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

Wigner--Dyson statistics for a class of integrable models

We construct an ensemble of second--quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one GOE or GUE statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely the boson number, and thus are integrable. To construct this ensemble we use some ``reverse engineering'' starting from the fact that $n$--bosons in a two--level system with random interactions have an integrable classical limit by the old Heisenberg association of boson operators to actions and angles. By choosing an $n$--body random interaction and degenerate levels we end up with GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.Comment: 3 pages, 1 figur

The functional analysis of distinct tospovirus movement proteins (NSM) reveals different capabilities in tubule formation, cell-to-cell and systemic virus movement among the tospovirus species

[EN] The lack of infectious tospovirus clones to address reverse genetic experiments has compromised the functional analysis of viral proteins. In the present study we have performed a functional analysis of the movement proteins (NSM) of four tospovirus species Bean necrotic mosaic virus (BeNMV), Chrysanthemum stem necrosis virus (CSNV), Tomato chlorotic spot virus (TCSV) and Tomato spotted wilt virus (TSWV), which differ biologically and molecularly, by using the Alfalfa mosaic virus (AMV) model system. All NSM proteins were competent to: i) support the cell-to-cell and systemic transport of AMV, ii) generate tubular structures on infected protoplast and iii) transport only virus particles. However, the NSM of BeNMV (one of the most phylogenetically distant species) was very inefficient to support the systemic transport. Deletion assays revealed that the C-terminal region of the BeNMV NSM, but not that of the CSNV, TCSV and TSWV NSM proteins, was dispensable for cell-to-cell transport, and that all the non-functional C-terminal NSM mutants were unable to generate tubular structures. Bimolecular fluorescence complementation analysis revealed that the C-terminus of the BeNMV NSM was not required for the interaction with the cognate nucleocapsid protein, showing a different protein organization when compared with other movement proteins of the `30K family¿. Overall, our results revealed clearly differences in functional aspects among movement proteins from divergent tospovirus species that have a distinct biological behavior.We thank L. Corachan for her excellent technical assistance. This work was supported by grant BIO2014-54862-R from the Spanish Direccion General de Investigacion Cientifica y Tecnica (DGICYT), the Prometeo Program GV2014/010 from the Generalitat Valenciana, CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico), Capes (Conselho de Aperfeicoamento de Pessoal de Nivel Superior) and FAP-DF (Fundacao de Apoio a Pesquisa do Distrito Federal)Leastro, MO.; Pallás Benet, V.; Resende, RO.; Sanchez Navarro, JA. (2017). The functional analysis of distinct tospovirus movement proteins (NSM) reveals different capabilities in tubule formation, cell-to-cell and systemic virus movement among the tospovirus species. Virus Research. 227:57-68. https://doi.org/10.1016/j.virusres.2016.09.023S576822

Multiple Components in Narrow Planetary Rings

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, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.Comment: 4 pages, 7 figures (some in colors

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

Slow cross-symmetry phase relaxation in complex collisions

We discuss the effect of slow phase relaxation and the spin off-diagonal $S$-matrix correlations on the cross section energy oscillations and the time evolution of the highly excited intermediate systems formed in complex collisions. Such deformed intermediate complexes with strongly overlapping resonances can be formed in heavy ion collisions, bimolecular chemical reactions and atomic cluster collisions. The effects of quasiperiodic energy dependence of the cross sections, coherent rotation of the hyperdeformed $\simeq (3:1)$ intermediate complex, Schr\"odinger cat states and quantum-classical transition are studied for $^{24}$Mg+$^{28}$Si heavy ion scattering.Comment: 10 pages including 2 color ps figures. To be published in Physics of Atomic Nuclei (Yadernaya fizika

Escape from the vicinity of fractal basin boundaries of a star cluster

The dissolution process of star clusters is rather intricate for theory. We investigate it in the context of chaotic dynamics. We use the simple Plummer model for the gravitational field of a star cluster and treat the tidal field of the Galaxy within the tidal approximation. That is, a linear approximation of tidal forces from the Galaxy based on epicyclic theory in a rotating reference frame. The Poincar\'e surfaces of section reveal the effect of a Coriolis asymmetry. The system is non-hyperbolic which has important consequences for the dynamics. We calculated the basins of escape with respect to the Lagrangian points $L_1$ and $L_2$. The longest escape times have been measured for initial conditions in the vicinity of the fractal basin boundaries. Furthermore, we computed the chaotic saddle for the system and its stable and unstable manifolds. The chaotic saddle is a fractal structure in phase space which has the form of a Cantor set and introduces chaos into the system.Comment: Accepted by MNRAS, Figures have lower qualit

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