Increasing the accuracy of positive displacement meters for the measurement of volume in liquid hydrocarbon logistics

Accuracy in the liquid hydrocarbons custody transfer is mandatory because it has a great economic impact. By far the most accurate meter is the positive displacement (PD) meter. Increasing such an accuracy may adversely affect the cost of the custody transfer, unless simple models are developed in order to lower the cost, which is the purpose of this work. PD meter consists of a fixed volume rotating chamber. For each turn a pulse is counted, hence, the measured volume is the number of pulses times the volume of the chamber. It does not coincide with the real volume, so corrections have to be made. All the corrections are grouped by a meter factor. Among corrections highlights the slippage flow. By solving the Navier-Stokes equations one can find an analytical expression for this flow. It is neither easy nor cheap to apply straightforward the slippage correction; therefore we have made a simple model where slippage is regarded as a single parameter with dimension of time. The model has been tested for several PD meters. In our careful experiments, the meter factor grows with temperature at a constant pace of 8?10?5?ºC?1. Be warned

Closures of positive braids and the Morton-Franks-Williams inequality

We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is an orthonormal basis for the inner product of the Hecke algebra of the braid group defined by Kálmán, who first obtained this result by using an interesting connection with Contact Topology. We also introduce a new technique to study the Homflypt polynomial for closures of positive braids, namely resolution trees whose leaves are simple braids. In terms of these simple resolution trees, we characterize closed positive braids for which the Morton-Franks-Williams inequality is strict. In particular, we determine explicitly the positive braid words on three strands whose closures have braid index three.

Physical stress and diversity-productivity relationships: The role of positive interactions

If environmental stress provides conditions under which positive relationships between plant species richness and productivity become apparent, then species that seem functionally redundant under constant conditions may add to community functioning under variable conditions. Using naturally co-occurring mosses and liverworts, we constructed bryophyte communities to test relationships between species diversity (1, 2, 4, 8, 16, 24, or 32 species) and productivity under constant conditions and when exposed to experimental drought. We found no relationship between species richness and biomass under constant conditions. However, when communities were exposed to experimental drought, biomass increased with species richness. Responses of individual species demonstrated that facilitative interactions rather than sampling effects or niche complementarity best explained results—survivorship increased for almost all species, and those species least resistant to drought in monoculture had the greatest increase in biomass. Positive interactions may be an important but previously underemphasized mechanism linking high diversity to high productivity under stressful environmental conditions.