314 research outputs found
Onset of thermal convection in a horizontal layer of granular gas
The Navier-Stokes granular hydrodynamics is employed for determining the
threshold of thermal convection in an infinite horizontal layer of granular
gas. The dependence of the convection threshold, in terms of the inelasticity
of particle collisions, on the Froude and Knudsen numbers is found. A simple
necessary condition for convection is formulated in terms of the
Schwarzschild's criterion, well-known in thermal convection of (compressible)
classical fluids. The morphology of convection cells at the onset is
determined. At large Froude numbers, the Froude number drops out of the
problem. As the Froude number goes to zero, the convection instability turns
into a recently discovered phase separation instability.Comment: 6 pages, 6 figures. An extended version. A simple and universal
necessary criterion for convection presente
Hydrodynamic singularities and clustering in a freely cooling inelastic gas
We employ hydrodynamic equations to follow the clustering instability of a
freely cooling dilute gas of inelastically colliding spheres into a
well-developed nonlinear regime. We simplify the problem by dealing with a
one-dimensional coarse-grained flow. We observe that at a late stage of the
instability the shear stress becomes negligibly small, and the gas flows solely
by inertia. As a result the flow formally develops a finite time singularity,
as the velocity gradient and the gas density diverge at some location. We argue
that flow by inertia represents a generic intermediate asymptotic of unstable
free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure
Model Flames in the Boussinesq Limit: The Effects of Feedback
We have studied the fully nonlinear behavior of pre-mixed flames in a
gravitationally stratified medium, subject to the Boussinesq approximation. Key
results include the establishment of criterion for when such flames propagate
as simple planar flames; elucidation of scaling laws for the effective flame
speed; and a study of the stability properties of these flames. The simplicity
of some of our scalings results suggests that analytical work may further
advance our understandings of buoyant flames.Comment: 11 pages, 14 figures, RevTex, gzipped tar fil
Velocity distribution of fluidized granular gases in presence of gravity
The velocity distribution of a fluidized dilute granular gas in the direction
perpendicular to the gravitational field is investigated by means of Molecular
Dynamics simulations. The results indicate that the velocity distribution can
be exactly described neither by a Gaussian nor by a stretched exponential law.
Moreover, it does not exhibit any kind of scaling. In fact, the actual shape of
the distribution depends on the number of monolayers at rest, on the
restitution coefficient and on the height at what it is measured. The role
played by the number of particle-particle collisions as compared with the
number of particle-wall collisions is discussed
Transversal inhomogeneities in dilute vibrofluidized granular fluids
The spontaneous symmetry breaking taking place in the direction perpendicular
to the energy flux in a dilute vibrofluidized granular system is investigated,
using both a hydrodynamic description and simulation methods. The latter
include molecular dynamics and direct Monte Carlo simulation of the Boltzmann
equation. A marginal stability analysis of the hydrodynamic equations, carried
out in the WKB approximation, is shown to be in good agreement with the
simulation results. The shape of the hydrodynamic profiles beyond the
bifurcation is discussed
Competition and Selection Among Conventions
In many domains, a latent competition among different conventions determines
which one will come to dominate. One sees such effects in the success of
community jargon, of competing frames in political rhetoric, or of terminology
in technical contexts. These effects have become widespread in the online
domain, where the data offers the potential to study competition among
conventions at a fine-grained level.
In analyzing the dynamics of conventions over time, however, even with
detailed on-line data, one encounters two significant challenges. First, as
conventions evolve, the underlying substance of their meaning tends to change
as well; and such substantive changes confound investigations of social
effects. Second, the selection of a convention takes place through the complex
interactions of individuals within a community, and contention between the
users of competing conventions plays a key role in the convention's evolution.
Any analysis must take place in the presence of these two issues.
