Quasi-periodic and periodic solutions for dynamical systems related to Korteweg-de Vries equation

We consider quasi-periodic and periodic (cnoidal) wave solutions of a set of n-component dynamical systems related to Korteweg-de Vries equation. Quasi-periodic wave solutions for these systems are expressed in terms of Novikov polynomials. Periodic solutions in terms of Hermite polynomials and generalized Hermite polynomials for dynamical systems related to Korteweg-de Vries equation are found. Received 15 October 2001 / Received in final form 6 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nakostov@ie.bas.bg     

Complexifications and real forms of Hamiltonian structures

We consider generalizations of the standard Hamiltonian dynamics to complex dynamical variables and introduce the notions of real Hamiltonian form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real Hamiltonian system we are able to relate several nonequivalent ones. On the example of the complex Toda chain we demonstrate how starting from a known integrable Hamiltonian system (e.g. the Toda chain) one can complexify it and then project onto different real forms. Received 18 October 2001 / Received in final form 24 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter ε, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(ε³), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy. Received 2 October 2001 / Received in final form 10 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: yasuhide@math.kyushu-u.ac.jp     

On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Hyperfine structure in the atomic spectrum of niobium

We report on hyperfine structure measurements in 21 lines of atomic niobium in the spectral region from 640 nm to 870 nm by means of optogalvanic laser spectroscopy and laser induced fluorescence spectroscopy using a hollow cathode discharge and a tunable single-mode cw ring laser. Hyperfine structure constants A and B of altogether 29 excited energy levels were determined, 18 of them for the first time. Received 18 July 2002 / Received in final form 8 November 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: sk@kalium.physik.tu-berlin.de     

Ultrametricity between states at different temperatures in spin-glasses

We prove the existence of correlations between the equilibrium states at different temperatures of the multi-p-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models. Furthermore, the overlaps satisfy ultrametric relations. As a consequence the Parisi tree is essentially the same at all temperatures with lower branches developing when lowering the temperature. We conjecture that the reference free energies of the clusters are also fixed at all temperatures as in the generalized random-energy model. Received 18 March 2002 / Received in final form 14 June 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: tommaso.rizzo@inwind.it     

Aging and energy landscapes: application to liquids and glasses

The equation of state for a liquid in equilibrium, written in the potential energy landscape formalism, is generalized to describe out-of-equilibrium conditions. The hypothesis that during aging the system explores basins associated to equilibrium configurations is the key ingredient in the derivation. Theoretical predictions are successfully compared with data from molecular dynamics simulations of different aging processes, such as temperature and pressure jumps. Received 7 August 2002 / Received in final form 8 October 2002 Published online 19 December 2002 RID="a" ID="a"Present address: Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 place Jussieu, Paris 75005, France e-mail: mossa@lptl.jussieu.fr     

Monte Carlo simulations of star-branched polyelectrolyte micelles

The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering data. Received 18 July 2002 and Received in final form 11 October 2002 RID="a" ID="a"e-mail: roger@drecam.saclay.cea.fr     

Birth and long-time stabilization of out-of-equilibrium coherent structures

We study an analytically tractable model with long-range interactions for which an out-of-equilibrium very long-lived coherent structure spontaneously appears. The dynamics of this model is indeed very peculiar: a bicluster forms at low energy and is stable for very long time, contrary to statistical mechanics predictions. We first explain the onset of the structure, by approximating the short time dynamics with a forced Burgers equation. The emergence of the bicluster is the signature of the shock waves present in the associated hydrodynamical equations. The striking quantitative agreement with the dynamics of the particles fully confirms this procedure. We then show that a very fast timescale can be singled out from a slower motion. This enables us to use an adiabatic approximation to derive an effective Hamiltonian that describes very well the long time dynamics. We then get an explanation of the very long time stability of the bicluster: this out-of-equilibrium state corresponds to a statistical equilibrium of an effective mean-field dynamics. Received 28 February 2002 / Received in final form 24 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: Thierry.Dauxois@ens-lyon.fr RID="b" ID="b"UMR-CNRS 5672 RID="c" ID="c"UMR 5582     

Resonance interaction between one excited and one ground state atom

The nature of the resonance interaction between two isotropic atoms in an excited configuration is reinvestigated. The currently accepted oscillatory form for the long-range retarded resonance interaction is shown to be a subtle artefact that arises due to too drastic approximations. Formulation of the resonance interaction energy problem in terms of the interacting system leads to a form that it is ∝ r ^-4 in the retarded limit. We also demonstrate that the resonance interaction energy at any finite temperature goes over to purely classical long-range asymptote. This manifestation of the correspondence principle is due to thermal excitation of the electromagnetic field. We finally discuss why the textbook result for the F?rster energy transfer between two atoms is incorrect for the same reasons. Received 31 January 2002 / Received in final form 25 July 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: mtb110@rsphysse.anu.edu.au     

