A discrete time relativistic Toda lattice

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe

The structure of invariant tori in a 3D galactic potential

We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.Comment: 26 pages, 34 figures, accepted for publication in the International Journal of Bifurcation and Chao

Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

Resummation of perturbation series and reducibility for Bryuno skew-product flows

We consider skew-product systems on T^d x SL(2,R) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a resummation procedure of the formal power series for the conjugation, and uses techniques of renormalisation group in quantum field theory.Comment: 30 pages, 12 figure

A new parameter identification method for induction machines.

The present paper describes a new parameter identification method for induction machines. This method requires only a start-up test during which speed as well as stator currents and voltages are measured. The processing ot these quantities by identification procedure allows the computation of the parameters of the equivalent circuits of different types of induction machines

Non-abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with Chern-Simons term

An exact time-dependent solution of field equations for the 3-d gauge field model with a Chern-Simons (CS) topological mass is found. Limiting cases of constant solution and solution with vanishing topological mass are considered. After Lorentz boost, the found solution describes a massive nonlinear non-abelian plane wave. For the more complicate case of gauge fields with CS mass interacting with a Higgs field, the stochastic character of motion is demonstrated.Comment: LaTeX 2.09, 13 pages, 11 eps figure

Periodic solutions for a class of nonlinear partial differential equations in higher dimension

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases where the bifurcation equation is infinite-dimensional, such as the nonlinear Schroedinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.Comment: 34 page

Families of Canonical Transformations by Hamilton-Jacobi-Poincar\'e equation. Application to Rotational and Orbital Motion

The Hamilton-Jacobi equation in the sense of Poincar\'e, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction. We illustrate our approach dealing with orbital and attitude dynamics. Based on the use of Whittaker and Andoyer symplectic charts, for which all but one coordinates are cyclic in the Hamilton-Jacobi equation, we provide whole families of canonical transformations, among which one recognizes the familiar ones used in orbital and attitude dynamics. In addition, new canonical transformations are demonstrated.Comment: 21 page

Stereotactic body radiotherapy in the treatment of Pancreatic Adenocarcinoma in elderly patients

Background: Treatment of pancreatic adenocarcinoma in the elderly is often complicated by comorbidities that preclude surgery, chemotherapy and/or conventional external beam radiation therapy (EBRT). Stereotactic body radiotherapy (SBRT) has thus garnered interest in this setting.Methods: A retrospective review of 26 patients of age ≥ 80 with pancreatic adenocarcinoma treated with definitive SBRT+/-chemotherapy from 2007-2011 was performed. Twenty-seven percent of patients were stage I, 38% were stage II, 27% were stage III and 8% were stage IV. Patients most commonly received 24 Gy/1 fraction or 30-36 Gy/3 fractions. Kaplan-Meier was used to estimate overall survival (OS), local control (LC), cause specific survival (CSS) and freedom-from-metastatic disease (FFMD).Results: The median age was 86 (range 80-91), and median follow-up was 11.6 months (3.5-24.6). The median planning target volume was 21.48 cm3 (6.1-85.09). Median OS was 7.6 months with 6/12 month OS rates of 65.4%/34.6%, respectively. Median LC was 11.5 months, 6-month and 12-month actuarial LC rates were 60.1% and 41.2%, respectively. There were no independent predictors for LC, but there was a trend for improved LC with prescription dose greater than 20 Gy (p = 0.063). Median CSS was 6.3 months, and 6-month and 12-month actuarial CSS were 53.8% and 23.1%, respectively. Median FFMD was 8.4 months, and 6-month and 12-month actuarial rates were 62.0% and 41.4%, respectively. Nine patients (47%) had local failures, 11 (58%) had distant metastasis, and 7 (37%) had both. There were no acute or late grade 3+ toxicities.Conclusions: Definitive SBRT is feasible, safe and effective in elderly patients who have unresectable disease, have comorbidities precluding surgery or decline surgery. © 2013 Kim et al.; licensee BioMed Central Ltd

Vertical distribution and migration of fish larvae in the NW Iberian upwelling system during the winter mixing period: implications for cross-shelf distribution

The vertical distribution and vertical migrations of fish larvae and implications for their cross-shelf distribution were investigated in the northern limit of the NE Atlantic upwelling region during the late winter mixing period of 2012. The average positive values of the upwelling index for February and March of this year were far from normal, although the average hydrographic conditions during the period of study were of downwelling and the water column was completely mixed. Fish larvae, most in the preflexion stage, were concentrated in the upper layers of the water column and their distribution was depth stratified, both day and night. However, the larval fish community was not structured in the vertical plane and fish larvae did not show significant diel vertical migration (DVM), although five species showed ontogenetic vertical migration. In regions of coastal upwelling and in the absence of DVM, the location of fish larvae in the water column is crucial for their cross-shelf distribution. Thus, the cross-shelf distribution of the six most abundant species collected in this study can be explained by the surface onshore flow associated with coastal downwelling, retaining larvae of the coastal spawning species with a relatively shallow distribution in the shelf region and transporting larvae of slope spawning species onto the shelf. The wide vertical distribution shown by larvae of the offshore spawning species could be an adaptation of these species to ensure that some larvae reach the inshore nursery areasPlan Nacional de I+D+i (CRAMERCTM2010- 21856-CO3-02), Junta de Galicia (ECOPREGA-10MMA602021PR), Principado de Asturias (GRUPIN14-144)Postprint2,044