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.

Resonance and chaos: II. Exterior resonances and asymmetric libration

The motion of a test particle in the vicinity of exterior resonances is examined in the context of the planar, circular, restricted three-body problem. The existence of asymmetric periodic orbits associated with the 1 : n resonances (where n = 2, 3, 4, 5) is confirmed; there is also evidence of asymmetric resonances associated with larger values of n. A detailed examination of the evolution of the family of orbits associated with the 1:2 resonance shows the sequence that leads to asymmetric libration. On the basis of numerical studies of the phase space it is concluded that the existence of asymmetric libration means that the region exterior to the perturbing mass is more chaotic than the interior region. The apparent absence of 'particles' in 1 : n resonances in the solar system may reflect this inherent bias.

Positron-helium scattering: Resonance and differential cross sections

We study positron-helium scattering using close coupling approximation (CCA) employing different combinations of the following basis functions: He(1s1s), He(1s2s), He(1s2p), Ps(1s). and Ps(2s), where Ps stands for the positronium atom. We observe a prominent S wave resonance of width 2 eV at about 30 eV, in excitation and rearrangement cross sections to He(1s2s), He(1s2p), Ps(1s) and Ps(2s) states. We also report results of differential cross sections for the excitation of helium and positronium formation.

Polarized structure functions of the nucleon in the resonance region

We present predictions for the spin structure functions of the proton in the framework of a unitary isobar model for one-pion photo- and electroproduction. Our results are compared with recent experimental data from SLAC. The first moments of the calculated structure functions fullfil the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules within an error of typically 5-10%.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.

Soliton spectrum of integrable models with local symmetries

The soliton spectrum (massive and massless) of a family of integrable models with local U(1) and U(1) ⊗U(1) symmetries is studied. These models represent relevant integrable deformations of SL(2,ℝ) ⊗U(1) n-1-WZW and SL(2,ℝ) ⊗ SL(2,ℝ) ⊗U(1) n-2-WZW models. Their massless solitons appear as specific topological solutions of the U(1)(or U(1) ⊗ U(1)-) CFTs. The nonconformal analog of the GKO-coset formula is derived and used in the construction of the composite massive solitons of the ungauged integrable models. © SISSA/ISAS 2002.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

Conformational basis for the biological activity of TOAC-labeled angiotensin II and bradykinin: Electron paramagnetic resonance, circular dichroism, and fluorescence studies

N-Terminally and internally labeled analogues of the hormones angiotensin (AII, DRVYIHPF) and bradykinin (BK, RPPGFSPFR) were synthesized containing the paramagnetic amino acid 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4- carboxylic acid (TOAC). TOAC replaced Asp 1 (TOAC 1-AII) and Val 3 (TOAC 3-AII) in AII and was inserted prior to Arg 1 (TOAC 0-BK) and replacing Pro 3 (TOAC 3-BK) in BK. The peptide conformational properties were examined as a function of trifluoroethanol (TFE) content and pH. Electron paramagnetic resonance spectra were sensitive to both variables and showed that internally labeled analogues yielded rotational correlation times (TC) considerably larger than N-terminally labeled ones, evincing the greater freedom of motion of the N-terminus. In TFE, τ C increased due to viscosity effects. Calculation of τ Cpeptide/τ CTOAC ratios indicated that the peptides acquired more folded conformations. Circular dichroism spectra showed that, except for TOAC 1-AII in TFE, the N-terminally labeled analogues displayed a conformational behavior similar to that of the parent peptides. In contrast, under all conditions, the TOAC 3 derivatives acquired more restricted conformations. Fluorescence spectra of All and its derivatives were especially sensitive to the ionization of Tyr 4. Fluorescence quenching by the nitroxide moiety was much more pronounced for TOAC 3-AII The conformational behavior of the TOAC derivatives bears excellent correlation with their biological activity, since, while the N-terminally labeled peptides were partially active, their internally labeled counterparts were inactive [Nakaie, C. R., et al., Peptides 2002, 23, 65-70]. The data demonstrate that insertion of TOAC in the middle of the peptide chain induces conformational restrictions that lead to loss of backbone flexibility, not allowing the peptides to acquire their receptor-bound conformation. © 2004 Wiley Periodicals, Inc.

