Thermodynamics of Chaplygin gas

We clarify thermodynamics of the Chaplygin gas by introducing the integrability condition. All thermal quantities are derived as functions of either volume or temperature. Importantly, we find a new general equation of state, describing the Chaplygin gas completely. We confirm that the Chaplygin gas could show a unified picture of dark matter and energy which cools down through the universe expansion without any critical point (phase transition).Comment: 5 pages, 4 figures, version "Accepted for publication in Astrophysics & Space Science

Minimal H\"older regularity implying finiteness of integral Menger curvature

We study two families of integral functionals indexed by a real number $p > 0$. One family is defined for 1-dimensional curves in $\R^3$ and the other one is defined for $m$-dimensional manifolds in $\R^n$. These functionals are described as integrals of appropriate integrands (strongly related to the Menger curvature) raised to power $p$. Given $p > m(m+1)$ we prove that $C^{1,\alpha}$ regularity of the set (a curve or a manifold), with $\alpha > \alpha_0 = 1 - \frac{m(m+1)}p$ implies finiteness of both curvature functionals ($m=1$ in the case of curves). We also show that $\alpha_0$ is optimal by constructing examples of $C^{1,\alpha_0}$ functions with graphs of infinite integral curvature

Behavior of tumors under nonstationary theraphy

We present a model for the interaction dynamics of lymphocytes-tumor cells population. This model reproduces all known states for the tumor. Futherly,we develop it taking into account periodical immunotheraphy treatment with cytokines alone. A detailed analysis for the evolution of tumor cells as a function of frecuency and theraphy burden applied for the periodical treatment is carried out. Certain threshold values for the frecuency and applied doses are derived from this analysis. So it seems possible to control and reduce the growth of the tumor. Also, constant values for cytokines doses seems to be a succesful treatment.Comment: 6 pages, 7 figure

Water requirements and footprint of a super intensive olive grove under Mediterranean climate

Abstract The water footprint of a product can be described as the volume of freshwater used to produce it, associated to a geographic and temporal resolution. For crops, the water footprint relates crop water requirements and yield. The components of water footprint, blue, green and grey water footprints, refer to the volumes of respectively, surface and groundwater, rainfall, and water required to assimilate pollution, used to produce the crop yield. The global standard for crop water footprint assessment relies on evapotranspiration models to estimate green and blue water evapotranspiration. This approach has been used in the present study to estimate the water footprint of a very high density drip irrigated olive grove and further compared with data obtained from evapotranspiration measurements or from its components: the eddy covariance method to quantify latent heat flux, a heat dissipation sap flow technique to determine transpiration and microlysimeters to evaluate soil evaporation. The eddy covariance technique was used for short periods in 2011 and 2012, while sap flow measurements were performed continuously, hence allowing the extension of the data series. Measurements of evapotranspiration with the eddy covariance method provided an average close to 3.4 mm d-1 (2011) and 2.5 mm d-1 (2012). The ratio of evapotranspiration to reference evapotranspiration approached 0.6 and 0.4 for the respective periods. The water footprint of the olive crop under study, calculated with field data, was higher than the water footprint simulated using the global standard assessment and was lower than that reported in literature for olives. Lower values are probably related to differences in cultural practices, e.g., the density of plantation, harvesting techniques and irrigation management. The irrigated high-density olive grove under study had a high yield, which compensates for high water consumption, thus leading to a water footprint lower than the ones of rainfed or less dense groves. Other differences may relate to the procedures used to determine evapotranspiration