Phase-Space Volume of Regions of Trapped Motion: Multiple Ring Components and Arcs

The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances. The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume occupied by the regions of trapped motion.Comment: 19 pages, 17 figure

Spectral statistics of the k-body random-interaction model

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.Comment: 17 pages, no figure

Motion Control of a heterogeneous fleet of mobile robots: Formation control for achieving agriculture task

International audienceLa nécessité de réduire l'impact environnemental des activités agricoles, tout en préservant le niveau de production pour satisfaire la demande croissante des populations nécessite une étude de nouveaux outils de production. Les robots mobiles peuvent constituer une solution prometteuse, puisque les dispositifs autonomes peuvent permettre une augmentation des niveaux de production, tout en préservant l'environnement grâce à leur grande précision. Dans cet article, l'utilisation de plusieurs robots mobiles autonomes pour effectuer l'opération sur le terrain est étudiée. En particulier, les techniques prédictives sont également proposées pour tenir compte des retards induits par des actionneurs à basse altitude. Les capacités de l'approche proposée sont étudiées au moyen d'expériences de la pleine échelle. / The necessity of decreasing the environmental impact of agricultural activities, while preserving the level of production to satisfy growing population demands requires investigation of new production tools. Mobile robots may constitute a promising solution, since autonomous devices may allow increasing production levels, while preserving the environment thanks to their high accuracy. In this paper, the use of several autonomous mobile robots to perform field operation is investigated. In particular, predictive techniques are also proposed to account for delays induced by low-level actuators. Capabilities of the proposed approach are investigated through full scale experiments

Fluctuations of wave functions about their classical average

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes. We compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators. The expectation is broadly confirmed, but deviations due to scars are observed.Comment: 9 pages, 6 figures. Sent to J. Phys.

Level Repulsion in Constrained Gaussian Random-Matrix Ensembles

Introducing sets of constraints, we define new classes of random-matrix ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE. We derive a sufficient condition for GUE-type level repulsion to persist in the presence of constraints. For special classes of constraints, we extend this approach to the orthogonal and to the symplectic ensembles. A generalized Fourier theorem relates the spectral properties of the constraining ensembles with those of the constrained ones. We find that in the DGUEs, level repulsion always prevails at a sufficiently short distance and may be lifted only in the limit of strictly enforced constraints.Comment: 20 pages, no figures. New section adde

Effect of phase relaxation on quantum superpositions in complex collisions

We study the effect of phase relaxation on coherent superpositions of rotating clockwise and anticlockwise wave packets in the regime of strongly overlapping resonances of the intermediate complex. Such highly excited deformed complexes may be created in binary collisions of heavy ions, molecules and atomic clusters. It is shown that phase relaxation leads to a reduction of the interference fringes, thus mimicking the effect of decoherence. This reduction is crucial for the determination of the phase--relaxation width from the data on the excitation function oscillations in heavy--ion collisions and bimolecular chemical reactions. The difference between the effects of phase relaxation and decoherence is discussed.Comment: Extended revised version; 9 pages and 3 colour ps figure

Age-based stereotype threat and negative outcomes in the workplace : exploring the role of identity integration

Previous studies have shown that the presence of age-based stereotypes in the workplace is often associated with lower levels of work engagement and adjustment among older employees. This study examines possible mediators and moderators of this relationship using data from a sample of 2,348 older (age > 50) employees at the Italian national rail company. We test a model in which the effects of age-based stereotype threat on organizational involvement, future time perspective and psychological well-being are mediated by work-age identity integration (how much individuals see their age and organizational identities as compatible and blended). Secondly, we explored whether these effects are moderated by gender and job status. Results indicate that age-based stereotypes are associated with negative outcomes for employees’ work and personal adjustment, and that these relationships are partially mediated by variations in work-age identity integration

Periodic Orbits and Escapes in Dynamical Systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central "bumpy" black hole. When the energy reaches its escape value a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical Astronomy

Review of the k-Body Embedded Ensembles of Gaussian Random Matrices

The embedded ensembles were introduced by Mon and French as physically more plausible stochastic models of many--body systems governed by one--and two--body interactions than provided by standard random--matrix theory. We review several approaches aimed at determining the spectral density, the spectral fluctuation properties, and the ergodic properties of these ensembles: moments methods, numerical simulations, the replica trick, the eigenvector decomposition of the matrix of second moments and supersymmetry, the binary correlation approximation, and the study of correlations between matrix elements.Comment: Final version. 29 pages, 4 ps figures, uses iopart.st

Measures Matter: Scales for Adaptation, Cultural Distance, and Acculturation Orientation Revisited

Building upon existing measures, four new brief acculturation scales are presented, measuring sociocultural adaptation, psychological adaptation, perceived cultural distance, and acculturation orientation. Following good scale reliability in initial samples, the English scales were translated into nine different languages (Chinese, French, German, Italian, Japanese, Portuguese, Spanish, Thai, and Turkish). The translated scales were administered to a large sample of sojourners (N = 1,929), demonstrating good reliability and adequate structural equivalence across languages. In line with existing theory, sociocultural adaptation and psychological adaptation were positively correlated, and showed a negative association with perceived cultural distance. General measures of well-being were correlated with adaptation and distance, with better adaptation relating to higher well-being, and more distance relating to lower well-being. Acculturation orientation toward the home and host culture were measured separately and a weak negative correlation was found between the two, supporting their independence. Arguing against dichotomization, these subscales were analyzed as continuous variables. Regression analysis showed sojourners to be better adapted, if they were oriented more toward the host culture and less toward the home culture. These new scales are proposed as alternatives to existing measures