64 research outputs found
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 Pb 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 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
and quantum parafermions of that a
shifted product of the two quantum parafermions of
generates the quantized W-algebra of
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