Integrable approximation to the overlap of resonances

We study the interaction of resonances with the same order in families of integrable Hamiltonian systems. This can occur when the unperturbed Hamiltonian is at least cubic in the actions. An integrable perturbation coupling the action-angle variables leads to the disappearance of an island through the coalescence of stable and unstable periodic orbits and originates a complex orbit plus an isolated cubic resonance. The chaotic layer that appears when a general term is added to the Hamiltonian survives even after the disappearance of the unstable periodic orbit. © 1992.

Connection between the affine and conformal affine Toda models and their Hirota solution

It is shown that the affine Toda models (AT) constitute a gauge fixed version of the conformal affine Toda model (CAT). This result enables one to map every solution of the AT models into an infinite number of solutions of the corresponding CAT models, each one associated to a point of the orbit of the conformal group. The Hirota τ-functions are introduced and soliton solutions for the AT and CAT models associated to SL̂ (r+1) and SP̂ (r) are constructed.

Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra script Ĝ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of script Ĝ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Resonance and chaos: I. First-order interior resonances

Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincaré surfaces of section with a mass ratio of 10-3 (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.

Electrodynamics of helium with retardation and self-interaction effects

We show that an extra constant of motion with an analytic form can exist in the neighborhood of some discrete circular orbits of helium when one includes retardation and self-interaction effects. The energies of these discrete stable circular orbits are in the correct atomic magnitude. The highest frequency in the stable manifold of one such orbit agrees with the highest frequency sharp line of parahelium to within 2%. The generic term of the frequency in the stable manifold to higher orbits is also in agreement with the asymptotic form of quantum mechanics for helium.

Fock terms in the quark-meson coupling model

The mean field description of nuclear matter in the quark-meson coupling model is improved by the inclusion of exchange contributions (Fock terms). The inclusion of Fock terms allows us to explore the momentum dependence of meson-nucleon vertices and the role of pionic degrees of freedom in matter. It is found that the Fock terms maintain the previous predictions of the model for the in-medium properties of the nucleon and for the nuclear incompressibility. The Fock terms significantly increase the absolute values of the single-particle, four-component scalar and vector potentials, a feature that is relevant for the spin-orbit splitting in finite nuclei. © 1999 Elsevier Science B.V.

A theoretical study of the A2 ∑+-X2∏ system of the SiP molecule

The A2∑+ and Z2∏ electronic states of the SiP species have been investigated theoretically at a very high level of correlation treatment (CASSCF/MRSDCI). Very accurate potential energy curves are presented for both states, as well as the associated spectroscopic constants as derived from the vib-rotational energy levels determined by means of the numerical solution of the radial Schrödinger equation. Electronic transition moment function, oscillator strengths, Einstein coefficients for spontaneous emission, and Franck-Condon factors for the A2∑+-X2∏ system have been calculated. Dipole moment functions and radiative lifetimes for both states have also been determined. Spin-orbit coupling constants are also reported. The radiative lifetimes for the A2∑+ state, taking into account the spin-orbit diagonal correction to the X2∏ state, decrease from a value of 138 ms at v′ = 0 to 0.48 ms at v′ = 8, and, for the X2∏ state, from 2.32 s at v″ = 1 to 0.59 s at v″ = 5. Vibrational and rotational transitions are expected to be relatively strong.

Evaluation of lacrimal system outflow in the newborn by dye tests

PURPOSE: The aim of this study was to evaluate the outflow from the lacrimal excretory system (LES) at birth. METHOD: Two-hundred LES were evaluated by the Milder Test (DDT) and the modified Jones I Test (JIT) in 100 newborns (NBs) from 31 (T 1) until 42 (T 3) weeks of gestational age. The occurrence of obstruction was related to sex, weight at birth, presence of ocular discharge and the degree of maturity. RESULTS: Both tests were in agreement and showed LES obstruction in 61.5% (DDT) and 78.5% (JIT), respectively, while the LES outflow increased with increasing maturity. CONCLUSION: Evaluation of LES outflow at birth reveals obstruction rates that are much higher than those clinically observed in children with complaints of epiphora.

Time analysis for temporary gravitational capture: Satellites of Uranus

We study the problem of gravitational capture in the framework of the Sun-Uranus-particle system. Part of the space of initial conditions is systematically explored, and the duration of temporary gravitational capture is measured. The location and size of different capture-time regions are given in terms of diagrams of initial semimajor axis versus eccentricity. The other initial orbital elements - inclination (i), longitude of the node (Ω), argument of pericenter (ω), and time of pericenter passage (τ) - are first taken to be zero. Then we investigate the cases with ω = 90°, 180°, and 270°. We also present a sample of results for Ω = 90°, considering the cases i = 60°, 120°, 150°, and 180°. Special attention is given to the influence of the initial orbital inclination, taking orbits initially in opposition at pericenter. In this case, the initial inclination is varied from 0° to 180° in steps of 10°. The success of the final stage of the capture problem, which involves the transformation of temporary captures into permanent ones, is highly dependent on the initial conditions associated with the longest capture times. The largest regions of the initial-conditions space with the longest capture times occur at inclinations of 60°-70° and 160°. The regions of possible stability as a function of initial inclination are also delimited. These regions include not only a known set of retrograde orbits, but also a new sort of prograde orbit with inclinations greater than zero.

Gelatinous polyethylene in the treatment of the anophthalmic cavity

PURPOSE: Gelatinous polyethylene (GP) has been used as an orbital implant to evaluate volume maintenance and tissue reaction in the anophthalmic socket in a rabbit model. METHODS: Twenty-eight Norfolk white rabbits underwent unilateral evisceration with placement of 2ml GP (GP group - 16 animals) or 2ml 0.9% sodium chloride solution (Control group - 12 animals). Animal behavior, postoperative tissue response and socket conditions were evaluated. The animals were sacrificed at 7, 15, 30 and 60 days after the surgery and the bulbs were enucleated; volume maintenance and histopathological evaluation were done in the enucleated bulbs. The results were submitted to statistical analysis. RESULTS: All animals showed normal behavior. The orbital volume maintenance was better in the GP group. Histopathology in the GP animals showed mild tissue inflammation throughout the evaluation period and a thin pseudocapsule formation surrounding the orbital implant material. CONCLUSION: The clinical findings, good orbital volume maintenance and mild inflammatory tissue response make GP a good choice to replace the lack of volume in anophthalmic socket reconstruction.

Trauma dos canalículos lacrimais

Purpose: To evaluate the canalicular trauma causes and the characteristics of the patients in our region. Local: Faculdade de Medicina de Botucatu - UNESP - Botucatu, São Paulo. Method: A retrospective observational study was conducted in a 7 years period evaluating 25 canalicular trauma carriers according gender, occupation, cause and lesion localization, associated structures affected, time to surgical procedure, surgery performed and results with the treatment. Results and conclusion: 68,0% of the patients were male and there is no age prevalence. The car accidents was the most important cause of canalicular trauma. The inferior canaliculus were the most frequently affected. The majority of the patients showed another structure lesioned (eye, eyelid or orbit) and most of patients presented good results with treatment.

Using cubic splines to mitigate systematic errors in GPS relative positioning

Systematic errors can have a significant effect on GPS observable. In medium and long baselines the major systematic error source are the ionosphere and troposphere refraction and the GPS satellites orbit errors. But, in short baselines, the multipath is more relevant. These errors degrade the accuracy of the positioning accomplished by GPS. So, this is a critical problem for high precision GPS positioning applications. Recently, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique. It uses a natural cubic spline to model the errors as a function which varies smoothly in time. The systematic errors functions, ambiguities and station coordinates, are estimated simultaneously. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method.

Spontaneous eye blink analysis in the normal individual

Purpose: Spontaneous eye blink activity in the primary eye position and its relationship to age and gender were assessed using digital image processing techniques to quantify blink opening and closing time. Methods: One hundred-and-eighty healthy volunteers (90 males and 90 females), divided into the age groups 0-3, 4-12, 13-20, 21-40, 41-60 and ≥60 years old, were evaluated prospectively. They were videotaped digitally in a standard setting and the images were transferred to a personal computer (Macintosh 400) and processed with the iMovie software. Blink opening and closing time were measured at 30 frames/second. The data were then subjected to statistical analysis. Results: The closing time was significantly longer than the opening time for all ages and both genders. Elderly individuals (≥41 years old) and women had significantly longer closing times. Conclusion: Image processing techniques made possible the observation of differences in spontaneous eye blink opening and closing time in relation to age and gender. Copyright © 2005 Taylor & Francis LLC.