3,793 research outputs found
Hyperuniformity and its Generalizations
Disordered many-particle hyperuniform systems are exotic amorphous states
characterized by anomalous suppression of large-scale density fluctuations.
Here we substantially broaden the hyperuniformity concept along four different
directions. This includes generalizations to treat fluctuations in the
interfacial area in heterogeneous media and surface-area driven evolving
microstructures, random scalar fields, divergence-free random vector fields, as
well as statistically anisotropic many-particle systems and two-phase media.
Interfacial-area fluctuations play a major role in characterizing the
microstructure of two-phase systems , physical properties that intimately
depend on the geometry of the interface, and evolving two-phase microstructures
that depend on interfacial energies (e.g., spinodal decomposition). In the
instances of divergence-free random vector fields and statistically anisotropic
structures, we show that the standard definition of hyperuniformity must be
generalized such that it accounts for the dependence of the relevant spectral
functions on the direction in which the origin in Fourier space
(nonanalyticities at the origin). Using this analysis, we place some well-known
energy spectra from the theory of isotropic turbulence in the context of this
generalization of hyperuniformity. We show that there exist many-particle
ground-state configurations in which directional hyperuniformity imparts exotic
anisotropic physical properties (e.g., elastic, optical and acoustic
characteristics) to these states of matter. Such tunablity could have
technological relevance for manipulating light and sound waves in ways
heretofore not thought possible. We show that disordered many-particle systems
that respond to external fields (e.g., magnetic and electric fields) are a
natural class of materials to look for directional hyperuniformity.Comment: In pres
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
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
Unexpected Density Fluctuations in Jammed Disordered Sphere Packings
We computationally study jammed disordered hard-sphere packings as large as a
million particles. We show that the packings are saturated and hyperuniform,
i.e., that local density fluctuations grow only as a logarithmically-augmented
surface area rather than the volume of the window. The structure factor shows
an unusual non-analytic linear dependence near the origin, . In
addition to exponentially damped oscillations seen in liquids, this implies a
weak power-law tail in the total correlation function, , and a
long-ranged direct correlation function.Comment: Submitted for publicatio
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