98 resultados para Chaotic solutions


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In this study we have investigated the uptake and distribution of arsenic (As) and phosphate (Pi) in roots, shoots, and grain of wheat grown in an uncontaminated soil irrigated with solutions containing As at three different concentrations (0.5, 1 and 2 mg l-1) and in the presence or in the absence of P fertilization. Arsenic in irrigation water reduced plants growth and decreased grain yield. When Pi was not added (P-), plants were more greatly impacted compared to the plus Pi (P+) treatments. The differences in mean biomass between P- and P+ treatments at the higher As concentrations demonstrated the role of Pi in preventing As toxicity and growth inhibition. Arsenic concentrations in root, shoot and grain increased with increasing As concentration in irrigation water. It appears that P fertilization minimizes the translocation of As to the shoots and grain whilst enhancing P status of plant. The observation that P fertilization minimises the translocation of arsenic to the shoots and grain is interesting and may be useful for certain regions of the world that has high levels of As in groundwater or soils. © 2008 Springer Science+Business Media B.V.

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In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC0([0,T];Lp(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are Lp–Lq-estimates, regularization property of the linear part of e−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.