A Proof of the Isoenergetic KAM-Theorem from the “Ordinary” One

A proof is given of the isoenergetic KAM-theorem for Hamiltonian systems, using the “ordinary” KAM-theorem and a transversality argument.

Cylindrical, periodic surface lattice — theory, dispersion analysis, and experiment

A two-dimensional surface lattice of cylindrical topology obtained via perturbing the inner surface of a cylinder is considered. Periodic perturbations of the surface lead to observation of high-impedance, dielectric-like media and resonant coupling of surface and non-propagating volume fields. This allows synthesis of tailored-for-purpose "coating" material with dispersion suitable, for instance, to mediate a Cherenkov type interaction. An analytical model of the lattice is discussed and coupled-wave equations are derived. Variations of the lattice dispersive properties with variation of parameters are shown, illustrating the tailoring of the structure's electromagnetic properties. Experimental results are presented showing agreement with the theoretical model

Diversity of thiosulfate-oxidizing bacteria from marine sediments and hydrothermal vents

Species diversity, phylogenetic affiliations, and environmental occurrence patterns of thiosulfate-oxidizing marine bacteria were investigated by using new isolates from serially diluted continental slope and deep-sea abyssal plain sediments collected off the coast of New England and strains cultured previously from Galapagos hydrothermal vent samples. The most frequently obtained new isolates, mostly from 103- and 104-fold dilutions of the continental slope sediment, oxidized thiosulfate to sulfate and fell into a distinct phylogenetic cluster of marine alpha-Proteobacteria. Phylogenetically and physiologically, these sediment strains resembled the sulfate-producing thiosulfate oxidizers from the Galapagos hydrothermal vents while showing habitat-related differences in growth temperature, rate and extent of thiosulfate utilization, and carbon substrate patterns. The abyssal deep-sea sediments yielded predominantly base-producing thiosulfate-oxidizing isolates related to Antarctic marine Psychroflexus species and other cold-water marine strains of the Cytophaga-Flavobacterium-Bacteroides phylum, in addition to gamma-proteobacterial isolates of the genera Pseudoalteromonas and Halomonas-Deleya. Bacterial thiosulfate oxidation is found in a wide phylogenetic spectrum of Flavobacteria and Proteobacteria

The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory

The compactification of five dimensional N=2 SUSY Yang-Mills (YM) theory onto a circle provides a four dimensional YM model with N=4 SUSY. This supersymmetry can be broken down to N=2 if non-trivial boundary conditions in the compact dimension, \phi(x_5 +R) = e^{2\pi i\epsilon}\phi(x_5), are imposed on half of the fields. This two-parameter (R,\epsilon) family of compactifications includes as particular limits most of the previously studied four dimensional N=2 SUSY YM models with supermultiplets in the adjoint representation of the gauge group. The finite-dimensional integrable system associated to these theories via the Seiberg-Witten construction is the generic elliptic Ruijsenaars-Schneider model. In particular the perturbative (weak coupling) limit is described by the trigonometric Ruijsenaars-Schneider model.Comment: 18 pages, LaTe

Quantitative predictions with detuned normal forms

The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original Hamiltonian. Attention is focused on the quantitative predictive ability of the normal form. We find analytical expressions for bifurcations of periodic orbits and compare them with other analytical approaches and with numerical results. The predictions are quite reliable even outside the convergence radius of the perturbation and we analyze this result using resummation techniques of asymptotic series.Comment: Accepted for publication on Celestial Mechanics and Dynamical Astronom

Resonance tongues in the quasi-periodic Hill-Schrödinger equation with three frequencies

n this article we investigate numerically the spectrum of some representative examples of discrete one-dimensional Schrödinger operators with quasi-periodic potential in terms of a perturbative constant b and the spectral parameter a. Our examples include the well-known Almost Mathieu model, other trigonometric potentials with a single quasi-periodic frequency and generalisations with two and three frequencies. We computed numerically the rotation number and the Lyapunov exponent to detect open and collapsed gaps, resonance tongues and the measure of the spectrum. We found that the case with one frequency was significantly different from the case of several frequencies because the latter has all gaps collapsed for a sufficiently large value of the perturbative constant and thus the spectrum is a single spectral band with positive Lyapunov exponent. In contrast, in the cases with one frequency considered, gaps are always dense in the spectrum, although some gaps may collapse either for a single value of the perturbative constant or for a range of values. In all cases we found that there is a curve in the (a, b)-plane which separates the regions where the Lyapunov exponent is zero in the spectrum and where it is positive. Along this curve, which is b = 2 in the Almost Mathieu case, the measure of the spectrum is zero.Peer ReviewedPostprint (published version