Tensor coupling and pseudospin symmetry in nuclei

In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy decomposition of the pseudospin energy splittings, we show that the changes in these splittings come by mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners, and by changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.Comment: 11 pages, 5 figures, uses REVTeX macro

The nuclear pseudospin symmetry along an isotopic chain

We investigate the isospin dependence of pseudospin symmetry in the chain of tin isotopes (from $^{120}$Sn until $^{170}$Sn). Using a Woods-Saxon parametrization of the nuclear potential for these isotopes we study in detail the effect of the vector-isovector $\rho$ and Coulomb potentials in the energy splittings of neutron and proton pseudospin partners in the isotopic chain. We conclude that the realization of nuclear pseudospin symmetry does not change considerably with the mass number, and is always favored for neutrons. We also find that the $\rho$ potential accounts for essentially all the pseudospin isospin asymmetry observed and that the Coulomb potential plays a negligible role in this asymmetry. This can be explained by the dynamical nature of pseudospin symmetry in nuclei, namely the dependence of the pseudospin splittings on the shape of the nuclear mean-field potential.Comment: 4 pages, 4 figures, to be published in Brazilian Journal of Physic

Discrete time piecewise affine models of genetic regulatory networks

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. When compared to other models of regulatory networks, these models have an additional parameter which is identified as quantifying interaction delays. In spite of their simplicity, their dynamics presents a rich variety of behaviours. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle -- with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.Comment: 34 page

Dynamical nature of the nuclear pseudospin and its isospin asymmetry

Pseudospin symmetry in nuclei is investigated by solving the Dirac equation with Woods-Saxon scalar and vector radial potentials. We relate the pseudospin interaction with a pseudospin-orbit term in a Schroedinger-like equation for the lower component of the Dirac spinor. We show that this term gives a large contribution to the energy splittings of pseudospin partners, so that the near pseudospin degeneracy arises from a significant cancellation among the different terms in that equation. This is a manifestation of the dynamical character of this symmetry in the nucleus. We analyze the isospin dependence of the pseudospin symmetry in a nuclear isotope chain by including a vector-isovector potential V_rho and a Coulomb potential and conclude that V_rho gives the main contribution to the observed pseudospin isospin asymmetry.Comment: 4 pages, 2 figures, uses World Scientific style file. Contribution presented at the VIII International Workshop on Hadron Physics, Bento Goncalves, RS, Brazil, April 14-19, 2002. To be published by World Scientific in the proceedings of the "International Workshop on Hadron Physics 2002

Spin and pseudospin symmetries in the antinucleon spectrum of nuclei

Spin and pseudospin symmetries in the spectra of nucleons and antinucleons are studied in a relativistic mean-field theory with scalar and vector Woods-Saxon potentials, in which the strength of the latter is allowed to change. We observe that, for nucleons and antinucleons, the spin symmetry is of perturbative nature and it is almost an exact symmetry in the physical region for antinucleons. The opposite situation is found in the pseudospin symmetry case, which is better realized for nucleons than for antinucleons, but is of dynamical nature and cannot be viewed in a perturbative way both for nucleons and antinucleons. This is shown by computing the spin-orbit and pseudospin-orbit couplings for selected spin and pseudospin partners in both spectra.Comment: 8 figures, uses revtex 4.1 macro

Flexibility of expressive timing in repeated musical performances

Performances by soloists in the Western classical tradition are normally highly prepared, yet must sound fresh and spontaneous. How do musicians manage this? We tested the hypothesis that they achieve the necessary spontaneity by varying the musical gestures that express their interpretation of a piece. We examined the tempo arches produced by final slowing at the ends of phrases in performances of J. S. Bach’s No. 6 (Prelude) for solo cello (12 performances) and the Italian Concerto (Presto) for solo piano (eight performances). The performances were given by two experienced concert soloists during a short time period (3½ months for the Prelude, 2 weeks for the Presto) after completing their preparations for public performance. We measured the tempo of each bar or half-bar, and the stability of tempo across performances (difference of the tempo of each bar/half bar from each of the other performances). There were phrase arches for both tempo and stability with slower, less stable tempi at beginnings and ends of phrases and faster, more stable tempi mid-phrase. The effects of practice were complex. Tempo decreased overall with practice, while stability increased in some bars and decreased in others. One effect of practice may be to imbue well-learned, automatic motor sequences with freshness and spontaneity through cognitive control at phrase boundaries where slower tempi and decreased stability provide opportunities for slower cognitive processes to modulate rapid automatic motor sequences

Relevance of pseudospin symmetry in proton-nucleus scattering

The manifestation of pseudospin-symmetry in proton-nucleus scattering is discussed. Constraints on the pseudospin-symmetry violating scattering amplitude are given which require as input cross section and polarization data, but no measurements of the spin rotation function. Application of these constraints to p-58Ni and p-208Pb scattering data in the laboratory energy range of 200 MeV to 800 MeV, reveals a significant violation of the symmetry at lower energies and a weak one at higher energies. Using a schematic model within the Dirac phenomenology, the role of the Coulomb potential in proton-nucleus scattering with regard to pseudospin symmetry is studied. Our results indicate that the existence of pseudospin-symmetry in proton-nucleus scattering is questionable in the whole energy region considered and that the violation of this symmetry stems from the long range nature of the Coulomb interaction.Comment: 22 pages including 9 figures, correction of 1 reference, revision of abstract and major modification of chapter 4, Fig. 6, and Fig. 7; addition of Fig. 8 and Fig.