8,559 research outputs found
Impurity in a granular gas under nonlinear Couette flow
We study in this work the transport properties of an impurity immersed in a
granular gas under stationary nonlinear Couette flow. The starting point is a
kinetic model for low-density granular mixtures recently proposed by the
authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been
considered. First, a hydrodynamic or normal solution is found by exploiting a
formal mapping between the kinetic equations for the gas particles and for the
impurity. We show that the transport properties of the impurity are
characterized by the ratio between the temperatures of the impurity and gas
particles and by five generalized transport coefficients: three related to the
momentum flux (a nonlinear shear viscosity and two normal stress differences)
and two related to the heat flux (a nonlinear thermal conductivity and a cross
coefficient measuring a component of the heat flux orthogonal to the thermal
gradient). Second, by means of a Monte Carlo simulation method we numerically
solve the kinetic equations and show that our hydrodynamic solution is valid in
the bulk of the fluid when realistic boundary conditions are used. Furthermore,
the hydrodynamic solution applies to arbitrarily (inside the continuum regime)
large values of the shear rate, of the inelasticity, and of the rest of
parameters of the system. Preliminary simulation results of the true Boltzmann
description show the reliability of the nonlinear hydrodynamic solution of the
kinetic model. This shows again the validity of a hydrodynamic description for
granular flows, even under extreme conditions, beyond the Navier-Stokes domain.Comment: 23 pages, 11 figures; v2: Preliminary DSMC results from the Boltzmann
equation included, Fig. 11 is ne
Exact String Solutions in 2+1-Dimensional De Sitter Spacetime
Exact and explicit string solutions in de Sitter spacetime are found. (Here,
the string equations reduce to a sinh-Gordon model). A new feature without flat
spacetime analogy appears: starting with a single world-sheet, several (here
two) strings emerge. One string is stable and the other (unstable) grows as the
universe grows. Their invariant size and energy either grow as the expansion
factor or tend to constant. Moreover, strings can expand (contract) for large
(small) universe radius with a different rate than the universe.Comment: 11 pages, Phyzzx macropackage used, PAR-LPTHE 92/32. Revised version
with a new understanding of the previous result
A method for solve integrable spin chains combining different representations
A non homogeneous spin chain in the representations and
of is analyzed. We find that the naive nested Bethe ansatz is not
applicable to this case. A method inspired in the nested Bethe ansatz, that can
be applied to more general cases, is developed for that chain. The solution for
the eigenvalues of the trace of the monodromy matrix is given as two coupled
Bethe equations different from that for a homogeneous chain. A conjecture about
the form of the solutions for more general chains is presented.
PACS: 75.10.Jm, 05.50+q 02.20 SvComment: PlainTeX, harvmac, 13 pages, 3 figures, to appear in Phys. Rev.
Computer simulations of an impurity in a granular gas under planar Couette flow
We present in this work results from numerical solutions, obtained by means
of the direct simulation Monte Carlo (DSMC) method, of the Boltzmann and
Boltzmann--Lorentz equations for an impurity immersed in a granular gas under
planar Couette flow. The DSMC results are compared with the exact solution of a
recent kinetic model for the same problem. The results confirm that, in steady
states and over a wide range of parameter values, the state of the impurity is
enslaved to that of the host gas: it follows the same flow velocity profile,
its concentration (relative to that of the granular gas) is constant in the
bulk region, and the impurity/gas temperature ratio is also constant. We
determine also the rheological properties and nonlinear hydrodynamic transport
coefficients for the impurity, finding a good semi-quantitative agreement
between the DSMC results and the theoretical predictions.Comment: 23 pages, 11 figures; v2: minor change
Multi-String Solutions by Soliton Methods in De Sitter Spacetime
{\bf Exact} solutions of the string equations of motion and constraints are
{\bf systematically} constructed in de Sitter spacetime using the dressing
method of soliton theory. The string dynamics in de Sitter spacetime is
integrable due to the associated linear system. We start from an exact string
solution and the associated solution of the linear system , and we construct a new solution differing from
by a rational matrix in with at least four
poles . The periodi-
city condition for closed strings restrict to discrete values
expressed in terms of Pythagorean numbers. Here we explicitly construct solu-
tions depending on -spacetime coordinates, two arbitrary complex numbers
(the 'polarization vector') and two integers which determine the string
windings in the space. The solutions are depicted in the hyperboloid coor-
dinates and in comoving coordinates with the cosmic time . Despite of
the fact that we have a single world sheet, our solutions describe {\bf multi-
ple}(here five) different and independent strings; the world sheet time
turns to be a multivalued function of .(This has no analogue in flat space-
time).One string is stable (its proper size tends to a constant for , and its comoving size contracts); the other strings are unstable (their
proper sizes blow up for , while their comoving sizes tend to cons-
tants). These solutions (even the stable strings) do not oscillate in time. The