In this work we study a setting in which we can cleanly track the competition
among conventions. Our analysis is based on the spread of low-level authoring
conventions in the eprint arXiv over 24 years: by tracking the spread of macros
and other author-defined conventions, we are able to study conventions that
vary even as the underlying meaning remains constant. We find that the
interaction among co-authors over time plays a crucial role in the selection of
them; the distinction between more and less experienced members of the
community, and the distinction between conventions with visible versus
invisible effects, are both central to the underlying processes. Through our
analysis we make predictions at the population level about the ultimate success
of different synonymous conventions over time--and at the individual level
about the outcome of "fights" between people over convention choices.Comment: To appear in Proceedings of WWW 2017, data at
https://github.com/CornellNLP/Macro
Hydrodynamics of thermal granular convection
A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular
convection, recently predicted in molecular dynamic simulations and observed in
experiment. The limit of a dilute flow is considered. The problem is fully
described by three scaled parameters. The convection occurs via a supercritical
bifurcation, the inelasticity of the collisions being the control parameter.
The theory is expected to be valid for small Knudsen numbers and nearly elastic
grain collisions.Comment: 4 pages, 4 EPS figures, some details adde
Merging of Components in Close Binaries: Type Ia Supernovae, Massive White Dwarfs, and Ap stars
The "Scenario Machine" (a computer code designed for studies of the evolution
of close binaries) was used to carry out a population synthesis for a wide
range of merging astrophysical objects: main-sequence stars with main-sequence
stars; white dwarfs with white dwarfs, neutron stars, and black holes; neutron
stars with neutron stars and black holes; and black holes with black holes.We
calculate the rates of such events, and plot the mass distributions for merging
white dwarfs and main-sequence stars. It is shown that Type Ia supernovae can
be used as standard candles only after approximately one billion years of
evolution of galaxies. In the course of this evolution, the average energy of
Type Ia supernovae should decrease by roughly 10%; the maximum and minimum
energies of Type Ia supernovae may differ by no less than by a factor of 1.5.
This circumstance should be taken into account in estimations of parameters of
acceleration of the Universe. According to theoretical estimates, the most
massive - as a rule, magnetic - white dwarfs probably originate from mergers of
white dwarfs of lower mass. At least some magnetic Ap and Bp stars may form in
mergers of low-mass main sequence stars (<1.5 mass of the Sun) with convective
envelopes.Comment: 15 pages, 4 figure
Symmetry-breaking instability in a prototypical driven granular gas
Symmetry-breaking instability of a laterally uniform granular cluster (strip
state) in a prototypical driven granular gas is investigated. The system
consists of smooth hard disks in a two-dimensional box, colliding inelastically
with each other and driven, at zero gravity, by a "thermal" wall. The limit of
nearly elastic particle collisions is considered, and granular hydrodynamics
with the Jenkins-Richman constitutive relations is employed. The hydrodynamic
problem is completely described by two scaled parameters and the aspect ratio
of the box. Marginal stability analysis predicts a spontaneous symmetry
breaking instability of the strip state, similar to that predicted recently for
a different set of constitutive relations. If the system is big enough, the
marginal stability curve becomes independent of the details of the boundary
condition at the driving wall. In this regime, the density perturbation is
exponentially localized at the elastic wall opposite to the thermal wall. The
short- and long-wavelength asymptotics of the marginal stability curves are
obtained analytically in the dilute limit. The physics of the symmetry-breaking
instability is discussed.Comment: 11 pages, 14 figure
Beating the news using social media: the case study of American Idol
We present a contribution to the debate on the predictability of social events using big data analytics. We focus on the elimination of contestants in the American Idol TV shows as an example of a well defined electoral phenomenon that each week draws millions of votes in the USA. This event can be considered as basic test in a simplified environment to assess the predictive power of Twitter signals. We provide evidence that Twitter activity during the time span defined by the TV show airing and the voting period following it correlates with the contestants ranking and allows the anticipation of the voting outcome. Twitter data from the show and the voting period of the season finale have been analyzed to attempt the winner prediction ahead of the airing of the official result. We also show that the fraction of tweets that contain geolocation information allows us to map the fanbase of each contestant, both within the US and abroad, showing that strong regional polarizations occur. The geolocalized data are crucial for the correct prediction of the final outcome of the show, pointing out the importance of considering information beyond the aggregated Twitter signal. Although American Idol voting is just a minimal and simplified version of complex societal phenomena such as political elections, this work shows that the volume of information available in online systems permits the real time gathering of quantitative indicators that may be able to anticipate the future unfolding of opinion formation events
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