602 research outputs found
Confined granular packings: structure, stress, and forces
The structure and stresses of static granular packs in cylindrical containers
are studied using large-scale discrete element molecular dynamics simulations
in three dimensions. We generate packings by both pouring and sedimentation and
examine how the final state depends on the method of construction. The vertical
stress becomes depth-independent for deep piles and we compare these stress
depth-profiles to the classical Janssen theory. The majority of the tangential
forces for particle-wall contacts are found to be close to the Coulomb failure
criterion, in agreement with the theory of Janssen, while particle-particle
contacts in the bulk are far from the Coulomb criterion. In addition, we show
that a linear hydrostatic-like region at the top of the packings unexplained by
the Janssen theory arises because most of the particle-wall tangential forces
in this region are far from the Coulomb yield criterion. The distributions of
particle-particle and particle-wall contact forces exhibit
exponential-like decay at large forces in agreement with previous studies.Comment: 11 pages, 11 figures, submitted to PRE (v2) added new references,
fixed typo
Geometry of Frictionless and Frictional Sphere Packings
We study static packings of frictionless and frictional spheres in three
dimensions, obtained via molecular dynamics simulations, in which we vary
particle hardness, friction coefficient, and coefficient of restitution.
Although frictionless packings of hard-spheres are always isostatic (with six
contacts) regardless of construction history and restitution coefficient,
frictional packings achieve a multitude of hyperstatic packings that depend on
system parameters and construction history. Instead of immediately dropping to
four, the coordination number reduces smoothly from as the friction
coefficient between two particles is increased.Comment: 6 pages, 9 figures, submitted to Phys. Rev.
Counter-propagating entangled photons from a waveguide with periodic nonlinearity
The conditions required for spontaneous parametric down-conversion in a
waveguide with periodic nonlinearity in the presence of an unguided pump field
are established. Control of the periodic nonlinearity and the physical
properties of the waveguide permits the quasi-phase matching equations that
describe counter-propagating guided signal and idler beams to be satisfied. We
compare the tuning curves and spectral properties of such counter-propagating
beams to those for co-propagating beams under typical experimental conditions.
We find that the counter-propagating beams exhibit narrow bandwidth permitting
the generation of quantum states that possess discrete-frequency entanglement.
Such states may be useful for experiments in quantum optics and technologies
that benefit from frequency entanglement.Comment: submitted to Phys. Rev.
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators
The article is devoted to the following question. Consider a periodic
self-adjoint difference (differential) operator on a graph (quantum graph) G
with a co-compact free action of the integer lattice Z^n. It is known that a
local perturbation of the operator might embed an eigenvalue into the
continuous spectrum (a feature uncommon for periodic elliptic operators of
second order). In all known constructions of such examples, the corresponding
eigenfunction is compactly supported. One wonders whether this must always be
the case. The paper answers this question affirmatively. What is more
surprising, one can estimate that the eigenmode must be localized not far away
from the perturbation (in a neighborhood of the perturbation's support, the
width of the neighborhood determined by the unperturbed operator only).
The validity of this result requires the condition of irreducibility of the
Fermi (Floquet) surface of the periodic operator, which is expected to be
satisfied for instance for periodic Schroedinger operators.Comment: Submitted for publicatio
The Diagnostic Potential of Transition Region Lines under-going Transient Ionization in Dynamic Events
We discuss the diagnostic potential of high cadence ultraviolet spectral data
when transient ionization is considered. For this we use high cadence UV
spectra taken during the impulsive phase of a solar flares (observed with
instruments on-board the Solar Maximum Mission) which showed excellent
correspondence with hard X-ray pulses. The ionization fraction of the
transition region ion O V and in particular the contribution function for the O
V 1371A line are computed within the Atomic Data and Analysis Structure, which
is a collection of fundamental and derived atomic data and codes which
manipulate them. Due to transient ionization, the O V 1371A line is enhanced in
the first fraction of a second with the peak in the line contribution function
occurring initially at a higher electron temperature than in ionization
equilibrium. The rise time and enhancement factor depend mostly on the electron
density. The fractional increase in the O V 1371A emissivity due to transient
ionization can reach a factor of 2--4 and can explain the fast response in the
line flux of transition regions ions during the impulsive phase of flares
solely as a result of transient ionization. This technique can be used to
diagnostic the electron temperature and density of solar flares observed with
the forth-coming Interface Region Imaging Spectrograph.Comment: 18 pages, 6 figure
Hydrodynamic Synchronisation of Model Microswimmers
We define a model microswimmer with a variable cycle time, thus allowing the
possibility of phase locking driven by hydrodynamic interactions between
swimmers. We find that, for extensile or contractile swimmers, phase locking
does occur, with the relative phase of the two swimmers being, in general,
close to 0 or pi, depending on their relative position and orientation. We show
that, as expected on grounds of symmetry, self T-dual swimmers, which are
time-reversal covariant, do not phase-lock. We also discuss the phase behaviour
of a line of tethered swimmers, or pumps. These show oscillations in their
relative phases reminiscent of the metachronal waves of cilia.Comment: 17 pages, 8 figure
On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature
We consider the Glauber dynamics for the 2D Ising model in a box of side L,
at inverse temperature and random boundary conditions whose
distribution P either stochastically dominates the extremal plus phase (hence
the quotation marks in the title) or is stochastically dominated by the
extremal minus phase. A particular case is when P is concentrated on the
homogeneous configuration identically equal to + (equal to -). For
large enough we show that for any there exists
such that the corresponding mixing time satisfies
. In the non-random case
(or ), this implies that . The same bound holds when the boundary conditions are all
+ on three sides and all - on the remaining one. The result, although still
very far from the expected Lifshitz behaviour , considerably
improves upon the previous known estimates of the form . The techniques are based on induction over length
scales, combined with a judicious use of the so-called "censoring inequality"
of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to
its equilibrium measure.Comment: 39 pages, 8 figures; v2: typos corrected, two references added. To
appear on Comm. Math. Phy
Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
We have studied how 2- and 3- dimensional systems made up of particles
interacting with finite range, repulsive potentials jam (i.e., develop a yield
stress in a disordered state) at zero temperature and applied stress. For each
configuration, there is a unique jamming threshold, , at which
particles can no longer avoid each other and the bulk and shear moduli
simultaneously become non-zero. The distribution of values becomes
narrower as the system size increases, so that essentially all configurations
jam at the same in the thermodynamic limit. This packing fraction
corresponds to the previously measured value for random close-packing. In fact,
our results provide a well-defined meaning for "random close-packing" in terms
of the fraction of all phase space with inherent structures that jam. The
jamming threshold, Point J, occurring at zero temperature and applied stress
and at the random close-packing density, has properties reminiscent of an
ordinary critical point. As Point J is approached from higher packing
fractions, power-law scaling is found for many quantities. Moreover, near Point
J, certain quantities no longer self-average, suggesting the existence of a
length scale that diverges at J. However, Point J also differs from an ordinary
critical point: the scaling exponents do not depend on dimension but do depend
on the interparticle potential. Finally, as Point J is approached from high
packing fractions, the density of vibrational states develops a large excess of
low-frequency modes. All of these results suggest that Point J may control
behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure
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