579 research outputs found
Long-time asymptotics of the long-range Emch-Radin model
The long-time asymptotic behavior is studied for a long-range variant of the
Emch-Radin model of interacting spins. We derive upper and lower bounds on the
expectation values of a class of observables. We prove analytically that the
time scale at which the system relaxes to equilibrium diverges with the system
size N, displaying quasistationary nonequilibrium behavior. This finding
implies that, for large enough N, equilibration will not be observed in an
experiment of finite duration.Comment: 12 pages, 2 figures. Compared to the published version, a 1/2 has
been corrected in Eq. (9) and subsequent equations; the modifications are
insubstantial and leave the main results of the article unaltered. arXiv
admin note: substantial text overlap with arXiv:1103.083
Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime
We model the dynamics of avalanches in granular assemblies in partly filled
rotating cylinders using a mean-field approach. We show that, upon varying the
cylinder angular velocity , the system undergoes a hysteresis cycle
between an intermittent and a continuous flow regimes. In the intermittent flow
regime, and approaching the transition, the avalanche duration exhibits
critical slowing down with a temporal power-law divergence. Upon adding a white
noise term, and close to the transition, the distribution of avalanche
durations is also a power-law. The hysteresis, as well as the statistics of
avalanche durations, are in good qualitative agreement with recent experiments
in partly filled rotating cylinders.Comment: 4 pages, RevTeX 3.0, postscript figures 1, 3 and 4 appended
Tracer diffusion in granular shear flows
Tracer diffusion in a granular gas in simple shear flow is analyzed. The
analysis is made from a perturbation solution of the Boltzmann kinetic equation
through first order in the gradient of the mole fraction of tracer particles.
The reference state (zeroth-order approximation) corresponds to a Sonine
solution of the Boltzmann equation, which holds for arbitrary values of the
restitution coefficients. Due to the anisotropy induced in the system by the
shear flow, the mass flux defines a diffusion tensor instead of a
scalar diffusion coefficient. The elements of this tensor are given in terms of
the restitution coefficients and mass and size ratios. The dependence of the
diffusion tensor on the parameters of the problem is illustrated in the
three-dimensional case. The results show that the influence of dissipation on
the elements is in general quite important, even for moderate values
of the restitution coefficients. In the case of self-diffusion (mechanically
equivalent particles), the trends observed in recent molecular dynamics
simulations are similar to those obtained here from the Boltzmann kinetic
theory.Comment: 5 figure
Diffusion as mixing mechanism in granular materials
We present several numerical results on granular mixtures. In particular, we
examine the efficiency of diffusion as a mixing mechanism in these systems. The
collisions are inelastic and to compensate the energy loss, we thermalize the
grains by adding a random force. Starting with a segregated system, we show
that uniform agitation (heating) leads to a uniform mixture of grains of
different sizes. We define a characteristic mixing time, , and
study theoretically and numerically its dependence on other parameters like the
density. We examine a model for bidisperse systems for which we can calculate
some physical quantities. We also examine the effect of a temperature gradient
and demonstrate the appearance of an expected segregation.Comment: 15 eps figures, include
Partially fluidized shear granular flows: Continuum theory and MD simulations
The continuum theory of partially fluidized shear granular flows is tested
and calibrated using two dimensional soft particle molecular dynamics
simulations. The theory is based on the relaxational dynamics of the order
parameter that describes the transition between static and flowing regimes of
granular material. We define the order parameter as a fraction of static
contacts among all contacts between particles. We also propose and verify by
direct simulations the constitutive relation based on the splitting of the
shear stress tensor into a``fluid part'' proportional to the strain rate
tensor, and a remaining ``solid part''. The ratio of these two parts is a
function of the order parameter. The rheology of the fluid component agrees
well with the kinetic theory of granular fluids even in the dense regime. Based
on the hysteretic bifurcation diagram for a thin shear granular layer obtained
in simulations, we construct the ``free energy'' for the order parameter. The
theory calibrated using numerical experiments with the thin granular layer is
applied to the surface-driven stationary two dimensional granular flows in a
thick granular layer under gravity.Comment: 20 pages, 19 figures, submitted to Phys. Rev.
