Divergent diagrams of folds and simultaneous conjugacy of involutions

In this work we show that the smooth classification of divergent diagrams of folds (f(1),..., f(s)) : (R-n, 0) -> (R-n x(...)xR(n), 0) can be reduced to the classification of the s-tuples (p(1)., W) of associated involutions. We apply the result to obtain normal forms when s <= n and {p(1),...,p(s)} is a transversal set of linear involutions. A complete description is given when s = 2 and n >= 2. We also present a brief discussion on applications of our results to the study of discontinuous vector fields and discrete reversible dynamical systems.

The adaptive compensations in endocrine pancreas from glucocorticoid-treated rats are reversible after the interruption of treatment

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A class of reversible quadratic polynomial vector fields on S-2

We study a class of quadratic reversible polynomial vector fields on S-2. We classify all the centers of this class of vector fields and we characterize its global phase portrait. (C) 2010 Elsevier B.V. All rights reserved.

On the reversible quadratic polynomial vector fields on S-2

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S-2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S-2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.

Reversible holographic glasses using visible lasers

Antimony based glasses have been investigated for the first time regarding the possibility of holographic data storage using visible lasers sources. Changes in both refractive index and the absorption coefficient were measured using a holographic setup. The modulation of the optical constants is reversible by heat treatment. Bragg gratings were written under visible light of an Ar laser and erased thermally.

Reversible equivariant Hopf bifurcation

In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues of the linearization of the vector field at the equilibrium point. The eigenvalue movements near such a degeneracy typically follow one of three scenarios: splitting (from two pairs of imaginary eigenvalues to a quadruplet on the complex plane), passing (on the imaginary axis), or crossing (a quadruplet crossing the imaginary axis). We give a complete description of the behaviour of reversible periodic orbits in the vicinity of such a bifurcation point. For non-reversible periodic solutions. in the case of Hopf bifurcation with crossing eigenvalues. we obtain a generalization of the equivariant Hopf Theorem.

Periodic orbits for a class of reversible quadratic vector field on R-3

For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.

Characterization of the reversible photoinduced optical changes in Sb-based glasses

Changes occurring in absorption coefficients when glasses in the SbPO4-WO3 binary system were irradiated by light, at the edge of the absorption band, were measured in real time. These glasses present good thermal and optical properties and photoinduced changes in the absorption coefficients are reversible by heat treatment around 150 degrees C. Subsequent recording/erasing cycles could be made without sample degradation. The sensitivity of the induced optical changes was studied for different wavelengths, light powers and energy of light dose exposures, and for different compositions of the glasses. The changes in the absorption coefficients of the glass samples were accompanied by a color change from yellow to blue, and were also characterized by visible spectroscopy. The color changes occurred through the entire volume of the glass (similar to 2 mm thickness) for the Ar-ion laser lines at the edge of the absorption band. (c) 2006 Elsevier B.V. All rights reserved.

Computational studies of the reversible domain swapping of p13suc1

A minimalist representation of protein structures using a Go- like potential for interactions is implemented to investigate the mechanisms of the domain swapping of p13suc1, a protein that exists in two native conformations: a monomer and a domain- swapped dimer formed by the exchange of a beta- strand. Inspired by experimental studies which showed a similarity of the transition states for folding of the monomer and the dimer, in this study we justify this similarity in molecular descriptions. When intermediates are populated in the simulations, formation of a domain- swapped dimer initiates from the ensemble of unfolded monomers, given by the fact that the dimer formation occurs at the folding/ unfolding temperature of the monomer ( T-f). It is also shown that transitions, leading to a dimer, involve the presence of two intermediates, one of them has a dimeric form and the other is monomeric; the latter is much more populated than the former. However, at temperatures lower than T-f, the population of intermediates decreases. It is argued that the two folded forms may coexist in absence of intermediates at a temperature much lower than T-f. Computational simulations enable us to find a mechanism, `` lock- and- dock'', for domain swapping of p13suc1. To explore the route toward dimer formation, the folding of unstructured monomers must be retarded by first locking one of the free ends of each chain. Then, the other free termini could follow and dock at particular regions, where most intrachain contacts are formed, and thus de. ne the transition states of the dimer. The simulations also showed that a decrease in the maximum distance between monomers increased their stability, which is explained based on confinement arguments. Although the simulations are based on models extracted from the native structure of the monomer and the dimer of p13suc1, the mechanism of the domain- swapping process could be general, not only for p13suc1.

Fold, transcritical and pitchfork singularities for time-reversible systems

This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and hetero-clinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

Reversible intermittent flow-injection determination of mercury in sediments and vinasses by cold vapor atomic absorption spectrometry

A reversible intermittent pow-injection procedure is proposed for the automated determination of mercury in sediments and vinasses by cold vapor atomic absorption spectrometry, CVAAS. Solutions of sample and stannous chloride are carried by two air streams and sequentially injected into the generator/separator chamber in a segmented asynchronous merging zone configuration. The intermittent flow in the forward direction carries the mercury vapor through the flow cell, and in the backward direction, if aspirates the the remaining solution from the vessel to waste. We investigated composition and concentration of reagents, pow rates, commutation times, reactor configuration, and conditions for mercury release. The accuracy was checked by mercury determination in a certified sediment and spiked vinasses and river waters. The system handles about 100 samples per hour (0.50-5.00 mu g L-1), consuming ca. 2.5 mL of sample and 50 mg of SnCl2 per determination; Good recoveries (92-103%) were obtained with spiked samples. Results are precise (RSD <3% for 2.5 mu g Hg L-1, n = 12) and in agreement with values for certified reference material at 95% confidence level. (C) 1999 John Wiley & Sons, Inc.

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.