Measurement of the epicycle frequency in the Galactic disc and initial velocities of open clusters

A new method to measure the epicycle frequency kappa in the Galactic disc is presented. We make use of the large data base on open clusters completed by our group to derive the observed velocity vector (amplitude and direction) of the clusters in the Galactic plane. In the epicycle approximation, this velocity is equal to the circular velocity given by the rotation curve, plus a residual or perturbation velocity, of which the direction rotates as a function of time with the frequency kappa. Due to the non-random direction of the perturbation velocity at the birth time of the clusters, a plot of the present-day direction angle of this velocity as a function of the age of the clusters reveals systematic trends from which the epicycle frequency can be obtained. Our analysis considers that the Galactic potential is mainly axis-symmetric, or in other words, that the effect of the spiral arms on the Galactic orbits is small; in this sense, our results do not depend on any specific model of the spiral structure. The values of kappa that we obtain provide constraints on the rotation velocity of the in particular, V(0) is found to be 230 +/- 15 km s(-1) even if the scale (R(0) = 7.5 kpc) of the Galaxy is adopted. The measured kappa at the solar radius is 43 +/- 5 km s(-1) kpc(-1). The distribution of initial velocities of open clusters is discussed.

Consequences of Simulated Loss of Open Cerrado Areas to Bird Functional Diversity

Over the past 35 years, more than two thirds of the Cerrado`s original expanse has been taken by agriculture. Even if some attempts have been made to conserve closed cerrado physiognomies, open cerrado physiognomies, richer in species and more fragile, have been systematically ignored. These open physiognomies are used by almost half of the Cerrado bird species, many of which being endemics. Using data from 11 surveys carried out in Cerrado landscapes, we asked what would happen to bird functional diversity if open cerrado species became extinct. Open cerrado birds would be able to keep on average 59% of the functional diversity. If they became extinct, on average 27% of the functional diversity would be lost. In this case, the remaining functional diversity would be lower than what would be expected by chance in five sites. Although many functions were shared by both open cerrado and forest species, there was some degree of complementarity between them, highlighted by the decrease in functional diversity when the former became extinct. Destruction of open cerrado physiognomies would lead to a habitat simplification, decrease in bird functional diversity, and, ultimately, to a considerable impact on community functioning. Thus, open cerrado physiognomies must receive much more conservation attention than they are currently receiving, because they maintain a high bird functional diversity that would otherwise be considerably diminished Were open cerrado species to become extinct.

Microgranitic Enclaves as Products of Self-mixing Events: a Study of Open-system Processes in the Maua Granite, Sao Paulo, Brazil, Based on in situ Isotopic and Trace Elements in Plagioclase

Felsic microgranular enclaves with structures indicating that they interacted in a plastic state with their chemically similar host granite are abundant in the Maua Pluton, SE Brazil. Larger plagioclase xenocrysts are in textural disequilibrium with the enclave groundmass and show complex zoning patterns with partially resorbed An-rich cores (locally with patchy textures) surrounded by more sodic rims. In situ laser ablation-(multi-collector) inductively coupled plasma mass spectrometry trace element and Sr isotopic analyses performed on the plagioclase xenocrysts indicate open-system crystallization; however, no evidence of derivation from more primitive basic melts is observed. The An-rich cores have more radiogenic initial Sr isotopic ratios that decrease towards the outermost part of the rims, which are in isotopic equilibrium with the matrix plagioclase. These profiles may have been produced by either (1) diffusional re-equilibration after rim crystallization from the enclave-forming magma, as indicated by relatively short calculated residence times, or (2) episodic contamination with a decrease of the contaminant ratio proportional to the extent to which the country rocks were isolated by the crystallization front. Profiles of trace elements with high diffusion coefficients would require unrealistically long residence times, and can be modeled in terms of fractional crystallization. A combination of trace element and Sr isotope data suggests that the felsic microgranular enclaves from the Maua Pluton are the products of interaction between end-member magmas that had similar compositions, thus recording `self-mixing` events.

The number of open paths in an oriented rho-percolation model

We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.