearly
constant for a range of shear loadings up to about .6 of the normal loading.
The spatial distribution of contact forces shows strong concentration along
``force chains". The probability of contact forces of magnitude f shows an
exponential falloff with f. The response to a local perturbing force is
concentrated along two characteristic rays directed downward and laterally.Comment: 8 pages, 8 figure
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Studies of the nonlinear dynamics effects of APPLE-II type EPUs at the ALS
Elliptically Polarizing Undulators (EPUs) have become more and more popular at synchrotron radiation sources, providing full polarization control of the photon beam. The fields of the most commonly used APPLE-II type EPUs have a very fast, intrinsic field roll-off, creating significant non-linearities of the beam motion with in some cases large impact on the dynamic (momentum) aperture. In general, the nonlinear effects get stronger with longer periods and higher undulator magnetic fields. One of the planned future beamlines at the ALS (MERLIN) will use a quasiperiodic EPU with 9 cm period and maximum B fields of about 1.3 T. We will present simulation studies for the proposed shimming schemes for this future device to reduce the nonlinear effects to acceptable values, as well as experimental studies for the existing 5 cm period EPUs already installed in the ALS
Stresses in silos: Comparison between theoretical models and new experiments
We present precise and reproducible mean pressure measurements at the bottom
of a cylindrical granular column. If a constant overload is added, the pressure
is linear in overload and nonmonotonic in the column height. The results are
{\em quantitatively} consistent with a local, linear relation between stress
components, as was recently proposed by some of us. They contradict the
simplest classical (Janssen) approximation, and may pose a rather severe test
of competing models.Comment: 4 pages, 2 figures, final version to appear in Phys. Rev. Let
Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies
It has been assumed until very recently that all long-range correlations are
screened in three-dimensional melts of linear homopolymers on distances beyond
the correlation length characterizing the decay of the density
fluctuations. Summarizing simulation results obtained by means of a variant of
the bond-fluctuation model with finite monomer excluded volume interactions and
topology violating local and global Monte Carlo moves, we show that due to an
interplay of the chain connectivity and the incompressibility constraint, both
static and dynamical correlations arise on distances . These
correlations are scale-free and, surprisingly, do not depend explicitly on the
compressibility of the solution. Both monodisperse and (essentially)
Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure
Statistical Mechanics of Stress Transmission in Disordered Granular Arrays
We give a statistical-mechanical theory of stress transmission in disordered
arrays of rigid grains with perfect friction. Starting from the equations of
microscopic force and torque balance we derive the fundamental equations of
stress equilibrium. We illustrate the validity of our approach by solving the
stress distribution of a homogeneous and isotropic array.Comment: 4 pages, to be published in PR
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