598 research outputs found
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
Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
The goal of this paper is to quantitatively describe some statistical
properties of higher-dimensional determinantal point processes with a primary
focus on the nearest-neighbor distribution functions. Toward this end, we
express these functions as determinants of matrices and then
extrapolate to . This formulation allows for a quick and accurate
numerical evaluation of these quantities for point processes in Euclidean
spaces of dimension . We also implement an algorithm due to Hough \emph{et.
al.} \cite{hough2006dpa} for generating configurations of determinantal point
processes in arbitrary Euclidean spaces, and we utilize this algorithm in
conjunction with the aforementioned numerical results to characterize the
statistical properties of what we call the Fermi-sphere point process for to 4. This homogeneous, isotropic determinantal point process, discussed
also in a companion paper \cite{ToScZa08}, is the high-dimensional
generalization of the distribution of eigenvalues on the unit circle of a
random matrix from the circular unitary ensemble (CUE). In addition to the
nearest-neighbor probability distribution, we are able to calculate Voronoi
cells and nearest-neighbor extrema statistics for the Fermi-sphere point
process and discuss these as the dimension is varied. The results in this
paper accompany and complement analytical properties of higher-dimensional
determinantal point processes developed in \cite{ToScZa08}.Comment: 42 pages, 17 figure
Disordered hyperuniformity in two-component non-additive hard disk plasmas
We study the behavior of a two-component plasma made up of non-additive hard
disks with a logarithmic Coulomb interaction. Due to the Coulomb repulsion,
long-wavelength total density fluctuations are suppressed and the system is
globally hyperuniform. Short-range volume effects lead to phase separation or
to hetero-coordination for positive or negative non-additivities, respectively.
These effects compete with the hidden long-range order imposed by
hyperuniformity. As a result, the critical behavior of the mixture is modified,
with long-wavelength concentration fluctuations partially damped when the
system is charged. It is also shown that the decrease of configurational
entropy due to hyperuniformity originates from contributions beyond the
two-particle level. Finally, despite global hyperuniformity, we show that in
our system, the spatial configuration associated with each component separately
is not hyperuniform, i.e., the system is not "multihyperuniform.
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
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
Collective Coordinate Control of Density Distributions
Real collective density variables [c.f.
Eq.\ref{Equation3})] in many-particle systems arise from non-linear
transformations of particle positions, and determine the structure factor
, where denotes the wave vector. Our objective is to
prescribe and then to find many-particle configurations
that correspond to such a target using a numerical optimization
technique. Numerical results reported here extend earlier one- and
two-dimensional studies to include three dimensions. In addition, they
demonstrate the capacity to control in the neighborhood of
0. The optimization method employed generates
multi-particle configurations for which , , and 1, 2, 4,
6, 8, and 10. The case 1 is relevant for the Harrison-Zeldovich
model of the early universe, for superfluid , and for jammed
amorphous sphere packings. The analysis also provides specific examples of
interaction potentials whose classical ground state are configurationally
degenerate and disordered.Comment: 26 pages, 8 figure
Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
We have formulated the problem of generating periodic dense paritcle packings
as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation
[S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the
objective function and impenetrability constraints can be exactly linearized
for sphere packings with a size distribution in -dimensional Euclidean space
, it is most suitable and natural to solve the corresponding ASC
optimization problem using sequential linear programming (SLP) techniques. We
implement an SLP solution to produce robustly a wide spectrum of jammed sphere
packings in for and with a diversity of disorder
and densities up to the maximally densities. This deterministic algorithm can
produce a broad range of inherent structures besides the usual disordered ones
with very small computational cost by tuning the radius of the {\it influence
sphere}. In three dimensions, we show that it can produce with high probability
a variety of strictly jammed packings with a packing density anywhere in the
wide range . We also apply the algorithm to generate various
disordered packings as well as the maximally dense packings for
and 6. Compared to the LS procedure, our SLP protocol is able to ensure that
the final packings are truly jammed, produces disordered jammed packings with
anomalously low densities, and is appreciably more robust and computationally
faster at generating maximally dense packings, especially as the space
dimension increases.Comment: 34 pages, 6 figure
Hyperuniformity of Quasicrystals
Hyperuniform systems, which include crystals, quasicrystals and special
disordered systems, have attracted considerable recent attention, but rigorous
analyses of the hyperuniformity of quasicrystals have been lacking because the
support of the spectral intensity is dense and discontinuous. We employ the
integrated spectral intensity, , to quantitatively characterize the
hyperuniformity of quasicrystalline point sets generated by projection methods.
The scaling of as tends to zero is computed for one-dimensional
quasicrystals and shown to be consistent with independent calculations of the
variance, , in the number of points contained in an interval of
length . We find that one-dimensional quasicrystals produced by projection
from a two-dimensional lattice onto a line of slope fall into distinct
classes determined by the width of the projection window. For a countable dense
set of widths, ; for all others, . This
distinction suggests that measures of hyperuniformity define new classes of
quasicrystals in higher dimensions as well.Comment: 12 pages, 14 figure
Transverse flow in thin superhydrophobic channels
We provide some general theoretical results to guide the optimization of
transverse hydrodynamic phenomena in superhydrophobic channels. Our focus is on
the canonical micro- and nanofluidic geometry of a parallel-plate channel with
an arbitrary two-component (low-slip and high-slip) coarse texture, varying on
scales larger than the channel thickness. By analyzing rigorous bounds on the
permeability, over all possible patterns, we optimize the area fractions, slip
lengths, geometry and orientation of the surface texture to maximize transverse
flow. In the case of two aligned striped surfaces, very strong transverse flows
are possible. Optimized superhydrophobic surfaces may find applications in
passive microfluidic mixing and amplification of transverse electrokinetic
phenomena.Comment: 4 page
- …