These notes correspond to a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularity and expose recent research in connection with semi-toric systems. The quantum and semiclassical counterpart will also be presented, in the viewpoint of the inverse question: from the quan...

208 Pb induced reactions at the CERN SPS are presented. Inclusive photon spectra down to a transverse momentum of 30 MeV/c measured with leadglass spectrometer LEDA of the WA98 experiment are compared to the VENUS Monte-Carlo model. The inverse slope of 0 spectra is studied as a function of the centrality of the reaction. A saturation of the extracted slope parameter for semi-central and centra...

In this paper a hybrid semi-analytical Finite Element formulation is proposed to efficiently calculate the time dependent response due to stress waves propagating in a slender solid with uniform cross-section when excited by impulsive forces. The formulation takes advantage of the direct and inverse Fourier transform to formulate and solve the governing wave equation. The framework is applied t...

A quasi-static analysis of an open-ended coaxial line terminated by a semi-infinite medium on ground plane is presented in this paper. The analysis is based on a vtiriation formulation of the problem. A comparison of results obtained by this method with the experimental and the other theoretical approaches shows an excellent agreement. This analysis is expected to be helpful in the inverse prob...

This paper obtains the soliton solutions to the Boussinesq equation with the effect of surface tension being taken into account. The power law nonlinearity is considered. Three integration tools are adopted in order to extract the soliton solutions. They are the traveling wave hypothesis, ansatz method and the semi-inverse variational principle. Finally, the Lie symmetry approach is adopted to ...

This paper derives sharp l∞ and l1 estimates of the error arising from an explicit approximation of the constant coefficient 1D convection/diffusion equation with Dirac initial data. The analysis embeds the discrete equations within a semi-discrete system of equations which can be solved by Fourier analysis. The error estimates are then obtained though asymptotic approximation of the integrals ...

The spectrum of quantum fluctuations of the electromagnetic field produced by quantized matter is determined. It is found that in a wide range of practically important frequencies, the spectral density of fluctuations exhibits an inverse frequency dependence. The magnitude of fluctuations produced by a conducting sample has a Gaussian distribution around its mean value which is inversely propor...

A Semi-Analytical Finite Element (SAFE) method is developed to model accurately the propagation velocity and leakage of guided waves along an immersed waveguide with arbitrary non-circular cross-section. Thus an accurate inverse model is provided to measure the density of the fluid by measuring the change of the torsional wave speed. Experimental results obtained with a rectangular bar in a ran...

We provide a complete analysis of the asymptotics for the semi-infinite Schur flow: αj(t) = (1 − |αj(t)|)(αj+1(t) − αj−1(t)) for α−1(t) = 1 boundary conditions and n = 0, 1, 2, . . . , with initial condition αj(0) ∈ (−1, 1). We also provide examples with αj(0) ∈ D for which α0(t) does not have a limit. The proofs depend on the solution via a direct/inverse spectral transform.