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     

The $-game

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In contrast with previous MG, the best strategies are not always targeting the minority but are shifting opportunistically between the minority and the majority. The emergent properties of the price dynamics and of the wealth of agents are strikingly different from those found in MG. As the memory of agents is increased, we find a phase transition between a self-sustained speculative phase in which a “stubborn majority” of agents effectively collaborate to arbitrage a market-maker for their mutual benefit and a phase where the market-maker always arbitrages the agents. A subset of agents exhibit a sustained non-equilibrium risk-return profile. Received 5 June 2002 / Received in final form 21 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sornette@unice.fr RID="b" ID="b"CNRS UMR7536 RID="c" ID="c"CNRS UMR6622     

Off-center Li ions: solid state rotators described by Mathieu's nonlinear-oscillator equation

Substitutional impurity ions in crystals are known to displace off-center and to perform hindered rotations around the ideal lattice positions. The vibronic theory to describe both the off-center displacements and the hindered rotations by a single angular equation incorporates terms up to 3rd order in the off-center displacement coordinates. When the rotation is confined to a single plane, the corresponding vibronic equation is equivalent to Mathieu's equation. Extending our earlier work, we derive here the dipole-dipole coupling to take into account cooperative phenomena. We also derive the optical absorption band arising from dipolar transitions across “Mexican Hat” surfaces, and we show that hindered rotations gives rise to magnetic moments quantized in rotational bands. Received 18 October 2001 / Received in final form 5 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: allxrose@hotmail.com     

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     

Selective advantage of topological disorder in biological evolution

We examine a model of biological evolution of Eigen's quasispecies in a so-called holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). The evolution dynamics is therefore determined by the topology of the genome space which is modelled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call “topological”. A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested. Received 9 August 2002 / Received in final form 7 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: slanina@fzu.cz     

Switching of banana liquid crystal mesophases under field

Taking advantage of the great number of bent-core or “banana" compounds synthesized and studied in the laboratory, we describe their behaviour under the application of an external electric field. If the field were a static one, we would work within the frame of an equilibrium phase diagram in a (field E, temperature T) space where some phases would be simple dielectrics and others ferroelectric ones with a macroscopic polarization, either spontaneous or induced by the field. In this paper, we deal with the basic responses of “banana” liquid crystals under the application of a low frequency (1 to 100 Hz) AC field. Firstly square-wave voltages allow us to locate the phase boundary between dielectric (at lower field) and ferroelectric phases (higher field) at a given temperature and field threshold. Then we apply slowly varying AC voltages with shapes like triangle or “triple-plateau” to check out the stability of the induced ferroelectric phase versus field removal. Three behaviours are encountered, the unstable one (short lifetime of the high-field ferroelectric phase) where the macroscopic polarization is destroyed and then rebuilt in the opposite direction during each half period and usually called “antiferroelectric”; the stable one (long lifetime) with a polarization that rotates at constant modulus which is labeled as “ferroelectric” and a new one where the macroscopic polarization is proportional to the applied fied, we named this behaviour as “superparaelectric”. Let us stress that these observations apply to the ferroelectric phases of the (E, T) phase diagram not to the zero field (0,T) phases observed in the usual phase characterization experiments except for an eventual spontaneous ferroelectric phase. Received 18 April 2002 and Received in final form 17 January 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: marcerou@crpp.u-bordeaux.fr RID="b" ID="b"URL: http://www.crpp-bordeaux.cnrs.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     

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     

Mixing and sorting of bidisperse two-dimensional bubbles

We have examined a number of candidates for the minimum-surface-energy arrangement of two-dimensional clusters composed of N bubbles of area 1 and N bubbles of area λ ( λ≤1). These include hexagonal bubbles sorted into two monodisperse honeycomb tilings, and various mixed periodic tilings with at most four bubbles per unit cell. We identify, as a function of λ, the minimal configuration for N → ∞. For finite N, the energy of the external (i.e., cluster-gas) boundary and that of the interface between honeycombs in “phase-separated” clusters have to be taken into account. We estimate these contributions and find the lowest total energy configuration for each pair (N,λ). As λ is varied, this alternates between a circular cluster of one of the mixed tilings, and “partial wetting” of the monodisperse honeycomb of bubble area 1 by the monodisperse honeycomb of bubble area λ. Received 1 August 2002 RID="a" ID="a"e-mail: paulo@ist.utl.pt     

Probability distribution of inherent states in models of granular media and glasses

The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a “tap dynamics” analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new “thermodynamical” parameters, called “configurational temperatures” (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single “configurational temperature”. Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed. Received 19 March 2002 and Received in final form 14 June 2002     

Gravitational decoherence of atomic interferometers

We study the decoherence of atomic interferometers due to the scattering of stochastic gravitational waves. We evaluate the “direct” gravitational effect registered by the phase of the matter waves as well as the “indirect” effect registered by the light waves used as beam-splitters and mirrors for the matter waves. Considering as an example the space project HYPER, we show that both effects are negligible for the presently studied interferometers. Received 15 February 2002 / Received in final form 12 April 2002 Published online 19 July 2002     

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     

Comment on¶“On the relationship between the entropy and enthalpy of interfacial segregation” by L. Rubinovich and M. Polak

