RESUMEN
A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, which is studied in a novel manner using statistical methods. The simulation data exhibit transport processes with both medium and long correlation length along the radius. A typical example of a phenomenon with long correlation length is avalanches. In order to investigate the evolution of the turbulent state, two basic configurations are studied, one flux-driven and one gradient-driven with decaying turbulence. The information length concept in tandem with Boltzmann-Gibbs and Tsallis entropy is used in the investigation. It is found that the dynamical states in both flux-driven and gradient-driven cases are surprisingly similar, but the Tsallis entropy reveals differences between them. This indicates that the types of probability distribution function are nevertheless quite different since the higher moments are significantly different.
RESUMEN
The numerical solutions to a non-linear Fractional Fokker-Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.
RESUMEN
Willow species have been suggested for use in the remediation of contaminated soils due to their high biomass production, fast growth, and high accumulation of heavy metals. The tolerance and accumulation of metals may vary among willow species and varieties, and the assessment of this variability is vital for selecting willow species/varieties for phytoremediation applications. Here, we examined the variations in lead (Pb) tolerance and accumulation of three cultivated varieties of Salix integra (Weishanhu, Yizhibi and Dahongtou), a shrub willow native to northeastern China, using hydroponic culture in a greenhouse. In general, the tolerance and accumulation of Pb varied among the three willow varieties depending on the Pb concentration. All three varieties had a high tolerance index (TI) and EC50 value (the effective concentration of Pb in the nutrient solution that caused a 50% inhibition on biomass production), but a low translocation factor (TF), indicating that Pb sequestration is mainly restricted in the roots of S. integra. Among the three varieties, Dahogntou was more sensitive to the increased Pb concentration than the other two varieties, with the lowest EC50 and TI for root and above-ground tissues. In this respect, Weishanhu and Yizhibi were more suitable for phytostabilization of Pb-contaminated soils. However, our findings also indicated the importance of considering the toxicity symptoms when selecting willow varieties for the use of phytoremediation, since we also found that the three varieties revealed various toxicity symptoms of leaf wilting, chlorosis and inhibition of shoot and root growth under the higher Pb concentrations. Such symptoms could be considered as a supplementary index in screening tests.