Classical Integrable N=1 and N=2N= 2 Super Sinh-Gordon Models with Jump Defects

The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the N=1 and N=2 super sinh-Gordon models are constructed and shown to generate the Backlund transformations for its soliton solutions. As a new and interesting example, a solution with an incoming boson and an outgoing fermion for the N=1 case is presented. The resulting integrable models are shown to be invariant under supersymmetric transformation.Comment: talk presented at the V International Symposium on Quantum Theory and Symmetries, Valladolid, Spain, July 22-28,200

Effect of the Resolution and Accuracy of DTM produced with Aerial Photogrammetry and Terrestrial Laser Scanning on Slope- and Catchment-scale Erosion Assessment in a Recently Burnt Forest Area: a Case Study

Wildfires are a common phenomenon in Portugal, affecting on average 100.000 ha of rural areas per year and up to 400.000 ha in dramatic years like 2003 and 2005. Wildfires can strongly enhance the hydrological response and associated sediment losses in recently burnt forest catchments and, thereby, negatively affect land-use sustain- ability of the affected terrains as well as ecosystem functioning of downstream aquatic habitats. Therefore, the EROSFIRE-I and –II projects aim at developing a GIS-tool for predicting soil erosion hazard following wildfire and, ultimately, for assessing the implications of alternative post-fire land management practices. Assessment of runoff and soil erosion rates critically depends on accurate estimates of the corresponding runoff areas. In the case of catchments as well as unbounded erosion plots (arguably, the only practical solution for slope-scale measurements), delineation of runoff area requires a Digital Terrain Model (DTM) with an adequate resolution and accuracy. The DTM that was available for the Colmeal study area, localized in the mountain range of Lousã, in the central part of Portugal, of EROSFIRE-II project is that of the 1:25.000 topographic map produced by the Military Geographic Institute. Since the Colmeal area involves a rather small experimental catchment of roughly 10 ha and relatively short study slopes of less than 100 m long, two different data acquisition techniques were used to produce high-resolution and high-accuracy DTM. One of the data acquisition techniques is aerial photogrammetry whilst the other is terrestrial laser scanning. In order to produce a DTM by photogrammetric means, a dedicated digital aerial photography mission was carried out. The images have a pixel size of 10 cm. Manual measurements permitted to measure breaklines and were complemented by automatic measurements. In this way, a DTM in a TIN format was produced. This was further converted to grid format using the ArcGIS software system. Signalized control points allowed obtaining the DTM in the same global reference system as that employed for terrestrial laser scanning. The terrestrial laser scanning was done using a Riegl LMS Z360I, stationed in 8 points within the area to provide a complete coverage. The resulting dense cloud of points was filtered – by the company carrying out the scanning mission - to remove the non-terrain points (in particular vegetation). Several grids of different sizes were produced (0.10 x 0.10, 0.20 x 0.20, 0.50 x 0.50, 1 x 1 and 2 x 2 m2). This work will study the effect on runoff and erosion rates at the slope- and catchment-scale of DTM with differ- ent resolution, but produced with data collected with the same acquisition technique, and of DTM with the same resolution, but produced with data collected with the two different acquisition techniques. The study is being carried out in ArcGIS using DTM in a grid format. Preliminary results suggest that the conver- sion of TIN-to-grid in ArcGIS produces results that depend on the procedure being applied. Therefore, the different algorithms available at ArcGIS for TIN-to-grid conversion are currently being tested, using an artificially produced DTM. This testing includes various interpolation techniques for grid generation, and will be extended to different algorithms for computation of drainage flow direction

The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector Nonlinear Schrodinger equations appear as lowest negative and second positive flows within the extended hierarchy. This is fully analogous to the well-known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the ``negative'' sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update

The Conserved Charges and Integrability of the Conformal Affine Toda Models

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.Comment: 18 pages, LaTeX, (one appendix and one reference added, small changes in introduction and conclusions, eqs.(5.14) and (5.19) improved, final version to appear in Int. J. Modern Phys. A

Gauged Thirring Model in the Heisenberg Picture

We consider the (2+1)-dimensional gauged Thirring model in the Heisenberg picture. In this context we evaluate the vacuum polarization tensor as well as the corrected gauge boson propagator and address the issues of generation of mass and dynamics for the gauge boson (in the limits of QED$_3$ and Thirring model as a gauge theory, respectively) due to the radiative corrections.Comment: 14 pages, LaTex, no figure