interpretation of these solutions and their dynamics in terms of the sinh-
Gordon model is particularly enlighting.Comment: 25 pages, latex. LPTHE 93-44. Figures available from the auhors under
reques
String Propagation through a Big Crunch/Big Bang Transition
We consider the propagation of classical and quantum strings on cosmological
space-times which interpolate from a collapsing phase to an expanding phase. We
begin by considering the classical propagation of strings on space-times with
isotropic and anisotropic cosmological singularities. We find that cosmological
singularities fall into two classes, in the first class the string evolution is
well behaved all the way up to the singularity, whilst in the second class it
becomes ill-defined. Then assuming the singularities are regulated by string
scale corrections, we consider the implications of the propagation through a
`bounce'. It is known that as we evolve through a bounce, quantum strings will
become excited giving rise to `particle transmutation'. We reconsider this
effect, giving qualitative arguments for the amount of excitation for each
class. We find that strings whose physical wavelength at the bounce is less
that inevitably emerge in highly excited states, and that in
this regime there is an interesting correspondence between strings on
anisotropic cosmological space-times and plane waves. We argue that long
wavelength modes, such as those describing cosmological perturbations, will
also emerge in mildly excited string scale mass states. Finally we discuss the
relevance of this to the propagation of cosmological perturbations in models
such as the ekpyrotic/cyclic universe.Comment: 15 page
Cosmological evolution of warm dark matter fluctuations II: Solution from small to large scales and keV sterile neutrinos
We solve the cosmological evolution of warm dark matter (WDM) density
fluctuations with the Volterra integral equations of paper I. In the absence of
neutrinos, the anisotropic stress vanishes and the Volterra equations reduce to
a single integral equation. We solve numerically this equation both for DM
fermions decoupling at equilibrium and DM sterile neutrinos decoupling out of
equilibrium. We give the exact analytic solution for the density fluctuations
and gravitational potential at zero wavenumber. We compute the density contrast
as a function of the scale factor a for a wide range of wavenumbers k. At fixed
a, the density contrast grows with k for k
k_c, (k_c ~ 1.6/Mpc). The density contrast depends on k and a mainly through
the product k a exhibiting a self-similar behavior. Our numerical density
contrast for small k gently approaches our analytic solution for k = 0. For
fixed k < 1/(60 kpc), the density contrast generically grows with a while for k
> 1/(60 kpc) it exhibits oscillations since the RD era which become stronger as
k grows. We compute the transfer function of the density contrast for thermal
fermions and for sterile neutrinos in: a) the Dodelson-Widrow (DW) model and b)
in a model with sterile neutrinos produced by a scalar particle decay. The
transfer function grows with k for small k and then decreases after reaching a
maximum at k = k_c reflecting the time evolution of the density contrast. The
integral kernels in the Volterra equations are nonlocal in time and their
falloff determine the memory of the past evolution since decoupling. This
falloff is faster when DM decouples at equilibrium than when it decouples out
of equilibrium. Although neutrinos and photons can be neglected in the MD era,
they contribute in the MD era through their memory from the RD era.Comment: 27 pages, 6 figures. To appear in Phys Rev
Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
The string propagation equations in axisymmetric spacetimes are exactly
solved by quadratures for a planetoid Ansatz. This is a straight
non-oscillating string, radially disposed, which rotates uniformly around the
symmetry axis of the spacetime. In Schwarzschild black holes, the string stays
outside the horizon pointing towards the origin. In de Sitter spacetime the
planetoid rotates around its center. We quantize semiclassically these
solutions and analyze the spin/(mass) (Regge) relation for the planetoids,
which turns out to be non-linear.Comment: Latex file, 14 pages, two figures in .ps files available from the
author
Granular mixtures modeled as elastic hard spheres subject to a drag force
Granular gaseous mixtures under rapid flow conditions are usually modeled by
a multicomponent system of smooth inelastic hard spheres with constant
coefficients of normal restitution. In the low density regime an adequate
framework is provided by the set of coupled inelastic Boltzmann equations. Due
to the intricacy of the inelastic Boltzmann collision operator, in this paper
we propose a simpler model of elastic hard spheres subject to the action of an
effective drag force, which mimics the effect of dissipation present in the
original granular gas. The Navier--Stokes transport coefficients for a binary
mixture are obtained from the model by application of the Chapman--Enskog
method. The three coefficients associated with the mass flux are the same as
those obtained from the inelastic Boltzmann equation, while the remaining four
transport coefficients show a general good agreement, especially in the case of
the thermal conductivity. Finally, the approximate decomposition of the
inelastic Boltzmann collision operator is exploited to construct a model
kinetic equation for granular mixtures as a direct extension of a known kinetic
model for elastic collisions.Comment: The title has been changed, 4 figures, and to be published in Phys.
Rev.
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