Probability distribution function of dipolar field in two-dimensional spin ensemble

We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is expressed in terms of special functions. At the surface concentrations of the dipoles as high as 0.6 the dipolar field obey the Gaussian law. To obtain the distribution function within transitional region c<0.6, we propose the method based on the cumulant expansion. We calculate the parameters of the distributions for some specific configurations of the dipoles. The distribution functions of the ordered ensembles of the dipoles at the low and moderate surface concentrations have asymmetric shape with respect to distribution medians. The distribution functions allow to calculate various physical parameters of two-dimensional interacting nanoparticle ensembles.Comment: 9 pages, 3 figure

On the Dynamics of Proto-Neutron Star Winds and r-Process Nucleosynthesis

We study here the formation of heavy r-process nuclei in the high-entropy environment of rapidly expanding neutrino-driven winds from compact objects. In particular, we explore the sensitivity of the element creation in the A>130 region to the low-temperature behavior of the outflows. For this purpose we employ a simplified model of the dynamics and thermodynamical evolution for radiation dominated, adiabatic outflows. It consists of a first stage of fast, exponential cooling, followed by a second phase of slower evolution, either assuming constant density and temperature or a power-law decay of these quantities. These cases are supposed to capture the most relevant effects of a strong deceleration or decreasing acceleration of the transsonic outflows, respectively, e.g. in a wind termination shock caused by the collision with the slower, preceding supernova ejecta. We find that not only the transition temperature between the two expansion phases can make a big difference in the formation of the platinum peak, but also the detailed cooling law during the later phase. Unless the transition temperature and corresponding (free neutron) density become too small (T < 2*10^8 K), a lower temperature or faster temperature decline during this phase allow for a stronger appearance of the third abundance peak. Since the nuclear photodisintegration rates between ~2*10^8 K and ~10^9 K are more sensitive to the temperature than the n-capture rates are to the free neutron density, a faster cooling in this temperature regime shifts the r-process path closer to the n-drip line. With low (gamma,n)- but high beta-decay rates, the r-processing then does not proceed through a (gamma,n)-(n,gamma) equilibrium but through a quasi-equilibrium of (n,gamma)-reactions and beta-decays, as recently also pointed out by Wanajo.Comment: 18 pages, 14 figures with 25 eps plots; referee comments included; accepted by Astronomy & Astrophysic