The quantum Neumann model: refined semiclassical results

We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching with the exact results for the whole range of parameters.Comment: 10 pages, 5 figures Minor edit

The quantum Neumann model: asymptotic analysis

We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.Comment: 14 pages, 3 figure

Tensor fields of mixed Young symmetry type and N-complexes

We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these $N$-complexes is non trivial, we prove a generalization of the Poincar\'e lemma. To that end we use a technique reminiscent of the Green ansatz for parastatistics. Several results which appeared in various contexts are shown to be particular cases of this generalized Poincar\'e lemma. We furthermore identify the nontrivial part of the generalized cohomology. Many of the results presented here were announced in [10].Comment: 47 page

The impact of systemic risk on the diversification benefits of a risk portfolio

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is lowComment: 17 pages, 5 tableau

On the effect of compressibility on the impact of a falling jet

At the first World Sloshing Dynamics Symposium that took place during the Nineteenth (2009) International Offshore and Polar Engineering (ISOPE) Conference in Osaka, Japan, it was made clear that simplified academic problems have an important role to play in the understanding of liquid impacts. The problem of the impact of a mass of liquid on a solid structure is considered. First the steady two-dimensional and irrotational flow of an inviscid and incompressible fluid falling from a vertical pipe, hitting a horizontal plate and flowing sideways, is considered. A parametric study shows that the flow can either leave the pipe tangentially or detach from the edge of the pipe. Two dimensionless numbers come into play: the Froude number and the aspect ratio between the falling altitude and the pipe width. When the flow leaves tangentially, it can either be diverted immediately by the plate or experience squeezing before being diverted. The profile of the pressure exerted on the plate is computed and discussed. Then the same problem is revisited with the inclusion of compressibility effects, both for the falling liquid and for the gas surrounding it. An additional dimensionless number comes into play, namely the Mach number. Finally, a discussion on the differences between the incompressible and compressible cases is provided