8,829 research outputs found
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
Observation of Landau quantization and standing waves in HfSiS
Recently, HfSiS was found to be a new type of Dirac semimetal with a line of
Dirac nodes in the band structure. Meanwhile, Rashba-split surface states are
also pronounced in this compound. Here we report a systematic study of HfSiS by
scanning tunneling microscopy/spectroscopy at low temperature and high magnetic
field. The Rashba-split surface states are characterized by measuring Landau
quantization and standing waves, which reveal a quasi-linear dispersive band
structure. First-principles calculations based on density-functional theory are
conducted and compared with the experimental results. Based on these
investigations, the properties of the Rashba-split surface states and their
interplay with defects and collective modes are discussed.Comment: 6 pages, 5 figure
Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
We extend the results from the first part of this series of two papers by
examining hyperuniformity in heterogeneous media composed of impenetrable
anisotropic inclusions. Specifically, we consider maximally random jammed
packings of hard ellipses and superdisks and show that these systems both
possess vanishing infinite-wavelength local-volume-fraction fluctuations and
quasi-long-range pair correlations. Our results suggest a strong generalization
of a conjecture by Torquato and Stillinger [Phys. Rev. E. 68, 041113 (2003)],
namely that all strictly jammed saturated packings of hard particles, including
those with size- and shape-distributions, are hyperuniform with signature
quasi-long-range correlations. We show that our arguments concerning the
constrained distribution of the void space in MRJ packings directly extend to
hard ellipse and superdisk packings, thereby providing a direct structural
explanation for the appearance of hyperuniformity and quasi-long-range
correlations in these systems. Additionally, we examine general heterogeneous
media with anisotropic inclusions and show for the first time that one can
decorate a periodic point pattern to obtain a hard-particle system that is not
hyperuniform with respect to local-volume-fraction fluctuations. This apparent
discrepancy can also be rationalized by appealing to the irregular distribution
of the void space arising from the anisotropic shapes of the particles. Our
work suggests the intriguing possibility that the MRJ states of hard particles
share certain universal features independent of the local properties of the
packings, including the packing fraction and average contact number per
particle.Comment: 29 pages, 9 figure
Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
We show that quasi-long-range (QLR) pair correlations that decay
asymptotically with scaling in -dimensional Euclidean space
, trademarks of certain quantum systems and cosmological
structures, are a universal signature of maximally random jammed (MRJ)
hard-particle packings. We introduce a novel hyperuniformity descriptor in MRJ
packings by studying local-volume-fraction fluctuations and show that
infinite-wavelength fluctuations vanish even for packings with size- and
shape-distributions. Special void statistics induce hyperuniformity and QLR
pair correlations.Comment: 10 pages, 3 figures; changes to figures and text based on review
process; accepted for publication at Phys. Rev. Let
Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
Hyperuniform many-particle distributions possess a local number variance that
grows more slowly than the volume of an observation window, implying that the
local density is effectively homogeneous beyond a few characteristic length
scales. Previous work on maximally random strictly jammed sphere packings in
three dimensions has shown that these systems are hyperuniform and possess
unusual quasi-long-range pair correlations, resulting in anomalous logarithmic
growth in the number variance. However, recent work on maximally random jammed
sphere packings with a size distribution has suggested that such
quasi-long-range correlations and hyperuniformity are not universal among
jammed hard-particle systems. In this paper we show that such systems are
indeed hyperuniform with signature quasi-long-range correlations by
characterizing the more general local-volume-fraction fluctuations. We argue
that the regularity of the void space induced by the constraints of saturation
and strict jamming overcomes the local inhomogeneity of the disk centers to
induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic
behavior in the spectral density, resulting in quasi-long-range spatial
correlations. A numerical and analytical analysis of the pore-size distribution
for a binary MRJ system in addition to a local characterization of the
n-particle loops governing the void space surrounding the inclusions is
presented in support of our argument. This paper is the first part of a series
of two papers considering the relationships among hyperuniformity, jamming, and
regularity of the void space in hard-particle packings.Comment: 40 pages, 15 figure
Density of States for a Specified Correlation Function and the Energy Landscape
The degeneracy of two-phase disordered microstructures consistent with a
specified correlation function is analyzed by mapping it to a ground-state
degeneracy. We determine for the first time the associated density of states
via a Monte Carlo algorithm. Our results are described in terms of the
roughness of the energy landscape, defined on a hypercubic configuration space.
The use of a Hamming distance in this space enables us to define a roughness
metric, which is calculated from the correlation function alone and related
quantitatively to the structural degeneracy. This relation is validated for a
wide variety of disordered systems.Comment: Accepted for publication in Physical Review Letter
Geometrical Ambiguity of Pair Statistics. I. Point Configurations
Point configurations have been widely used as model systems in condensed
matter physics, materials science and biology. Statistical descriptors such as
the -body distribution function is usually employed to characterize
the point configurations, among which the most extensively used is the pair
distribution function . An intriguing inverse problem of practical
importance that has been receiving considerable attention is the degree to
which a point configuration can be reconstructed from the pair distribution
function of a target configuration. Although it is known that the pair-distance
information contained in is in general insufficient to uniquely determine
a point configuration, this concept does not seem to be widely appreciated and
general claims of uniqueness of the reconstructions using pair information have
been made based on numerical studies. In this paper, we introduce the idea of
the distance space, called the space. The pair distances of a
specific point configuration are then represented by a single point in the
space. We derive the conditions on the pair distances that can be
associated with a point configuration, which are equivalent to the
realizability conditions of the pair distribution function . Moreover, we
derive the conditions on the pair distances that can be assembled into distinct
configurations. These conditions define a bounded region in the
space. By explicitly constructing a variety of degenerate point configurations
using the space, we show that pair information is indeed
insufficient to uniquely determine the configuration in general. We also
discuss several important problems in statistical physics based on the
space.Comment: 28 pages, 8 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
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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