A nonlinear hydrodynamical approach to granular materials
We propose a nonlinear hydrodynamical model of granular materials. We show
how this model describes the formation of a sand pile from a homogeneous
distribution of material under gravity, and then discuss a simulation of a
rotating sandpile which shows, in qualitative agreement with experiment, a
static and dynamic angle of repose.Comment: 17 pages, 14 figures, RevTeX4; minor changes to wording and some
additional discussion. Accepted by Phys. Rev.
Diffusion of impurities in a granular gas
Diffusion of impurities in a granular gas undergoing homogeneous cooling
state is studied. The results are obtained by solving the Boltzmann--Lorentz
equation by means of the Chapman--Enskog method. In the first order in the
density gradient of impurities, the diffusion coefficient is determined as
the solution of a linear integral equation which is approximately solved by
making an expansion in Sonine polynomials. In this paper, we evaluate up to
the second order in the Sonine expansion and get explicit expressions for
in terms of the restitution coefficients for the impurity--gas and gas--gas
collisions as well as the ratios of mass and particle sizes. To check the
reliability of the Sonine polynomial solution, analytical results are compared
with those obtained from numerical solutions of the Boltzmann equation by means
of the direct simulation Monte Carlo (DSMC) method. In the simulations, the
diffusion coefficient is measured via the mean square displacement of
impurities. The comparison between theory and simulation shows in general an
excellent agreement, except for the cases in which the gas particles are much
heavier and/or much larger than impurities. In theses cases, the second Sonine
approximation to improves significantly the qualitative predictions made
from the first Sonine approximation. A discussion on the convergence of the
Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.
Diving deep into digital literacy:emerging methods for research
Literacy studies approaches have tended to adopt a position which enables ethnographic explorations of a wide range of ‘literacies’. An important issue arising is the new challenge required for researchers to capture, manage, and analyse data that highlight the unique character of practices around texts in digital environments. Such inquiries, we argue, require multiple elements of data to be captured and analysed as part of effective literacy ethnographies. These include such things as the unfolding of digital texts, the activities around them, and features of the surrounding social and material environment. This paper addresses these methodological issues drawing from three educationally focused studies, and reporting their experiences and insights within uniquely different contexts. We deal with the issue of adopting new digital methods for literacy research through the notion of a ‘deep dive’ to explore educational tasks in classrooms. Through a discussion of how we approached the capture and analysis of our data, we present methods to better understand digital literacies in education. We then outline challenges posed by our methods, how they can be used more broadly for researching interaction in digital environments, and how they augment transdisciplinary debates and trends in research methods
Kepler-22b: A 2.4 Earth-radius Planet in the Habitable Zone of a Sun-like Star
A search of the time-series photometry from NASA's Kepler spacecraft reveals
a transiting planet candidate orbiting the 11th magnitude G5 dwarf KIC 10593626
with a period of 290 days. The characteristics of the host star are well
constrained by high-resolution spectroscopy combined with an asteroseismic
analysis of the Kepler photometry, leading to an estimated mass and radius of
0.970 +/- 0.060 MSun and 0.979 +/- 0.020 RSun. The depth of 492 +/- 10ppm for
the three observed transits yields a radius of 2.38 +/- 0.13 REarth for the
planet. The system passes a battery of tests for false positives, including
reconnaissance spectroscopy, high-resolution imaging, and centroid motion. A
full BLENDER analysis provides further validation of the planet interpretation
by showing that contamination of the target by an eclipsing system would rarely
mimic the observed shape of the transits. The final validation of the planet is
provided by 16 radial velocities obtained with HIRES on Keck 1 over a one year
span. Although the velocities do not lead to a reliable orbit and mass
determination, they are able to constrain the mass to a 3{\sigma} upper limit
of 124 MEarth, safely in the regime of planetary masses, thus earning the
designation Kepler-22b. The radiative equilibrium temperature is 262K for a
planet in Kepler-22b's orbit. Although there is no evidence that Kepler-22b is
a rocky planet, it is the first confirmed planet with a measured radius to
orbit in the Habitable Zone of any star other than the Sun.Comment: Accepted to Ap
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