Damping of quasi-2D internal wave attractors by rigid-wall friction

The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto 'wave attractors'. For small-amplitude internal waves, the projection of energy onto higher wave numbers by geometric focusing can be balanced by viscous dissipation at high wave numbers. Contrary to what was previously suggested, viscous dissipation in interior shear layers may not be sufficient to explain the experiments on wave attractors in the classical quasi-2D trapezoidal laboratory set-ups. Applying standard boundary layer theory, we provide an elaborate description of the viscous dissipation in the interior shear layer, as well as at the rigid boundaries. Our analysis shows that even if the thin lateral Stokes boundary layers consist of no more than 1% of the wall-to-wall distance, dissipation by lateral walls dominates at intermediate wave numbers. Our extended model for the spectrum of 3D wave attractors in equilibrium closes the gap between observations and theory by Hazewinkel et al. (2008)

Quasi-BiHamiltonian Systems and Separability

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997

Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator

The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these additional structures are a consequence of the existence of dynamical symmetries of non-symplectic (non-canonical) type. The associated recursion operators are also obtained.Comment: 10 pages, submitted to J. Phys. A:Math. Ge

The quasi-bi-Hamiltonian formulation of the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation.Comment: 12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen. (March 2002

Quantization of Nonstandard Hamiltonian Systems

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of the quantum theory. A spin-1/2 system is taken as an example in which all the steps can be completed. It is shown that the geometry of the quantum theory imposes restrictions on the physically allowed nonstandard quantum theories.Comment: Revtex file, 23 pages, no figure

The SPS as accelerator of Pb82+^{82+} ions

In 1994 the CERN SPS was used for the first time to accelerate fully stripped ions of the Pb208 isotope from the equivalent proton momentum of 13 GeV/c to 400 GeV/c. In the CERN PS, which was used as injector, the lead was accelerated as Pb53+ ions and then fully stripped in the transfer line from PS to SPS. The radio frequency swing which is needed in order to keep the synchronism during acceleration is too big to have the SPS cavities deliver enough voltage for all frequencies. For that reason a new technique of fixed frequency acceleration was used. With this technique up to 70% of the injected beam could be captured and accelerated up to the extraction energy, the equivalent of 2.2 1010 charges. The beam was extracted over a 5 sec. long spill and was then delivered to different experiments at the same time

Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy

We discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.Comment: 20 pages, LaTeX2e, report to NEEDS in Leeds (1998), to be published in Theor. Math. Phy

The SPS as lead-ion accelerator

In 1995 the CERN SPS was used during two months to accelerate fully stripped ions of the Pb208 isotope from the equivalent proton momentum of 13 GeV/c to 400 GeV/c. The radio frequency swing which is needed in order to keep the synchronism during acceleration is too big to have the SPS cavities deliver enough voltage for all frequencies. In a first stage, the beam is accelerated from 13 GeV/c to 26 GeV/c using the fixed frequency mode. During this stage the beam is grouped in four 2msec batches, separated by 3msec holes during which the frequency is changed in order to keep synchronism. At 26 GeV the beams are de-bunched and recaptured in order to fill the 3msec holes. From there on the lead ions are then accelerated up to 400 GeV/c with the normal frequency program. The de-bunching and recapture at 26 GeV improved the effective spill at extraction by a factor of three. Intensities up to 3.9 1010 charges could be obtained at 400 GeV/c. The total efficiency of the two RF captures was 64%

Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure

Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2))

In this paper, we establish the connection between the quantized W-algebra of ${\frak sl}(2,1)$ and quantum parafermions of $U_q(\hat {\frak sl}(2))$ that a shifted product of the two quantum parafermions of $U_q(\hat {\frak sl}(2))$ generates the quantized W-algebra of ${\frak sl}(2,1)$