551 research outputs found
Spectral responses in granular compaction
The slow compaction of a gently tapped granular packing is reminiscent of the
low-temperature dynamics of structural and spin glasses. Here, I probe the
dynamical spectrum of granular compaction by measuring a complex
(frequency-dependent) volumetric susceptibility . While the
packing density displays glass-like slow relaxations (aging) and
history-dependence (memory) at low tapping amplitudes, the susceptibility
displays very weak aging effects, and its spectrum shows no
sign of a rapidly growing timescale. These features place in
sharp contrast to its dielectric and magnetic counterparts in structural and
spin glasses; instead, bears close similarities to the complex
specific heat of spin glasses. This, I suggest, indicates the glass-like
dynamics in granular compaction are governed by statistically rare relaxation
processes that become increasingly separated in timescale from the typical
relaxations of the system. Finally, I examine the effect of finite system size
on the spectrum of compaction dynamics. Starting from the ansatz that low
frequency processes correspond to large scale particle rearrangements, I
suggest the observed finite size effects are consistent with the suppression of
large-scale collective rearrangements in small systems.Comment: 18 pages, 17 figures. Submitted to PR
Free-energy functional for freezing transitions: Hard sphere systems freezing into crystalline and amorphous structures
A free-energy functional that contains both the symmetry conserved and
symmetry broken parts of the direct pair correlation function has been used to
investigate the freezing of a system of hard spheres into crystalline and
amorphous structures. The freezing parameters for fluid-crystal transition have
been found to be in very good agreement with the results found from
simulations. We considered amorphous structures found from the molecular
dynamics simulations at packing fractions lower than the glass close
packing fraction and investigated their stability compared to that
of a homogeneous fluid. The existence of free-energy minimum corresponding to a
density distribution of overlapping Gaussians centered around an amorphous
lattice depicts the deeply supercooled state with a heterogeneous density
profile
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
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
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
Surface versus bulk characterization of the electronic inhomogeneity in a VO_{2} film
We investigated the inhomogeneous electronic properties at the surface and
interior of VO_{2} thin films that exhibit a strong first-order metal-insulator
transition (MIT). Using the crystal structural change that accompanies a VO_{2}
MIT, we used bulk-sensitive X-ray diffraction (XRD) measurements to estimate
the fraction of metallic volume p^{XRD} in our VO_{2} film. The temperature
dependence of the p was very closely correlated with the dc
conductivity near the MIT temperature, and fit the percolation theory
predictions quite well: (p - p_{c})^{t} with t = 2.00.1
and p_{c} = 0.160.01. This agreement demonstrates that in our VO
thin film, the MIT should occur during the percolation process. We also used
surface-sensitive scanning tunneling spectroscopy (STS) to investigate the
microscopic evolution of the MIT near the surface. Similar to the XRD results,
STS maps revealed a systematic decrease in the metallic phase as temperature
decreased. However, this rate of change was much slower than the rate observed
with XRD, indicating that the electronic inhomogeneity near the surface differs
greatly from that inside the film. We investigated several possible origins of
this discrepancy, and postulated that the variety in the strain states near the
surface plays an important role in the broad MIT observed using STS. We also
explored the possible involvement of such strain effects in other correlated
electron oxide systems with strong electron-lattice interactions.Comment: 27 pages and 7 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
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
Properties of the energy landscape of network models for covalent glasses
We investigate the energy landscape of two dimensional network models for
covalent glasses by means of the lid algorithm. For three different particle
densities and for a range of network sizes, we exhaustively analyse many
configuration space regions enclosing deep-lying energy minima. We extract the
local densities of states and of minima, and the number of states and minima
accessible below a certain energy barrier, the 'lid'. These quantities show on
average a close to exponential growth as a function of their respective
arguments. We calculate the configurational entropy for these pockets of states
and find that the excess specific heat exhibits a peak at a critical
temperature associated with the exponential growth in the local density of
states, a feature of the specific heat also observed in real glasses at the
glass transition.Comment: RevTeX, 19 pages, 7 figure
Classical Spin Models with Broken Continuous Symmetry: Random Field Induced Order and Persistence of Spontaneous Magnetization
We consider a classical spin model, of two-dimensional spins, with continuous
symmetry, and investigate the effect of a symmetry breaking unidirectional
quenched disorder on the magnetization of the system. We work in the mean field
regime. We show, by numerical simulations and by perturbative calculations in
the low as well as in the high temperature limits, that although the continuous
symmetry of the magnetization is lost, the system still magnetizes, albeit with
a lower value as compared to the case without disorder. The critical
temperature at which the system starts magnetizing, also decreases with the
introduction of disorder. However, with the introduction of an additional
constant magnetic field, the component of magnetization in the direction that
is transverse to the disorder field increases with the introduction of the
quenched disorder. We discuss the same effects also for three-dimensional
spins.Comment: 12 pages, 12 figures, RevTeX
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