Genetic Algorithms as a tool in the study of aperiodic order,with application to the case of X-Ray diffraction spectra of GaAs-AlAs multilayer heterostructures

We present the first application of Genetic Algorithms to the analysis of data from an aperiodically ordered system, high resolution X-Ray diffraction spectra from multilayer heterostructures arranged according to a deterministic or random scheme. This method paves the way to the solution of the “inverse problem”, that is the retrieval of the generating disorder from the investigation of the spectra of an unknown sample having non crystallographic, non quasi-crystallographic order. Received 18 March 2002 / Received in final form 3 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: Evelyne.Lutton@inria.fr RID="b" ID="b"CNRS UMR 8502     

Induced bubble shape oscillations and their impact on the rise velocity

When a 2-4 mm diameter bubble rising with constant velocity hits a thin wire, bubble shape oscillations can be induced. As a consequence also the bubble rise velocity strongly oscillates. With the help of a force balance we show that these velocity oscillations are an added-mass effect. Received 9 April 2002 / Received in final form 11 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: lohse@tn.utwente.nl     

Transmittance anomalies of a ring with lead-positional asymmetry

We examine the anomalous behavior of the transmittance through a one-dimensional ring having two branches of different lengths, as determined by the lead positions. Jumps in the transmittance phase are occurring in correspondence to both (a) zeros in the transmission at the eigenstates of the isolated ring and (b) destructive interference events. It is also found that when the ratio of the branch lengths is given by p/q satisfying p + q = 0(mod 4), the two characteristic zeros merge into a single point and the transmittance phase becomes identical to the so-called Friedel phase. Received 7 June 2002 / Received in final form 11 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: juyeon.yi@physik.uni-regensburg.de     

Interaction of coupled higher order nonlinear Schrödinger equation solitons

The novel inelastic collision properties of two-soliton interaction for an n-component coupled higher order nonlinear Schr?dinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the n-component coupled higher order nonlinear Schr?dinger equation are also discussed. Received 17 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: abhijit@iitg.ernet.in RID="b" ID="b"e-mail: sasanka@iitg.ernet.in RID="c" ID="c"e-mail: sudipta@iitg.ernet.in     

Skyrmions on an elastic cylinder

For a spin-polarized electron gas on an elastic cylinder in an external axial magnetic field and an axial electric field we find that the corresponding Euler-Lagrange equation is the double sine-Gordon (DSG) equation with an exact 2π-skyrmion solution. The DSG skyrmion is stabilized, without Coulomb repulsion, by the curvature of the cylinder. It adopts a characteristic length ξ which is smaller than the radius of the cylinder. For an elastic cylinder this mismatch of length scales causes a deformation of the cylinder in the region of the skyrmion. Received 23 October 2001 / Received in final form 8 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: rossen.dandoloff@ptm.u-cergy.fr     

Generalizations of Heisenberg uncertainty relation

A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and canonical quantum observables, and spin and quasi-spin components. Several new uncertainty relations are displayed. Received 10 October 2001 / Received in final form 6 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: dtrif@inrne.bas.bg     

Lagrangian and Eulerian velocity intermittency

Usual turbulence experiments, based on the Taylor hypothesis, differ from true Eulerian measurements. This is the origin of the apparent discrepancy between a recent two point correlation analysis and the multiplicative cascade picture. Indeed, both Eulerian and Lagrangian observations perfectly agree with this picture. Received 19 June 2002 / Received in final form 29 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: bcastain@ens-lyon.fr     

Hedgehog production in spatially correlated noise

The production of topological defects during a quench in a φ⁴ model is investigated. The influence of a spatially correlated noise on defect production in two and three dimensions is demonstrated. Received 28 August 2001 / Received in final form 11 February 2002 Published online 2 October 2002 RID="a" ID="a"Paper supported in part by ESF “COSLAB” Programme RID="b" ID="b"e-mail: sfdobrow@kinga.cyf-kr.edu.pl     

NMR study of the dissolution of laser-polarized xenon

NMR of laser-polarized xenon is used to probe the dissolution behaviour of the noble gas in different liquids. The dissolution and self-relaxation rates are extracted via a macroscopic model, and comparison of the decay rate of the xenon magnetization in deuterated and non-deuterated solvent pairs allows the determination of the pure dipole-dipole contribution to relaxation. A transient convective effect, tentatively assigned to the xenon concentration gradient, is observed and characterized by diffusion encoding MRI experiments. The flow of xenon penetrates inside the solvent near the walls of the NMR tube, the longitudinal images showing a “” shape, the transverse ones a “O” shape. This convection effect has implications for delivery conditions of laser-polarized xenon in continuous flow experiments and magnetic resonance imaging. Received 29 April 2002 / Received in final form 26 July 2002 Published online 22 October 2002 RID="a" ID="a"e-mail: hdesvaux@cea.fr RID="b" ID="b"URA CNRS/CEA 331