The paper of L. Rubinovich and M. Polak [Eur. Phys. J. B 22, 267 (2001)] contains some controversial items. The notation “excess” in connection with various thermodynamic quantities describing solute segregation on the basis of the Langmuir-McLean isotherm is used in a meaning contradictory to general thermodynamics. The approach used to interpret the linear relationship between segregation entropy and enthalpy results in rather strange conclusions. These items are discussed, and it is shown how a formulation with standard terms is in accordance with general thermodynamics. Received 14 January 2002 / Received in final form 27 September 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: lejcekp@fzu.cz     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Quantum chemical modelling of “green” luminescence in ABO perovskites

The origin of the intrinsic excitonic (“green”) luminescence in ABO₃ perovskites remains a hot topic over the last quarter of a century. We suggest as a theoretical interpretation for the “green” luminescence in these crystals, the recombination of electron and hole polarons forming a charge transfer vibronic exciton. In order to check quantitatively the proposed model, we performed quantum chemical calculations using the Intermediate Neglect of Differential Overlap (INDO) method combined with the periodic defect model. The luminescence energies calculated for four perovskite crystals are found to be in good agreement with experimental data. Received 19 December 2001 and Received in final form 14 March 2002 Published online 25 June 2002     

Slow regions percolate near glass transition

A nanosecond scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as it nears the glass transition. The scaling behaviour is in the same universality class as percolation. The exponents γ and β are found to be 1.7±0.1 and 0.41±0.01 in agreement with the best percolation results in three dimensions. Received 29 August 2002 RID="a" ID="a"e-mail: erzan@gursey.gov.tr e-mail: erzan@itu.edu.tr     

Nonlinear dynamics of dimers on periodic substrates

We study the dynamics of a dimer moving on a periodic one-dimensional substrate as a function of the initial kinetic energy at zero temperature. The aim is to describe, in a simplified picture, the microscopic dynamics of diatomic molecules on periodic surfaces, which is of importance for thin film formation and crystal growth. We find a complex behaviour, characterized by a variety of dynamical regimes, namely oscillatory, “quasi-diffusive” (chaotic) and drift motion. Parametrically resonant excitations of internal vibrations can be induced both by oscillatory and drift motion of the centre of mass. For weakly bound dimers a chaotic regime is found for a whole range of velocities between two non-chaotic phases at low and high kinetic energy. The chaotic features have been monitored by studying the Lyapunov exponents and the power spectra. Moreover, for a short-range interaction, the dimer can dissociate due to the parametric excitation of the internal motion. Received 8 July 2002 / Received in final form 15 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: fusco@sci.kun.nl.     

Modelling of magnetic effects in near-field optics

Green's dyadic technique represents a powerful tool for calculations in electrodynamics, especially in modelling optical properties of nanoscopic objects. The method does not only provide field distributions, but also maps of susceptibilities and densities of states. Whereas the formalism is well established for dielectrics and electric fields, I present here a straight forward extension to tensors of both electric and magnetic type as well as mixed ones and furthermore to the situation where objects with dielectric and magnetic permeabilities are present together. As examples, characteristic field patterns are compared for elementary dielectric and magnetic perturbations. Green's tensors calculated for a coral structure reveal that mixed susceptibilities can exhibit other symmetries than pure electric or magnetic ones. Maps of all tensor components can thus give essential clues to the interpretation of near-field images. Received 15 December 2002 Published online 20 June 2003 RID="a" ID="a"Files “maths.ps” and “tensors.ps” are only available in electronic form at http://www.edpsciences.org RID="b" ID="b"e-mail: Ursula.Schroeter@uni-konstanz.de     

Advanced simulations of spectroscopic signatures of charge exchange in laser-produced plasmas

We present an advanced theory of charge-exchange-caused dips (also called X-dips) in spectral lines from laser-produced plasmas. We compare predictions of this advanced theory with our previously published experimental results where, in the process of a laser irradiation of targets made out of aluminum carbide, we observed two X-dips in the L _γ line of Al XIII perturbed by fully stripped carbon. We show that our advanced theory is in excellent agreement with our experimental results. From the practical point of view, our results open up a way to experimentally produce not-yet-available fundamental data on charge exchange between multicharged ions, virtually inaccessible by other experimental methods. From the theoretical viewpoint, the results are important because the X-dips are the only one signature of charge exchange in profiles of spectral lines emitted by plasmas and they are the only one quasimolecular phenomenon that could be observed at relatively “low” densities of laser-produced plasmas. Received 25 March 2002 Published online 19 July 2002     

Coexistence of superconductivity and ferromagnetism in ferromagnet/superconductor proximity structures

The Nambu spinor Green's function approach is applied to calculating the density of states (DOS) and superconducting order parameter in normal-metal/insulator/ferromagnet/superconductor (NM/I/FM/SC) junctions. It is found that the s-wave superconductivity and ferromagnetism can coexist near the FM/SC interface, which is induced by proximity effect. On the SC side, the spin-dependent DOS appears both within and without the energy gap. On the FM side, the superconducting order parameter displays a damped oscillation and the DOS exhibits some superconducting behavior. The calculated result for the DOS in FM for “0 state” and “π state” can reproduce recent tunneling spectra in Al/Al₂O₃/PdNi/Nb tunnel junctions. Received 1st July 2002 Published online 19 November 2002