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     

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram. Received 8 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: demartino@hmi.de     

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     

Thermal instability of a rotating saturated porous medium heated from below and submitted to rotation

In this work, we study the problem of onset of thermal convection in a rotating saturated porous medium heated from below. The effect of rotation is restricted to the Coriolis force, neglecting thus the centrifugal effects, the porous medium is described by Brinkman's model. The linear eigenvalue problem is solved by means of a modified Galerkin method. The behavior of the critical temperature gradient is discussed in terms of various parameters of the system for both stationary and overstable convections. Finally a weakly nonlinear analysis is provided to derive amplitude equations and to study the onset of Küppers-Lortz instability. Received 24 June 2002 / Received in final form 11 September 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: tdesaive@ulg.ac.be     

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     

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     

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     

New solutions of the shape equation

The general shape equation describing the forms of vesicles is a highly nonlinear partial differential equation for which only a few explicit solutions are known. These solvable cases are briefly reviewed and a new analytical solution which represents the class of the constant mean curvature surfaces is described. Pearling states of the tubular fluid membranes can be explained as a continuous deformation preserving membrane mean curvature. Received 2 February 2002 / Received in final form 4 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: mladenov@obzor.bio21.bas.bg     

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     

The role of pinning and instability in a class of non-equilibrium growth models

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the “perturbative” limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically “irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed. Received 23 April 2002 / Received in final form 24 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: akc@mpipks-dresden.mpg.de     

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     

Non-linear dynamics of spinodal decomposition

We develop a new technique describing the non linear growth of interfaces. We apply this analytical approach to the one dimensional Cahn-Hilliard equation. The dynamics is captured through a solvability condition performed over a particular family of quasi-static solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the non-linear growth is also well characterized. Numerical simulations are compared in a satisfactory way with the analytical results through three different fitting methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold. Received 16 October 2001 / Received in final form 15 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: josseran@lmm.jussieu.fr RID="b" ID="b"UMR CNRS 7607     

Proton-neutron structure of collective excitations in 94Mo

Due to the recent development of radioactive beam production, various direct reaction studies in reversed kinematics have been made to investigate the behavior of the N = 20 shell closure in the neutron-rich region. Coulomb excitation, proton inelastic scattering, and fragmentation of unstable nuclei have been studied with γ-ray detection. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: motobaya@rikkyo.ne.jp     

Gamma-ray tracking: Utilizing new concepts in the detection of gamma-radiation

Gamma-ray tracking in a closed array of highly segmented HPGe detectors is a new concept for the detection of γ-radiation. Each of the interacting γ-rays is identified and separated by measuring the energies and positions of individual interactions and by applying tracking algorithms to reconstruct the scattering sequences, even if many γ-rays hit the array at the same time. The three-dimensional position and the energy of interactions are determined by using two-dimensionally segmented Ge detectors along with pulse-shape analysis of the signals. Such a detector will have new and much improved capabilities compared to current γ-ray spectrometer. One implementation of this concept, called GRETA (Gamma-Ray Energy Tracking Array), is currently being under development at LBNL. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: kvetter@lbl.gov     

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     

Line shape analysis of two-colour photoassociation spectra on the example of the Cs ground state

Two-photon photoassociation spectra in a Λ-type excitation scheme are analysed under the systematically varied experimental conditions of frequency detunings and laser intensities. Line shape fits are presented as well as the investigation of intensity and detuning dependent line shifts. From both we determine the attained spectroscopic precision, that is corrected for a systematic line shift due to the thermal distribution of atoms in the trap. An energy correction for this effect is given. Information about the feasibility of generating translationally cold molecules in a well defined rotational and vibrational level by the photoassociation process is derived from the analysis. Received 21 May 2002 Published online 15 October 2002 RID="a" ID="a"Current address e-mail: christian.lisdat@ptb.de RID="b" ID="b"e-mail: pierre.pillet@lac.u-psud.fr     

Exciton-polariton solitary waves

Effects of the exciton and polariton dispersions and the nonlinear exciton and photon interactions on the properties of polariton solitons in molecular crystals are investigated. Higher-order terms and phase-modulation (chirp) are taken into account. Bright- and dark-soliton solutions of the resulting modified nonlinear Schr?dinger (NLS) equation are presented. Nonlinearity- and dispersion-induced critical points on the polariton dispersion curve are obtained, separating regions with different solutions. Received 2 October 2001 / Received in final form 23 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: Stoychev@issp.bas.bg     

Dynamics of modulated and composite aperiodic crystals

We compare within an unifying formalism the dynamical properties of modulated and composite aperiodic (incommensurate) crystals. We discuss the concept of inner polarization and we define an inner polarization parameter β that distinguishes between different acoustic modes of aperiodic crystals. Although this concept has its limitations, we show that it can be used to extract valuable information from neutron coherent inelastic scattering experiments. Within certain conditions, the ratio between the dynamic and the static structure factors at various Bragg peaks depends only on β. We show how the knowledge of β for modes of an unknown structure can be used to decide whether the structure is composite or modulated. The same information can be used to predict scattered intensity within unexplored regions of the reciprocal space, being thus a guide for experiments. Received 9 June 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: Ovidiu.Radulescu@univ-rennes1.fr