On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

Producción CientíficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry axis of the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations

The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.Comment: 20 page

PAMELA results on the cosmic-ray antiproton flux from 60 MeV to 180 GeV in kinetic energy

The satellite-borne experiment PAMELA has been used to make a new measurement of the cosmic-ray antiproton flux and the antiproton-to-proton flux ratio which extends previously published measurements down to 60 MeV and up to 180 GeV in kinetic energy. During 850 days of data acquisition approximately 1500 antiprotons were observed. The measurements are consistent with purely secondary production of antiprotons in the galaxy. More precise secondary production models are required for a complete interpretation of the results.Comment: 11 pages, 3 figures, 1 table. Accepted for publication in Physical Review Letter

Formation and structure of ionomer complexes from grafted polyelectrolytes

We discuss the structure and formation of Ionomer Complexes formed upon mixing a grafted block copolymer (poly(acrylic acid)-b-poly(acrylate methoxy poly(ethylene oxide)), PAA21-b-PAPEO14) with a linear polyelectrolyte (poly(N-methyl 2-vinyl pyridinium iodide), P2MVPI), called grafted block ionomer complexes (GBICs), and a chemically identical grafted copolymer (poly(acrylic acid)-co-poly(acrylate methoxy poly(ethylene oxide)), PAA28-co-PAPEO22) with a linear polyelectrolyte, called grafted ionomer complexes (GICs). Light scattering measurements show that GBICs are much bigger (~70–100 nm) and GICs are much smaller or comparable in size (6–22 nm) to regular complex coacervate core micelles (C3Ms). The mechanism of GICs formation is different from the formation of regular C3Ms and GBICs, and their size depends on the length of the homopolyelectrolyte. The sizes of GBICs and GICs slightly decrease with temperature increasing from 20 to 65 °C. This effect is stronger for GBICs than for GICs, is reversible for GICs and GBIC-PAPEO14/P2MVPI228, and shows some hysteresis for GBIC-PAPEO14/P2MVPI43. Self-consistent field (SCF) calculations for assembly of a grafted block copolymer (having clearly separated charged and grafted blocks) with an oppositely charged linear polyelectrolyte of length comparable to the charged copolymer block predict formation of relatively small spherical micelles (~6 nm), with a composition close to complete charge neutralization. The formation of micellar assemblies is suppressed if charged and grafted monomers are evenly distributed along the backbone, i.e., in case of a grafted copolymer. The very large difference between the sizes found experimentally for GBICs and the sizes predicted from SCF calculations supports the view that there is some secondary association mechanism. A possible mechanism is discussed

Grafted block complex coacervate core micelles and their effect on protein adsorption on silica and polystyrene

We have studied the formation and the stability of grafted block complex coacervate core micelles (C3Ms) in solution and the influence of grafted block C3M coatings on the adsorption of the proteins β-lactoglobulin, bovine serum albumin, and lysozyme. The C3Ms consist of a grafted block copolymer PAA21-b-PAPEO14 (poly(acrylic acid)-b-poly(acrylate methoxy poly(ethylene oxide)), with a negatively charged PAA block and a neutral PAPEO block and a positively charged homopolymer P2MVPI (poly(N-methyl 2-vinyl pyridinium iodide). In solution, these C3Ms partly disintegrate at salt concentrations between 50 and 100 mM NaCl. Adsorption of C3Ms and proteins has been studied with fixed-angle optical reflectometry, at salt concentrations ranging from 1 to 100 mM NaCl. In comparison with the adsorption of PAA21-b-PAPEO14 alone adsorption of C3Ms significantly increases the amount of PAA21-b-PAPEO14 on the surface. This results in a higher surface density of PEO chains. The stability of the C3M coatings and their influence on protein adsorption are determined by the composition and the stability of the C3Ms in solution. A C3M-PAPEO14/P2MVPI43 coating strongly suppresses the adsorption of all proteins on silica and polystyrene. The reduction of protein adsorption is the highest at 100 mM NaCl (>90%). The adsorbed C3M-PAPEO14/P2MVPI43 layer is partly removed from the surface upon exposure to an excess of β-lactoglobulin solution, due to formation of soluble aggregates consisting of β-lactoglobulin and P2MVPI43. In contrast, C3M-PAPEO14/P2MVPI228 which has a fivefold longer cationic block enhances adsorption of the negatively charged proteins on both surfaces at salt concentrations above 1 mM NaCl. A single PAA21-b-PAPEO14 layer causes only a moderate reduction of protein adsorption

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal