Study of chaos in hamiltonian systems via convergent normal forms

We use Moser's normal forms to study chaotic motion in two-degree hamiltonian systems near a saddle point. Besides being convergent, they provide a suitable description of the cylindrical topology of the chaotic flow in that vicinity. Both aspects combined allowed a precise computation of the homoclinic interaction of stable and unstable manifolds in the full phase space, rather than just the Poincar\'e section. The formalism was applied to the H\'enon-Heiles hamiltonian, producing strong evidence that the region of convergence of these normal forms extends over that originally established by Moser.Comment: 29 pages, REVTEX, 22 postscript figures on reques

First electron beam polarization measurements with a Compton polarimeter at Jefferson Laboratory

A Compton polarimeter has been installed in Hall A at Jefferson Laboratory. This letter reports on the first electron beam polarization measurements performed during the HAPPEX experiment at an electron energy of 3.3 GeV and an average current of 40 $\mu$A. The heart of this device is a Fabry-Perot cavity which increased the luminosity for Compton scattering in the interaction region so much that a 1.4% statistical accuracy could be obtained within one hour, with a 3.3% total error

Uniform approximations for non-generic bifurcation scenatios including bifurcations of ghost orbits

Gutzwiller's trace formula allows interpreting the density of states of a classically chaotic quantum system in terms of classical periodic orbits. It diverges when periodic orbits undergo bifurcations, and must be replaced with a uniform approximation in the vicinity of the bifurcations. As a characteristic feature, these approximations require the inclusion of complex ``ghost orbits''. By studying an example taken from the Diamagnetic Kepler Problem, viz. the period-quadrupling of the balloon-orbit, we demonstrate that these ghost orbits themselves can undergo bifurcations, giving rise to non-generic complicated bifurcation scenarios. We extend classical normal form theory so as to yield analytic descriptions of both bifurcations of real orbits and ghost orbit bifurcations. We then show how the normal form serves to obtain a uniform approximation taking the ghost orbit bifurcation into account. We find that the ghost bifurcation produces signatures in the semiclassical spectrum in much the same way as a bifurcation of real orbits does.Comment: 56 pages, 21 figure, LaTeX2e using amsmath, amssymb, epsfig, and rotating packages. To be published in Annals of Physic

Back-flow ripples in troughs downstream of unit bars: Formation, preservation and value for interpreting flow conditions

Back-flow ripples are bedforms created within the lee-side eddy of a larger bedform with migration directions opposed or oblique to that of the host bedform. In the flume experiments described in this article, back-flow ripples formed in the trough downstream of a unit bar and changed with mean flow velocity; varying from small incipient back-flow ripples at low velocities, to well-formed back-flow ripples with greater velocity, to rapidly migrating transient back-flow ripples formed at the greatest velocities tested. In these experiments back-flow ripples formed at much lower mean back-flow velocities than predicted from previously published descriptions. This lower threshold mean back-flow velocity is attributed to the pattern of velocity variation within the lee-side eddy of the host bedform. The back-flow velocity variations are attributed to vortex shedding from the separation zone, wake flapping and increases in the size of, and turbulent intensity within, the flow separation eddy controlled by the passage of superimposed bedforms approaching the crest of the bar. Short duration high velocity packets, whatever their cause, may form back-flow ripples if they exceed the minimum bed shear stress for ripple generation for long enough or, if much faster, may wash them out. Variation in back-flow ripple cross-lamination has been observed in the rock record and, by comparison with flume observations, the preserved back-flow ripple morphology may be useful for interpreting formative flow and sediment transport dynamics

Stability of axial orbits in galactic potentials

We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform. Attention is focused on the stability properties of the axial periodic orbits that play an important role in galactic models. Using energy and ellipticity as parameters, we find analytical expressions of bifurcations and compare them with numerical results available in the literature.Comment: 20 pages, accepted for publication on Celestial Mechanics and Dynamical Astronom

Bohr-Sommerfeld Quantization of Periodic Orbits

We show, that the canonical invariant part of $\hbar$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the improvement of precision on the example of the three disk scattering system.Comment: revte

Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant

We here present a high sensitivity gravity-gradiometer based on atom interferometry. In our apparatus, two clouds of laser-cooled rubidium atoms are launched in fountain configuration and interrogated by a Raman interferometry sequence to probe the gradient of gravity field. We recently implemented a high-flux atomic source and a newly designed Raman lasers system in the instrument set-up. We discuss the applications towards a precise determination of the Newtonian gravitational constant G. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement precision below the 100 ppm level

Investigation Into the Humaneness of Slaughter Methods for Guinea Pigs (Cavia porcelus) in the Andean Region

Guinea pigs (Cavia porcelus) are an important source of nonhuman animal protein in the Andean region of South America. Specific guidelines regarding the welfare of guinea pigs before and during slaughter have yet to be developed. This study critically assessed the humaneness of 4 different stunning/slaughter methods for guinea pigs: cervical neck dislocation (n = 60), electrical head-only stunning (n = 83), carbon dioxide (CO(2)) stunning (n = 21), and penetrating captive bolt (n = 10). Following cervical neck dislocation, 97% of guinea pigs had at least 1 behavioral or cranial/spinal response. Six percent of guinea pigs were classified as mis-stunned after electrical stunning, and 1% were classified as mis-stunned after captive bolt. Increased respiratory effort was observed during CO(2) stunning. Apart from this finding, there were no other obvious behavioral responses that could be associated with suffering. Of the methods assessed, captive bolt was deemed the most humane, effective, and practical method of stunning guinea pigs. Cervical neck dislocation should not be recommended as a slaughter method for guinea pigs

A light in the shadow: the use of Lucifer Yellow technique to demonstrate nectar reabsorption

Abstract Background Nectar reabsorption is a widely known phenomenon, related to the strategy of resource-recovery and also to maintain the nectar homeostasis at the nectary. The method currently performed to demonstrate nectar being reabsorbed involves the use of radioactive tracers applied to the nectary. Although this method works perfectly, it is complex and requires specific supplies and equipment. Therefore, here we propose an efficient method to obtain a visual demonstration of nectar reabsorption, adapting the use of Lucifer Yellow CH (LYCH), a fluorescent membrane-impermeable dye that can enter the vacuole by endocytosis. Results We applied a LYCH solution to the floral nectary (FN) of Cucurbita pepo L., which is a species known for its ability of nectar reabsorption, and to the extrafloral nectary (EFN) of Passiflora edulis Sims which does not reabsorb the secreted nectar. In all tests performed, we observed that LYCH stained the nectary tissues differentially according to the reabsorption ability of the nectary. The treated FN of C. pepo presented a concentrated fluorescence at the epidermis that decreased at the deeper nectary parenchyma, until reaching the vascular bundles, indicating nectar reabsorption in the flowers of the species. In contrast, treated EFN of P. edulis presented fluorescence only at the cuticle surface, indicating that nectar is not reabsorbed by that particular tissue. Conclusion LYCH is an efficient marker to demonstrate nectar reabsorption.The authors thank the Pró-Reitoria de Pesquisa of the University of São Paulo for the help with the cost of the publishing. PCG and JMRBVA thank the grant provided by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES). The authors thank the staff of Instituto de Botânica for providing assistance with cultivated material of P. edulis and Joel Caitano (Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto) for providing material of C. pepo. PCG also thank Wilton José da Rocha Lima (Central Analítica – Instituto de Química, Universidade de São Paulo) for technical assistance with confocal microscopy. JMRBVA thanks Laura de Castro Lamonica for helping with practical work. FB acknowledges the research productivity grant received from the Brazilian National Council for Scientific and Technological Development (CNPq). We thank the two anonymous referees for their valuable comments to the manuscript and their constructive suggestions.The authors thank the PróReitoria de Pesquisa of the University of São Paulo for the help with the cost of the publishing. PCG and JMRBVA thank the grant provided by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES). The authors thank the staff of Instituto de Botânica for providing assistance with cultivated material of P. edulis and Joel Caitano (Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto) for providing material of C. pepo. PCG also thank Wilton José da Rocha Lima (Central Analítica – Instituto de Química, Universidade de São Paulo) for technical assistance with confocal microscopy. JMRBVA thanks Laura de Castro Lamonica for helping with practical work. FB acknowledges the research productivity grant received from the Brazilian National Council for Scientific and Technological Development (CNPq). We thank the two anonymous referees for their valuable comments to the manuscript and their constructive suggestions