Collective Modes in Neutrino `Beam' Electron-Positron Plasma Interactions

We derive semiclassical neutrino-electron transport equations in the collisionless (Vlasov) limit from the coupled Dirac equations, incorporating the charged and neutral weak current-current as well as electromagnetic interactions. A corresponding linear response theory is derived. In particular, we calculate the response functions for a variety of beam-plasma geometries, which are of interest in a supernova scenario. We apply this to the study of plasmons and to a new class of collective {\it pharon} resonance modes, which are characterized by $\omega < q$. We find that the growth rates of the unstable modes correspond to a strongly temperature ($\propto T_\nu^2T_e^3$) and linearly momentum dependent e-folding length of about $10^{10}$ km under typical conditions for Type II supernovae. This appears to rule out such long-wavelength collective modes as an efficient means of depositing neutrino energy into the plasma sphere.Comment: 27 pages; LaTex. Replaced by published version. - Appendix about neutrino Wigner functions added and main text correspondingly revised. Conclusions unchange

Diet of two syntopic species of Crenuchidae (Ostariophysi: Characiformes) in an Amazonian rocky stream

Abstract This study assessed the diet of two poorly known syntopic fish species of the family Crenuchidae, Characidium aff. declivirostre and Leptocharacidium omospilus, in a Presidente Figueiredo´ rocky stream, Amazonas, Brazil. The stomach contents were analyzed and their Frequency of Occurrence (FO %) and Relative Volume (Vol %) were combined in a Feeding Index (IAi). We examined 20 individuals of C. aff. declivirostre and 23 of L. omospilus. The Morisita-Horn Index was used to estimate the overlap between the diets of these species. Immature insects were the most valuable items consumed by both fish species. The diet of C. aff. declivirostre was mainly composed of larvae and pupae of Chironomidae, while L. omospilus predominantly consumed larvae of Hydroptilidae, Hydropyschidae and Pyralidae. Thus, both species were classified as autochthonous insectivorous. Characidium aff. declivirostre was considered a more specialized species, probably reflecting lower feeding plasticity or the use of more restricted microhabitats compared to L. omospilus. When the food items were analyzed at the family taxonomic level, the diet overlap between these species was considered moderate (Morisita-Horn Index = 0.4). However, a more thorough analysis, at the genus level, indicates a very low diet overlap. Therefore, we conclude that the feeding segregation between C. aff. declivirostre and L. omospilus may favor their co-existence, despite their high phylogenetic closeness