10,185 research outputs found
Non-Universality of Density and Disorder in Jammed Sphere Packings
We show for the first time that collectively jammed disordered packings of
three-dimensional monodisperse frictionless hard spheres can be produced and
tuned using a novel numerical protocol with packing density as low as
0.6. This is well below the value of 0.64 associated with the maximally random
jammed state and entirely unrelated to the ill-defined ``random loose packing''
state density. Specifically, collectively jammed packings are generated with a
very narrow distribution centered at any density over a wide density
range with variable disorder. Our results
support the view that there is no universal jamming point that is
distinguishable based on the packing density and frequency of occurence. Our
jammed packings are mapped onto a density-order-metric plane, which provides a
broader characterization of packings than density alone. Other packing
characteristics, such as the pair correlation function, average contact number
and fraction of rattlers are quantified and discussed.Comment: 19 pages, 4 figure
Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra
The determination of the densest packings of regular tetrahedra (one of the
five Platonic solids) is attracting great attention as evidenced by the rapid
pace at which packing records are being broken and the fascinating packing
structures that have emerged. Here we provide the most general analytical
formulation to date to construct dense periodic packings of tetrahedra with
four particles per fundamental cell. This analysis results in six-parameter
family of dense tetrahedron packings that includes as special cases recently
discovered "dimer" packings of tetrahedra, including the densest known packings
with density . This study strongly suggests that
the latter set of packings are the densest among all packings with a
four-particle basis. Whether they are the densest packings of tetrahedra among
all packings is an open question, but we offer remarks about this issue.
Moreover, we describe a procedure that provides estimates of upper bounds on
the maximal density of tetrahedron packings, which could aid in assessing the
packing efficiency of candidate dense packings.Comment: It contains 25 pages, 5 figures
Modeling Heterogeneous Materials via Two-Point Correlation Functions: II. Algorithmic Details and Applications
In the first part of this series of two papers, we proposed a theoretical
formalism that enables one to model and categorize heterogeneous materials
(media) via two-point correlation functions S2 and introduced an efficient
heterogeneous-medium (re)construction algorithm called the "lattice-point"
algorithm. Here we discuss the algorithmic details of the lattice-point
procedure and an algorithm modification using surface optimization to further
speed up the (re)construction process. The importance of the error tolerance,
which indicates to what accuracy the media are (re)constructed, is also
emphasized and discussed. We apply the algorithm to generate three-dimensional
digitized realizations of a Fontainebleau sandstone and a boron
carbide/aluminum composite from the two- dimensional tomographic images of
their slices through the materials. To ascertain whether the information
contained in S2 is sufficient to capture the salient structural features, we
compute the two-point cluster functions of the media, which are superior
signatures of the micro-structure because they incorporate the connectedness
information. We also study the reconstruction of a binary laser-speckle pattern
in two dimensions, in which the algorithm fails to reproduce the pattern
accurately. We conclude that in general reconstructions using S2 only work well
for heterogeneous materials with single-scale structures. However, two-point
information via S2 is not sufficient to accurately model multi-scale media.
Moreover, we construct realizations of hypothetical materials with desired
structural characteristics obtained by manipulating their two-point correlation
functions.Comment: 35 pages, 19 figure
Dense Packings of Superdisks and the Role of Symmetry
We construct the densest known two-dimensional packings of superdisks in the
plane whose shapes are defined by |x^(2p) + y^(2p)| <= 1, which contains both
convex-shaped particles (p > 0.5, with the circular-disk case p = 1) and
concave-shaped particles (0 < p < 0.5). The packings of the convex cases with p
1 generated by a recently developed event-driven molecular dynamics (MD)
simulation algorithm [Donev, Torquato and Stillinger, J. Comput. Phys. 202
(2005) 737] suggest exact constructions of the densest known packings. We find
that the packing density (covering fraction of the particles) increases
dramatically as the particle shape moves away from the "circular-disk" point (p
= 1). In particular, we find that the maximal packing densities of superdisks
for certain p 6 = 1 are achieved by one of the two families of Bravais lattice
packings, which provides additional numerical evidence for Minkowski's
conjecture concerning the critical determinant of the region occupied by a
superdisk. Moreover, our analysis on the generated packings reveals that the
broken rotational symmetry of superdisks influences the packing characteristics
in a non-trivial way. We also propose an analytical method to construct dense
packings of concave superdisks based on our observations of the structural
properties of packings of convex superdisks.Comment: 15 pages, 8 figure
Reduced dynamics with renormalization in solid-state charge qubit measurement
Quantum measurement will inevitably cause backaction on the measured system,
resulting in the well known dephasing and relaxation. In this report, in the
context of solid--state qubit measurement by a mesoscopic detector, we show
that an alternative backaction known as renormalization is important under some
circumstances. This effect is largely overlooked in the theory of quantum
measurement.Comment: 12 pages, 4 figure
Magnetic structure of superconducting Eu(Fe0.82Co0.18)2As2 as revealed by single-crystal neutron diffraction
The magnetic structure of superconducting Eu(Fe0.82Co0.18)2As2 is
unambiguously determined by single-crystal neutron diffraction. A long-range
ferromagnetic order of the Eu2+ moments along the c-direction is revealed below
the magnetic phase transition temperature Tc = 17 K. In addition, the
antiferromagnetism of the Fe2+ moments still survives and the
tetragonal-to-orthorhombic structural phase transition is also observed,
although the transition temperatures of the Fe-spin density wave (SDW) order
and the structural phase transition are significantly suppressed to Tn = 70 K
and Ts = 90 K, respectively, compared to the parent compound EuFe2As2.We
present the microscopic evidences for the coexistence of the Eu-ferromagnetism
(FM) and the Fe-SDW in the superconducting crystal. The superconductivity (SC)
competes with the Fe-SDW in Eu(Fe0.82Co0.18)2As2.Moreover, the comparison
between Eu(Fe1-xCox)2As2 and Ba(Fe1-xCox)2As2 indicates a considerable
influence of the rare-earth element Eu on the magnetism of the Fe sublattice.Comment: 7 pages, 7 figures, accepted for publication in Physical Review
Novel Features Arising in the Maximally Random Jammed Packings of Superballs
Dense random packings of hard particles are useful models of granular media
and are closely related to the structure of nonequilibrium low-temperature
amorphous phases of matter. Most work has been done for random jammed packings
of spheres, and it is only recently that corresponding packings of nonspherical
particles (e.g., ellipsoids) have received attention. Here we report a study of
the maximally random jammed (MRJ) packings of binary superdisks and
monodispersed superballs whose shapes are defined by |x_1|^2p+...+|x_2|^2p<=1
with d = 2 and 3, respectively, where p is the deformation parameter with
values in the interval (0, infinity). We find that the MRJ densities of such
packings increase dramatically and nonanalytically as one moves away from the
circular-disk and sphere point. Moreover, the disordered packings are
hypostatic and the local arrangements of particles are necessarily nontrivially
correlated to achieve jamming. We term such correlated structures "nongeneric".
The degree of "nongenericity" of the packings is quantitatively characterized
by determining the fraction of local coordination structures in which the
central particles have fewer contacting neighbors than average. We also show
that such seemingly special packing configurations are counterintuitively not
rare. As the anisotropy of the particles increases, the fraction of rattlers
decreases while the minimal orientational order increases. These novel
characteristics result from the unique rotational symmetry breaking manner of
the particles.Comment: 20 pages, 8 figure
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