The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation

We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.

Dispersion relations and the spin polarizabilities of the nucleon

A forward dispersion calculation is implemented for the spin polarizabilities γ1, ⋯, γ4 of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at script O sign(ω3). In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory. © 1998 Elsevier Science B.V.

The δ expansion and the principle of minimal sensitivity

The δ-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. Different ways of implementing the principle of minimal sensitivity to the δ-expansion produce in general different results for observables. For illustration we use the Nambu-Jona-Lasinio model for chiral symmetry restoration at finite density and compare results with those obtained with the Hartree-Fock approximation.

Gerasimov-Drell-Hearn sum rule and the single-pion photoproduction multipole E0+ close to threshold

The long-standing discrepancy between the Gerasimov-Drell-Hearn sum rule and the analysis of pion photoproduction multipoles is greatly diminished by use of s-wave multipoles that are in accord with the predictions of chiral perturbation theory and describe the experimental data in the threshold region. The remaining difference may be due to contributions of channels with more pions and/or heavier mesons whose contributions to the sum rule remain to be investigated by a direct measurement of the photoabsorption cross sections.

Study of water and dimethylformamide interaction by computer simulation

Monte Carlo simulations of water-dimethylformamide (DMF) mixtures were performed in the isothermal and isobaric ensemble at 298.15 K and 1 atm. The intermolecular interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term. The TIP4P model was used for simulating water molecules, and a six-site model previously optimised by us was used to represent DMF. The potential energy for the water-DMF interaction was obtained via standard geometric combining rules using the original potential parameters for the pure liquids. The radial distribution functions calculated for water-DMF mixtures show well characterised hydrogen bonds between the oxygen site of DMF and hydrogen of water. A structureless correlation curve was observed for the interaction between the hydrogen site of the carbonyl group and the oxygen site of water. Hydration effects on the stabilisation of the DMF molecule in aqueous solution have been investigated using statistical perturbation theory. The results show that energetic changes involved in the hydration process are not strong enough to stabilise another configuration of DMF than the planar one.

Generalized polarizabilities and electroexcitation of the nucleon

Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer Q2. In particular, the sum of the generalized electric and magnetic polarizabilities ∑ = α + β and the spin polarizability γ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predictions of chiral perturbation theory. © 1999 Elsevier Science B.V. All rights reserved.

Chiral corrections in hadron spectroscopy

We show that the implementation of chiral symmetry in recent studies of the hadron spectrum in the context of the constituent quark model is inconsistent with chiral perturbation theory. In particular, we show that the leading nonanalytic (LNA) contributions to the hadron masses are incorrect in such approaches. The failure to implement the correct chiral behaviour of QCD results in incorrect systematics for the corrections to the masses. © 1999 Published by Elsevier Science B.V. All rights reserved.

First measurement of π-e→π-eγ pion virtual compton scattering

Pion virtual compton scattering (VCS) via the reaction π-e→π-eγ was observed in the Fermilab E781 SELEX experiment. SELEX used a 600 GeV/c π- beam incident on target atomic electrons, detecting the incident π- and the final state π-, electron and γ. Theoretical predictions based on chiral perturbation theory are incorporated into a Monte Carlo simulation of the experiment and are compared to the data. The number of reconstructed events (=9) and their distribution with respect to the kinematic variables (for the kinematic region studied) are in reasonable accord with the predictions. The corresponding π- VCS experimental cross section is σ=38.8±13 nb, in agreement with the theoretical expectation of σ=34.7 nb.

One loop conformal invariance of the superstring in an AdS5 × S5 background

It is proven that the pure spinor superstring in an AdS5 × S5 background remains conformally invariant at one loop level in the sigma model perturbation theory. © SISSA/ISAS 2003.

Quantum consistency of the superstring

Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS 5×S 5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level. © SISSA 2005.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

Probing the infraed behavior of the ghost-gluon vertex in quantum chromodynamics

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica não linear de m Pêndula eletromecânico com excitação vertical

Pós-graduação em Matemática - IBILCE

Um estudo da dinâmica fracamente não-linear de um sistema nanomecânico

Pós-graduação em Matemática - IBILCE

Áxions, májorons e neutrinos em extensões do modelo padrão

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)