34,381 research outputs found
Hopf solitons and area preserving diffeomorphisms of the sphere
We consider a (3+1)-dimensional local field theory defined on the sphere. The
model possesses exact soliton solutions with non trivial Hopf topological
charges, and infinite number of local conserved currents. We show that the
Poisson bracket algebra of the corresponding charges is isomorphic to that of
the area preserving diffeomorphisms of the sphere. We also show that the
conserved currents under consideration are the Noether currents associated to
the invariance of the Lagrangian under that infinite group of diffeomorphisms.
We indicate possible generalizations of the model.Comment: 6 pages, LaTe
Spatial variability of soil properties and soil erodibility in the Alqueva reservoir watershed
The aim of this work is to investigate how the spatial variability of soil properties and soil erodibility (K factor) were affected by the changes in land use allowed by irrigation with water from a reservoir in a semiarid area. To this end, three areas representative of different land uses (agroforestry grassland, lucerne crop and olive orchard) were studied within a 900 ha farm. The interrelationships between variables were analyzed by multivariate techniques and extrapolated using geostatistics. The results confirmed differences between land uses for all properties analyzed, which was explained mainly by the existence of diverse management practices (tillage, fertilization and irrigation), vegetation cover and local soil characteristics. Soil organic matter, clay and nitrogen content decreased significantly, while the K factor increased with intensive cultivation. The HJ-Biplot methodology was used to represent the variation of soil erodibility properties grouped in land uses. Native grassland was the least correlated with the other land uses. The K factor demonstrated high correlation mainly with very fine sand and silt. The maps produced with geostatistics were crucial to understand the current spatial variability in the Alqueva region. Facing the intensification of land-use conversion, a sustainable management is needed to introduce protective measures to control soil erosion
Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems
We associate to an arbitrary -gradation of the Lie algebra of a
Lie group a system of Riccati-type first order differential equations. The
particular cases under consideration are the ordinary Riccati and the matrix
Riccati equations. The multidimensional extension of these equations is given.
The generalisation of the associated Redheffer--Reid differential systems
appears in a natural way. The connection between the Toda systems and the
Riccati-type equations in lower and higher dimensions is established. Within
this context the integrability problem for those equations is studied. As an
illustration, some examples of the integrable multidimensional Riccati-type
equations related to the maximally nonabelian Toda systems are given.Comment: LaTeX2e, 18 page
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