Search

The oriented associativity equation plays a fundamental role in the theory of integrable systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order non-local homogeneous Hamiltonian operator belonging to a class which has been recently studied, thus providing a highly non-trivial example in that class and showing intriguing connections with algebraic geometry. [ABSTRACT FROM AUTHOR] more...

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in Pn+2 satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2, classify n-tuples of skew-symmetric 2-forms Aα∈Λ2(W) such that ϕβγAβ∧Aγ=0,for some non-degenerate symmetric ϕ. [ABSTRACT FROM AUTHOR] more...

A recently launched project under the auspices of the World Climate Research Program's (WCRP) Coordinated Regional Downscaling Experiments Flagship Pilot Studies program (CORDEX-FPS) is presented. This initiative aims to build first-of-its-kind ensemble climate experiments of convection permitting models to investigate present and future convective processes and related extremes over Europe and the Mediterranean. In this manuscript the rationale, scientific aims and approaches are presented along with some preliminary results from the testing phase of the project. Three test cases were selected in order to obtain a first look at the ensemble performance. The test cases covered a summertime extreme precipitation event over Austria, a fall Foehn event over the Swiss Alps and an intensively documented fall event along the Mediterranean coast. The test cases were run in both "weather-like" (WL, initialized just before the event in question) and "climate" (CM, initialized 1 month before the event) modes. Ensembles of 18–21 members, representing six different modeling systems with different physics and modelling chain options, was generated for the test cases (27 modeling teams have committed to perform the longer climate simulations). Results indicate that, when run in WL mode, the ensemble captures all three events quite well with ensemble correlation skill scores of 0.67, 0.82 and 0.91. They suggest that the more the event is driven by large-scale conditions, the closer the agreement between the ensemble members. Even in climate mode the large-scale driven events over the Swiss Alps and the Mediterranean coasts are still captured (ensemble correlation skill scores of 0.90 and 0.62, respectively), but the inter-model spread increases as expected. In the case over Mediterranean the effects of local-scale interactions between flow and orography and land–ocean contrasts are readily apparent. However, there is a much larger, though not surprising, increase in the spread for the Austrian event, which was weakly forced by the large-scale flow. Though the ensemble correlation skill score is still quite high (0.80). The preliminary results illustrate both the promise and the challenges that convection permitting modeling faces and make a strong argument for an ensemble-based approach to investigating high impact convective processes. [ABSTRACT FROM AUTHOR] more...