Dynamics of bright matter wave solitons in a Bose-Einstein condensate

Recent experimental and theoretical advances in the creation and description of bright matter wave solitons are reviewed. Several aspects are taken into account, including the physics of soliton train formation as the nonlinear Fresnel diffraction, soliton-soliton interactions, and propagation in the presence of inhomogeneities. The generation of stable bright solitons by means of Feshbach resonance techniques is also discussed. © World Scientific Publishing Company.

Magnetic resonance study of the crystallization behavior of InF3-based glasses doped with Cu2+, Mn2+ and Gd3+

The crystallization of fluoroindate glasses doped with Gd3+, Mn2+ and Cu2+ heat treated at different temperatures, ranging from the glass transition temperature (Tg) to the crystallization temperature (Tc), are investigated by electron paramagnetic resonance (EPR) and 19F nuclear magnetic resonance (NMR). The EPR spectra indicate that the Cu2+ ions in the glass are located in axially distorted octahedral sites. In the crystallized glass, the g-values agreed with those reported for Ba2ZnF6, which correspond to Cu2+ in a tetragonal compressed F- octahedron and to Cu2+ on interstitial sites with a square-planar F- co-ordination. The EPR spectra of the Mn2+ doped glasses exhibit a sextet structure due to the Mn2+ hyperfine interaction. These spectra suggest a highly ordered environment for the Mn2+ ions (close to octahedral symmetry) in the glass. The EPR spectra of the recrystallized sample exhibit resonances at the same position, suggesting that the Mn2+ ions are located in sites of highly symmetric crystalline field. The increase of the line intensity of the sextet and the decrease of the background line in the thermal treated samples suggest that the Mn2+ ions move to the highly ordered sites which contribute to the sextet structure. The EPR spectra of the Gd3+ doped glasses exhibit the typical U-spectrum of a s-state ion in a low symmetry site in disordered systems. The EPR of the crystallized glasses, in contrast, have shown a strong resonance in g ≈ 2.0, suggesting Gd3+ ions in environment close to cubic symmetry. The 19F NMR spin-lattice relaxation rates were also strongly influenced by the crystallization process that takes over in samples annealed above Tc. For the glass samples (doped or undoped) the 19F magnetization recoveries were found to be adjusted by an exponential function and the spin-lattice relaxation was characterized by a single relaxation time. In contrast, for the samples treated above Tc, the 19F magnetization-recovery becomes non-exponential. A remarkable feature of our results is that the changes in the Cu2+, Mn2+, Gd3+ EPR spectra and NMR relaxation, are always observed for the samples annealed above Tc. © 2006 Elsevier B.V. All rights reserved.

New contributions to the determination of resonance frequencies of rectangular microstrip antennas by neural networks

This paper uses artificial neural networks (ANN) to compute the resonance frequencies of rectangular microstrip antennas (MSA), used in mobile communications. Perceptron Multi-layers (PML) networks were used, with the Quasi-Newton method proposed by Broyden, Fletcher, Goldfarb and Shanno (BFGS). Due to the nature of the problem, two hundred and fifty networks were trained, and the resonance frequency for each test antenna was calculated by statistical methods. The estimate resonance frequencies for six test antennas were compared with others results obtained by deterministic and ANN based empirical models from the literature, and presented a better agreement with the experimental values.

Search for a resonance decaying into WZ boson Pairs in pp̄ collisions

We present the first search for an electrically charged resonance W′ decaying to a WZ boson pair using 4.1fb-1 of integrated luminosity collected with the D0 detector at the Fermilab Tevatron pp̄ collider. The WZ pairs are reconstructed through their decays into three charged leptons (≤=e, μ). A total of 9 data events is observed in good agreement with the background prediction. We set 95% C.L. limits on the W′WZ coupling and on the W′ production cross section multiplied by the branching fractions. We also exclude W′ masses between 188 and 520 GeV within a simple extension of the standard model and set the most restrictive limits to date on low-scale technicolor models. © 2010 The American Physical Society.

State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

Artificial satellites: Resonance effects produced by terrestrial tide

Effects due to resonances in the orbital motion of artificial satellites disturbed by the terrestrial tide are analyzed. The nodal co-rotation resonance, apsidal co-rotation resonance and the Lidov-Kozai's mechanism are studied. The effects of the resonances are analyzed through the variations of the metric orbital elements. Libration and circulation motions for high orbits with high eccentricities are verified for the Lidov-Kozai's mechanism.