Nonextensive entropy approach to space plasma fluctuations and turbulence

Spatial intermittency in fully developed turbulence is an established feature of astrophysical plasma fluctuations and in particular apparent in the interplanetary medium by in situ observations. In this situation the classical Boltzmann-Gibbs extensive thermo-statistics, applicable when microscopic interactions and memory are short ranged, fails. Upon generalization of the entropy function to nonextensivity, accounting for long-range interactions and thus for correlations in the system, it is demonstrated that the corresponding probability distributions (PDFs) are members of a family of specific power-law distributions. In particular, the resulting theoretical bi-kappa functional reproduces accurately the observed global leptokurtic, non-Gaussian shape of the increment PDFs of characteristic solar wind variables on all scales. Gradual decoupling is obtained by enhancing the spatial separation scale corresponding to increasing kappa-values in case of slow solar wind conditions where a Gaussian is approached in the limit of large scales. Contrary, the scaling properties in the high speed solar wind are predominantly governed by the mean energy or variance of the distribution. The PDFs of solar wind scalar field differences are computed from WIND and ACE data for different time-lags and bulk speeds and analyzed within the nonextensive theory. Consequently, nonlocality in fluctuations, related to both, turbulence and its large scale driving, should be related to long-range interactions in the context of nonextensive entropy generalization, providing fundamentally the physical background of the observed scale dependence of fluctuations in intermittent space plasmas.Comment: 21 pages, 8 figures, accepted for publication, to appear in Advances in Geosciences 2, chapter 04, 2006 (with minor corrections

A nonextensive entropy approach to solar wind intermittency

The probability distributions (PDFs) of the differences of any physical variable in the intermittent, turbulent interplanetary medium are scale dependent. Strong non-Gaussianity of solar wind fluctuations applies for short time-lag spacecraft observations, corresponding to small-scale spatial separations, whereas for large scales the differences turn into a Gaussian normal distribution. These characteristics were hitherto described in the context of the log-normal, the Castaing distribution or the shell model. On the other hand, a possible explanation for nonlocality in turbulence is offered within the context of nonextensive entropy generalization by a recently introduced bi-kappa distribution, generating through a convolution of a negative-kappa core and positive-kappa halo pronounced non-Gaussian structures. The PDFs of solar wind scalar field differences are computed from WIND and ACE data for different time lags and compared with the characteristics of the theoretical bi-kappa functional, well representing the overall scale dependence of the spatial solar wind intermittency. The observed PDF characteristics for increased spatial scales are manifest in the theoretical distribution functional by enhancing the only tuning parameter $\kappa$, measuring the degree of nonextensivity where the large-scale Gaussian is approached for $\kappa \to \infty$. The nonextensive approach assures for experimental studies of solar wind intermittency independence from influence of a priori model assumptions. It is argued that the intermittency of the turbulent fluctuations should be related physically to the nonextensive character of the interplanetary medium counting for nonlocal interactions via the entropy generalization.Comment: 17 pages, 7 figures, accepted for publication in Astrophys.

Artificial trapping of a stable high-density dipolar exciton fluid

We present compelling experimental evidence for a successful electrostatic trapping of two-dimensional dipolar excitons that results in stable formation of a well confined, high-density and spatially uniform dipolar exciton fluid. We show that, for at least half a microsecond, the exciton fluid sustains a density higher than the critical density for degeneracy if the exciton fluid temperature reaches the lattice temperature within that time. This method should allow for the study of strongly interacting bosons in two dimensions at low temperatures, and possibly lead towards the observation of quantum phase transitions of 2D interacting excitons, such as superfluidity and crystallization.Comment: 11 pages 4 figure

Vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under axial loads and end moments

A finite element model with seven degrees of freedom per node is developed to study vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under constant axial loads and equal end moments. This model is based on the classical lamination theory, and accounts for all the structural coupling coming from material anisotropy. The governing differential equations are derived from the Hamilton’s principle. Numerical results are obtained for thin-walled composite I-beams to investigate the effects of axial force, bending moment and fiber orientation on the buckling moments, natural frequencies, and corresponding vibration mode shapes as well as axial-moment-frequency interaction curves

Anatomy of quantum chaotic eigenstates

The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.Comment: Corrected typos, added a few references and updated some result

T-systems and Y-systems in integrable systems

The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras with coefficients, periodicity conjectures of Zamolodchikov and others, dilogarithm identities in conformal field theory, difference analogue of L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem, AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and so forth. This review article is a collection of short reviews on these topics which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5, eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical review) also needs these correction

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste

Azimuthal Anisotropy of Photon and Charged Particle Emission in Pb+Pb Collisions at 158 A GeV/c

The azimuthal distributions of photons and charged particles with respect to the event plane are investigated as a function of centrality in Pb + Pb collisions at 158 A GeV/c in the WA98 experiment at the CERN SPS. The anisotropy of the azimuthal distributions is characterized using a Fourier analysis. For both the photon and charged particle distributions the first two Fourier coefficients are observed to decrease with increasing centrality. The observed anisotropies of the photon distributions compare well with the expectations from the charged particle measurements for all centralities.Comment: 8 pages and 6 figures. The manuscript has undergone a major revision. The unwanted correlations were enhanced in the random subdivision method used in the earlier version. The present version uses the more established method of division into subevents separated in rapidity to minimise short range correlations. The observed results for charged particles are in agreement with results from the other experiments. The observed anisotropy in photons is explained using flow results of pions and the correlations arising due to the decay of the neutral pion

Central Pb+Pb Collisions at 158 A GeV/c Studied by Pion-Pion Interferometry

Two-particle correlations have been measured for identified negative pions from central 158 AGeV Pb+Pb collisions and fitted radii of about 7 fm in all dimensions have been obtained. A multi-dimensional study of the radii as a function of kT is presented, including a full correction for the resolution effects of the apparatus. The cross term Rout-long of the standard fit in the Longitudinally CoMoving System (LCMS) and the vl parameter of the generalised Yano-Koonin fit are compatible with 0, suggesting that the source undergoes a boost invariant expansion. The shapes of the correlation functions in Qinv and Qspace have been analyzed in detail. They are not Gaussian but better represented by exponentials. As a consequence, fitting Gaussians to these correlation functions may produce different radii depending on the acceptance of the experimental setup used for the measurement.Comment: 13 pages including 10 figure