On a priori energy estimates for characteristic boundary value problems

Motivated by the study of certain non linear free-boundary value problems for hyperbolic systems of partial differential equations arising in Magneto-Hydrodynamics, in this paper we show that an a priori estimate of the solution to certain boundary value problems, in the conormal Sobolev space H1_tan, can be transformed into an L2 a priori estimate of the same problem

A variational principle for volume-preserving dynamics

We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae

Local and nonlocal solvable structures in ODEs reduction

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure

Clutter and rainfall discrimination by means of doppler-polarimetric measurements and vertical reflectivity profile analysis

International audienceThe estimation of rainfall rate and other parameters from radar scattering volume is heavily affected by the presence of intense sea and ground clutter and echoes which appears in anomalous propagation condition. To deal with these non meteorological echoes we present a new clutter removal algorithm which combines the results of previous works. The algorithm fully exploits both the Doppler and polarimetric capabilities of the radar used and the analysis of vertical reflectivity profile in order to achieve the better identification of the meteorological and non-meteorological targets. The algorithm has been applied to the C-band radar of Monte Settepani (Savona, Italy), which runs in a high-topography environment. Preliminary results are presented

Clutter and rainfall discrimination by means of doppler-polarimetric measurements and vertical reflectivity profile analysis

The estimation of rainfall rate and other parameters from radar scattering volume is heavily affected by the presence of intense sea and ground clutter and echoes which appears in anomalous propagation condition. To deal with these non meteorological echoes we present a new clutter removal algorithm which combines the results of previous works. The algorithm fully exploits both the Doppler and polarimetric capabilities of the radar used and the analysis of vertical reflectivity profile in order to achieve the better identification of the meteorological and non-meteorological targets. The algorithm has been applied to the C-band radar of Monte Settepani (Savona, Italy), which runs in a high-topography environment. Preliminary results are presented

A priori estimates for 3D incompressible current-vortex sheets

We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions to the linearized equations. The existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. However, under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front, we prove an a priori estimate in Sobolev spaces for smooth solutions with no loss of derivatives. The result of this paper gives some hope for proving the local existence of smooth current-vortex sheets without resorting to a Nash-Moser iteration. Such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instabilities, which is well known in astrophysics

Root reinforcement dynamics in subalpine spruce forests following timber harvest: A case study in Canton Schwyz, Switzerland

Root reinforcement is a key factor when dealing with slope stability problems and is an important quantitative criterion for the evaluation of the protective function of forests against shallow landslides, as well as for the adoption of appropriate practices in protection forest management. Although many models have been developed to estimate root reinforcement, a reliable quantification that considers both its spatial and temporal variability still remains a challenge. This work aims to extend the understanding of the long term spatial and temporal dynamics of root reinforcement after forest harvest in subalpine spruce forests by supplying new experimental data and applying a state-of-the-art model.We estimated root reinforcement decay 5, 10 and 15 years after timber had been harvested in spruce stands in a small catchment in the Swiss Alps. We collected root distribution data at different distances from the trees and calibrated and validated a root distribution model (RootDis). To estimate root mechanical properties, we tested roots up to 12 mm diameter in the field, and computed root reinforcement for each case study with the Root Bundle Model. Finally, we developed a new model for the estimation of root reinforcement decay, based on the observed change in root distribution after felling and on the decay of the root pullout force. The final result is a model for the spatial-temporal prediction of root reinforcement heterogeneity and dynamics in subalpine spruce forest stands. Five year old harvested spruce forest in the climatic conditions of the study area provides 40% of the root reinforcement of live forest, while 15 years old harvested forest provides no reinforcement at all. Shrub species and natural regeneration could guarantee almost the 30% of the root reinforcement of a live forest after 15 years from cutting. Additional work is now required to further validate the model and implement these results in a slope stability analysis

On the relation between standard and μ\mu-symmetries for PDEs

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.

Stratification of the orbit space in gauge theories. The role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map. Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur

New results from the NA57 experiment

We report results from the experiment NA57 at CERN SPS on hyperon production at midrapidity in Pb-Pb collisions at 158 $A$ GeV/$c$ and 40 $A$ GeV/$c$. $\Lambda$, $\Xi$ and $\Omega$ yields are compared with those from the STAR experiment at the higher energy of the BNL RHIC. $\Lambda$, $\Xi$, $\Omega$\ and preliminary $K_S^0$ transverse mass spectra are presented and interpreted within the framework of a hydro-dynamical blast wave model.Comment: 8 pages, 3 figures, contribution to the proceedings of The XXXVIIIth Rencontres de Moriond "QCD and High Energy Hadronic Interactions