312 research outputs found
Comment on "Jamming at zero temperature and zero applied stress: The epitome of disorder"
O'Hern, Silbert, Liu and Nagel [Phys. Rev. E. 68, 011306 (2003)] (OSLN) claim
that a special point of a "jamming phase diagram" (in density, temperature,
stress space) is related to random close packing of hard spheres, and that it
represents, for their suggested definitions of jammed and random, the recently
introduced maximally random jammed state. We point out several difficulties
with their definitions and question some of their claims. Furthermore, we
discuss the connections between their algorithm and other hard-sphere packing
algorithms in the literature.Comment: 4 pages of text, already publishe
Inertial Coupling Method for particles in an incompressible fluctuating fluid
We develop an inertial coupling method for modeling the dynamics of
point-like 'blob' particles immersed in an incompressible fluid, generalizing
previous work for compressible fluids. The coupling consistently includes
excess (positive or negative) inertia of the particles relative to the
displaced fluid, and accounts for thermal fluctuations in the fluid momentum
equation. The coupling between the fluid and the blob is based on a no-slip
constraint equating the particle velocity with the local average of the fluid
velocity, and conserves momentum and energy. We demonstrate that the
formulation obeys a fluctuation-dissipation balance, owing to the
non-dissipative nature of the no-slip coupling. We develop a spatio-temporal
discretization that preserves, as best as possible, these properties of the
continuum formulation. In the spatial discretization, the local averaging and
spreading operations are accomplished using compact kernels commonly used in
immersed boundary methods. We find that the special properties of these kernels
make the discrete blob a particle with surprisingly physically-consistent
volume, mass, and hydrodynamic properties. We develop a second-order
semi-implicit temporal integrator that maintains discrete
fluctuation-dissipation balance, and is not limited in stability by viscosity.
Furthermore, the temporal scheme requires only constant-coefficient Poisson and
Helmholtz linear solvers, enabling a very efficient and simple FFT-based
implementation on GPUs. We numerically investigate the performance of the
method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and
associated discussion) relative to published versio
Tetratic Order in the Phase Behavior of a Hard-Rectangle System
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found
two unusual phases in two-dimensional systems of anisotropic hard particles: a
tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science
and Tech., 10: 235-255, 2004], and a nonperiodic degenerate solid phase for
hard-disk dimers [Phys. Rev. Lett., 66: 3168-3171, 1991]. In this work, we
study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers
(or dominos), and demonstrate that it exhibits a solid phase with both of these
unusual properties. The solid shows tetratic, but not nematic, order, and it is
nonperiodic having the structure of a random tiling of the square lattice with
dominos. We obtain similar results with both a classical Monte Carlo method
using true rectangles and a novel molecular dynamics algorithm employing
rectangles with rounded corners. It is remarkable that such simple convex
two-dimensional shapes can produce such rich phase behavior. Although we have
not performed exact free-energy calculations, we expect that the random domino
tiling is thermodynamically stabilized by its degeneracy entropy, well-known to
be per particle from previous studies of the dimer problem on the
square lattice. Our observations are consistent with a KTHNY two-stage phase
transition scenario with two continuous phase transitions, the first from
isotropic to tetratic liquid, and the second from tetratic liquid to solid.Comment: Submitted for publicatio
The packing of granular polymer chains
Rigid particles pack into structures, such as sand dunes on the beach, whose
overall stability is determined by the average number of contacts between
particles. However, when packing spatially extended objects with flexible
shapes, additional concepts must be invoked to understand the stability of the
resulting structure. Here we study the disordered packing of chains constructed
out of flexibly-connected hard spheres. Using X-ray tomography, we find long
chains pack into a low-density structure whose mechanical rigidity is mainly
provided by the backbone. On compaction, randomly-oriented, semi-rigid loops
form along the chain, and the packing of chains can be understood as the
jamming of these elements. Finally we uncover close similarities between the
packing of chains and the glass transition in polymers.Comment: 11 pages, 4 figure
Fractal analysis of resting state fMRI signals in adults with ADHD
The fractal concept developed by Mandelbrot provides a useful tool for examining a variety of naturally occurring phenomena. Fractals are signals that display scale-invariant or self-similar behaviour. They can be found everywhere in nature including fractional Gaussian noise (fGn). Resting state fMRI signals can be modelled as fGn which makes them appropriate for fractal analysis. The Hurst exponent, H, is a measure of fractal processes and has values ranging between 0 and 1. Fractional Gaussian noise with 0<H<0.5 demonstrates negatively autocorrelated or antipersistent behaviour; fGn with 0.5<H<1 demonstrates a positively correlated, relatively persistent, predictable, long memory behaviour; and fGn with H = 0.5 corresponds to classical Gaussian white noise. In the present study, we aim to estimate the fractal behaviour of adult ADHD patients when compared to age-matched healthy controls using dispersional analysis. We hypothesize that ADHD patients will demonstrate more predictable (higher H values) fractal behaviour. Ten ADHD patients (5 female, mean age (32.60±10.46)) and ten controls (7 female, mean age (30.10±8.49)) were brain imaged by 3T MRI scanner. All patients and control participants completed the Conners’ Adult ADHD Rating Scales (ADHD scores). Our analysis shows that the ADHD patients demonstrate more positively correlated, relatively persistent, predictable and longer memory fractal behaviour in regards to healthy controls. The discriminated brain regions are part of the frontal-striatal-cerebellar circuits and are consistent with the hypothesis of abnormal frontal-striatal-cerebellar circuits in ADHD. We have shown that the analysis of fractal behaviour may be a useful tool in revealing abnormalities in ADHD brain dynamics
Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
Continuing on recent computational and experimental work on jammed packings
of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider
jamming in packings of smooth strictly convex nonspherical hard particles. We
explain why the isocounting conjecture, which states that for large disordered
jammed packings the average contact number per particle is twice the number of
degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to
nonspherical particles. We develop first- and second-order conditions for
jamming, and demonstrate that packings of nonspherical particles can be jammed
even though they are hypoconstrained (\bar{Z}<2d_{f}). We apply an algorithm
using these conditions to computer-generated hypoconstrained ellipsoid and
ellipse packings and demonstrate that our algorithm does produce jammed
packings, even close to the sphere point. We also consider packings that are
nearly jammed and draw connections to packings of deformable (but stiff)
particles. Finally, we consider the jamming conditions for nearly spherical
particles and explain quantitatively the behavior we observe in the vicinity of
the sphere point.Comment: 33 pages, third revisio
Random manifolds in non-linear resistor networks: Applications to varistors and superconductors
We show that current localization in polycrystalline varistors occurs on
paths which are, usually, in the universality class of the directed polymer in
a random medium. We also show that in ceramic superconductors, voltage
localizes on a surface which maps to an Ising domain wall. The emergence of
these manifolds is explained and their structure is illustrated using direct
solution of non-linear resistor networks
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