Shear thinning and thixotropy of HMHEC and HEC water solutions

Steady state viscosity and thixotropy of hydrophobically modified hydroxyethyl cellulose HMHEC and nonassociative cellulose water solutions are studied. Although all the samples are shear thinning, only the HMHEC is thixotropic, since the migration of hydrophobes to micelles is controlled by diffusion. The Cross model fits steady state curves. The Mewis model, a phenomenological model that proposes that the rate of change of viscosity when the shear rate is suddenly changed is related to the difference between the steady state and current values of viscosity raised to an exponent, fits structure construction experiments when the exponent, n, is estimated to be around 2. The Newtonian assumption used by Mewis cannot be used here, however. This seems to be related to the fact that the thickening is due to bridged micelle formation, which is a slow process, and also to topological constraints and entanglements, which are rapid processes. The kinetic parameter was redefined to kn in order to make it independent of initial conditions. So, kn depends only on how the shear affects the structure. kn reaches a plateau at shear rates too low to produce structure destruction and decreases at higher shear rates.

Assessing the environmental impact of water consumption by energy crops grown in Spain

The environmental impact of the water consumption of four typical crop rotations grown in Spain, including energy crops, was analyzed and compared against Spanish agricultural and natural reference situations. The life cycle assessment (LCA) methodology was used for the assessment of the potential environmental impact of blue water (withdrawal from water bodies) and green water (uptake of soil moisture) consumption. The latter has so far been disregarded in LCA. To account for green water, two approaches have been applied: the first accounts for the difference in green water demand of the crops and a reference situation. The second is a green water scarcity index, which measures the fraction of the soil-water plant consumption to the available green water. Our results show that, if the aim is to minimize the environmental impacts of water consumption, the energy crop rotations assessed in this study were most suitable in basins in the northeast of Spain. In contrast, the energy crops grown in basins in the southeast of Spain were associated with the greatest environmental impacts. Further research into the integration of quantitative green water assessment in LCA is crucial in studies of systems with a high dependence on green water resources.

Comparison of flag leaf and ear photosynthesis with biomass and grain yield of durum wheat under various water conditions and genotypes

Photosynthetic activity of cereals has traditionally been studied using leaves, thus neglecting the role of other organs such as ears. Here, we studied the effects of water status and genotypes on the photosynthetic activity of the flag leaf blade and the ear of durum wheat. The various parameters related to the photosynthetic activity were analysed in relation to the total above-ground plant biomass and grain yield at maturity. Four local varieties plus two cultivars adapted to the semiarid areas of South Morocco were grown in pots in a greenhouse. Five different water treatments were maintained from the beginning of stem elongation to maturity, when shoot biomass and grain yield were recorded. The net photosynthesis (A), stomatal conductance (gs) and transpiration (T) of the ear and the flag leaf were measured at anthesis. In both organs these factors decreased significantly with water deficit, whereas the A/T and A/gs ratios increased. The genotype effect was also significant for all traits studied. Whole-organ photosynthesis was much higher in the ear than in the flag leaf in well-watered conditions. As water stress developed, photosynthesis decreased less in the ear than in the flag leaf. Whole-ear photosynthesis correlated better than flag leaf photosynthesis with biomass and yield. Nevertheless, the relationships of the whole flag leaf with biomass and yield improved as the water stress became more severe, suggesting a progressive shift of yield from sink to source limitation. For all water regimes the ratios A/gs and A/T of the ear also showed a higher (negative) correlation with both biomass and yield than those of the flag leaf. The results indicate that the ear has a greater photosynthetic role than the flag leaf in determining grain yield, not only in drought but also in the absence of stress.

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.