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 $J$ 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 $1.79k_{B}$ 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

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

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

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