31,976 research outputs found
Spectra of primordial fluctuations in two-perfect-fluid regular bounces
We introduce analytic solutions for a class of two components bouncing
models, where the bounce is triggered by a negative energy density perfect
fluid. The equation of state of the two components are constant in time, but
otherwise unrelated. By numerically integrating regular equations for scalar
cosmological perturbations, we find that the (would be) growing mode of the
Newtonian potential before the bounce never matches with the the growing mode
in the expanding stage. For the particular case of a negative energy density
component with a stiff equation of state we give a detailed analytic study,
which is in complete agreement with the numerical results. We also perform
analytic and numerical calculations for long wavelength tensor perturbations,
obtaining that, in most cases of interest, the tensor spectral index is
independent of the negative energy fluid and given by the spectral index of the
growing mode in the contracting stage. We compare our results with previous
investigations in the literature.Comment: 11 pages, 5 figure
The Redner - Ben-Avraham - Kahng cluster system
We consider a coagulation model first introduced by Redner, Ben-Avraham and
Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J.
Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that
the reaction between a j-cluster and a k-cluster results in the creation of a
|j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this
paper we prove existence and uniqueness of solutions under reasonably general
conditions on the coagulation coefficients, and we also establish
differenciability properties and continuous dependence of solutions. Some
interesting invariance properties are also proved. Finally, we study the
long-time behaviour of solutions, and also present a preliminary analysis of
their scaling behaviour.Comment: 24 pages. 2 figures. Dedicated to Carlos Rocha and Luis Magalhaes on
the occasion of their sixtieth birthday
On the convergence to critical scaling profiles in submonolayer deposition models
In this work we study the rate of convergence to similarity profiles in a
mean field model for the deposition of a submonolayer of atoms in a crystal
facet, when there is a critical minimal size for the stability of the
formed clusters. The work complements recently published related results by the
same authors in which the rate of convergence was studied outside of a critical
direction in the cluster size vs. time plane. In this paper
we consider a different similarity variable, ,
corresponding to an inner expansion of that critical direction, and prove the
convergence of solutions to a similarity profile when with fixed, as well as the rate at which the limit is
approached.Comment: Dedicated to the memory of Jack Car
Flux-tube geometry and solar wind speed during an activity cycle
The solar wind speed at 1 AU shows variations in latitude and in time which
reflect the evolution of the global background magnetic field during the
activity cycle. It is commonly accepted that the terminal wind speed in a
magnetic flux-tube is anti-correlated with its expansion ratio, which motivated
the definition of widely-used semi-empirical scaling laws relating one to the
other. In practice, such scaling laws require ad-hoc corrections. A predictive
law based solely on physical principles is still missing. We test whether the
flux-tube expansion is the controlling factor of the wind speed at all phases
of the cycle and at all latitudes using a very large sample of wind-carrying
open magnetic flux-tubes. We furthermore search for additional physical
parameters based on the geometry of the coronal magnetic field which have an
influence on the terminal wind flow speed. We use MHD simulations of the corona
and wind coupled to a dynamo model to provide a large statistical ensemble of
open flux-tubes which we analyse conjointly in order to identify relations of
dependence between the wind speed and geometrical parameters of the flux-tubes
which are valid globally (for all latitudes and moments of the cycle). Our
study confirms that the terminal speed of the solar wind depends very strongly
on the geometry of the open magnetic flux-tubes through which it flows. The
total flux-tube expansion is more clearly anti-correlated with the wind speed
for fast rather than for slow wind flows, and effectively controls the
locations of these flows during solar minima. Overall, the actual asymptotic
wind speeds attained are also strongly dependent on field-line inclination and
magnetic field amplitude at the foot-points. We suggest ways of including these
parameters on future predictive scaling-laws for the solar wind speed.Comment: Accepted for publicaton on Astronomy & Astrophysic
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