600 research outputs found
Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition
The small wavenumber behavior of the structure factor of
overcompressed amorphous hard-sphere configurations was previously studied for
a wide range of densities up to the maximally random jammed state, which can be
viewed as a prototypical glassy state [A. Hopkins, F. H. Stillinger and S.
Torquato, Phys. Rev. E, 86, 021505 (2012)]. It was found that a precursor to
the glassy jammed state was evident long before the jamming density was reached
as measured by a growing nonequilibrium length scale extracted from the volume
integral of the direct correlation function , which becomes long-ranged
as the critical jammed state is reached. The present study extends that work by
investigating via computer simulations two different atomic models: the
single-component Z2 Dzugutov potential in three dimensions and the
binary-mixture Kob-Andersen potential in two dimensions. Consistent with the
aforementioned hard-sphere study, we demonstrate that for both models a
signature of the glass transition is apparent well before the transition
temperature is reached as measured by the length scale determined from from the
volume integral of the direct correlation function in the single-component case
and a generalized direct correlation function in the binary-mixture case. The
latter quantity is obtained from a generalized Orstein-Zernike integral
equation for a certain decoration of the atomic point configuration. We also
show that these growing length scales, which are a consequence of the
long-range nature of the direct correlation functions, are intrinsically
nonequilibrium in nature as determined by an index that is a measure of
deviation from thermal equilibrium. It is also demonstrated that this
nonequilibrium index, which increases upon supercooling, is correlated with a
characteristic relaxation time scale.Comment: 26 pages, 14 figure
Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
We have discovered a new family of three-dimensional crystal sphere packings
that are strictly jammed (i.e., mechanically stable) and yet possess an
anomalously low density. This family constitutes an uncountably infinite number
of crystal packings that are subpackings of the densest crystal packings and
are characterized by a high concentration of self-avoiding "tunnels" (chains of
vacancies) that permeate the structures. The fundamental geometric
characteristics of these tunneled crystals command interest in their own right
and are described here in some detail. These include the lattice vectors (that
specify the packing configurations), coordination structure, Voronoi cells, and
density fluctuations. The tunneled crystals are not only candidate structures
for achieving the jamming threshold (lowest-density rigid packing), but may
have substantially broader significance for condensed matter physics and
materials science.Comment: 19 pages, 5 figure
Basic Understanding of Condensed Phases of Matter via Packing Models
Packing problems have been a source of fascination for millenia and their
study has produced a rich literature that spans numerous disciplines.
Investigations of hard-particle packing models have provided basic insights
into the structure and bulk properties of condensed phases of matter, including
low-temperature states (e.g., molecular and colloidal liquids, crystals and
glasses), multiphase heterogeneous media, granular media, and biological
systems. The densest packings are of great interest in pure mathematics,
including discrete geometry and number theory. This perspective reviews
pertinent theoretical and computational literature concerning the equilibrium,
metastable and nonequilibrium packings of hard-particle packings in various
Euclidean space dimensions. In the case of jammed packings, emphasis will be
placed on the "geometric-structure" approach, which provides a powerful and
unified means to quantitatively characterize individual packings via jamming
categories and "order" maps. It incorporates extremal jammed states, including
the densest packings, maximally random jammed states, and lowest-density jammed
structures. Packings of identical spheres, spheres with a size distribution,
and nonspherical particles are also surveyed. We close this review by
identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal
of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298
Irreversibility and Chaos in Active Particle Suspensions
Active matter has been the object of huge amount of research in recent years
for its important fundamental and applicative properties. In this paper we
investigate active suspensions of micro-swimmers through direct numerical
simulation, so that no approximation is made at the continuous level other than
the numerical one. We consider both pusher and puller organisms, with a
spherical or ellipsoidal shape. We analyse the velocity and the characteristic
scales for an homogeneous two-dimensional suspension and the effective
viscosity under shear. We bring evidences that the complex features displayed
are related to a spontaneous breaking of the time-reversal symmetry. We show
that chaos is not a key ingredient, whereas a large enough number of
interacting particles and a non-spherical shape are needed to break the
symmetry and are therefore at the basis of the phenomenology. Our numerical
study also shows that pullers display some collective motion, though with
different characteristics from pushers
Hyperuniformity Order Metric of Barlow Packings
The concept of hyperuniformity has been a useful tool in the study of
large-scale density fluctuations in systems ranging across the natural and
mathematical sciences. One can rank a large class of hyperuniform systems by
their ability to suppress long-range density fluctuations through the use of a
hyperuniformity order metric . We apply this order metric to the
Barlow packings, which are the infinitely degenerate densest packings of
identical rigid spheres that are distinguished by their stacking geometries and
include the commonly known fcc lattice and hcp crystal. The "stealthy stacking"
theorem implies that these packings are all stealthy hyperuniform, a strong
type of hyperuniformity which involves the suppression of scattering up to a
wavevector . We describe the geometry of three classes of Barlow packings,
two disordered classes and small-period packings. In addition, we compute a
lower bound on for all Barlow packings. We compute for the
aforementioned three classes of Barlow packings and find that to a very good
approximation, it is linear in the fraction of fcc-like clusters, taking values
between those of least-ordered hcp and most-ordered fcc. This implies that the
of all Barlow packings is primarily controlled by the local
cluster geometry. These results indicate the special nature of anisotropic
stacking disorder, which provides impetus for future research on the
development of anisotropic order metrics and hyperuniformity properties.Comment: 13 pages, 7 figure
Spatial modeling of the 3D morphology of hybrid polymer-ZnO solar cells, based on electron tomography data
A spatial stochastic model is developed which describes the 3D nanomorphology
of composite materials, being blends of two different (organic and inorganic)
solid phases. Such materials are used, for example, in photoactive layers of
hybrid polymer zinc oxide solar cells. The model is based on ideas from
stochastic geometry and spatial statistics. Its parameters are fitted to image
data gained by electron tomography (ET), where adaptive thresholding and
stochastic segmentation have been used to represent morphological features of
the considered ET data by unions of overlapping spheres. Their midpoints are
modeled by a stack of 2D point processes with a suitably chosen correlation
structure, whereas a moving-average procedure is used to add the radii of
spheres. The model is validated by comparing physically relevant
characteristics of real and simulated data, like the efficiency of exciton
quenching, which is important for the generation of charges and their transport
toward the electrodes.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS468 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
Systems of hard nonspherical particles exhibit a variety of stable phases
with different degrees of translational and orientational order, including
isotropic liquid, solid crystal, rotator and a variety of liquid crystal
phases. In this paper, we employ a Monte Carlo implementation of the
adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to
ascertain with high precision the equilibrium phase behavior of systems of
congruent Archimedean truncated tetrahedra over the entire range of possible
densities up to the maximal nearly space-filling density. In particular, we
find that the system undergoes two first-order phase transitions as the density
increases: first a liquid-solid transition and then a solid-solid transition.
The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase
at intermediate densities. At higher densities, we find that the CT phase
undergoes another first-order phase transition to one associated with the
densest-known crystal. We find no evidence for stable rotator (or plastic) or
nematic phases. We also generate the maximally random jammed (MRJ) packings of
truncated tetrahedra, which may be regarded to be the glassy end state of a
rapid compression of the liquid. We find that such MRJ packings are
hyperuniform with an average packing fraction of 0.770, which is considerably
larger than the corresponding value for identical spheres (about 0.64). We
conclude with some simple observations concerning what types of phase
transitions might be expected in general hard-particle systems based on the
particle shape and which would be good glass formers
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