Cooper pairing and finite-size effects in a NJL-type four-fermion model

Starting from a NJL-type model with N fermion species fermion and difermion condensates and their associated phase structures are considered at nonzero chemical potential $\mu$ and zero temperature in spaces with nontrivial topology of the form $S^1\otimes S^1\otimes S^1$ and $R^2\otimes S^1$. Special attention is devoted to the generation of the superconducting phase. In particular, for the cases of antiperiodic and periodic boundary conditions we have found that the critical curve of the phase transitions between the chiral symmetry breaking and superconducting phases as well as the corresponding condensates and particle densities strongly oscillate vs $\lambda\sim 1/L$, where $L$ is the length of the circumference $S^1$. Moreover, it is shown that at some finite values of $L$ the superconducting phase transition is shifted to smaller values both of $\mu$ and particle density in comparison with the case of $L=\infty$.Comment: 13 pages, 13 figures; minor changes; new references added; version accepted to PR

Nonperturbative Yukawa theory at finite density and temperature

In-medium Yukawa theory is part of the thermodynamics of the Standard Model of particle physics and is one of the main building blocks of most effective field theories of fermionic systems. By computing its pressure we investigate the nonperturbative thermodynamics at finite temperature and density using the optimized perturbation theory (OPT) framework. Our calculations are valid for arbitrary fermion and scalar masses, temperature, chemical potential, and not restricted to weak coupling. The model is considered in the presence as well as in the absence of condensates. Comparison with nonperturbative results shows that second order perturbation theory (PT) fails in the first case but performs rather well when condensates are absent, even at high-temperature regimes.Comment: 18 pages, 15 figures; v2: references added, improved discussion in the Conclusions, matches published versio

Current and Future Perspectives of Ethnomathematics as a Program

Mathematics Education; Learning; Teachin

The effect of best crop practices in the pig and poultry production on water productivity in a Southern Brazilian Watershed.

This study analyzes the relation between Brazilian broiler and pig production and water productivity using recently developed reference guidelines on water footprinting for livestock production systems and supply chains. Dierent rainfed crop arrangements, in dierent scenarios and producer regions in Brazil, were assessed. Water productivity of broiler feed consumption ranged from 0.63 to 1.38 kg perm3 water input to rainfed summer maize (safra) and from 1.20 to 2.21 kg perm3 water input to winter maize (safrinha) while it ranged from 0.28 to 0.95 kg perm3 water input to rainfed soy. For pig feed consumption, rainfed maize ranged from 0.68 to 1.49 kg per m3 water input (safra) and from 1.30 to 2.38 kg perm3 water input (safrinha) while it ranged from 0.30 to 1.03 kg per m3 water input to rainfed soy. A potential amount of water saving of 0.0336 km3 year-1 and 0.0202 km3 year-1 could be attained for producing broiler and pig feed, respectively, depending on the crop rotation and producer region. The results showed that the evapotranspiration of animal feed production represents more than 99% of the total water consumption for broiler and pig production in the study area. The implementation of best crop practices resulted in higher water productivity values of chicken and pork meat and also improved the rainfall water-saving in comparison to conventional agriculture. Hence, the water productivity of the animal production chain in tropical regions demands a close relation to agriculture in order to attain a better understanding and improvement of rainfall water productivity for animal feed production