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

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 $n\geq 2$ 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 $x=\tau$ in the cluster size $x$ vs. time $\tau$ plane. In this paper we consider a different similarity variable, $\xi := (x-\tau)/\sqrt{\tau}$, corresponding to an inner expansion of that critical direction, and prove the convergence of solutions to a similarity profile $\Phi_{2,n}(\xi)$ when $x, \tau\to +\infty$ with $\xi$ fixed, as well as the rate at which the limit is approached.Comment: Dedicated to the memory of Jack Car

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

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