TAXONOMIC POSITION of GUIRATINGIA MENDESI (MEGADESMIDAE) and THE EVOLUTION of PERMIAN ENDEMIC BIVALVE FAUNA of THE PARANA BASIN, BRAZIL

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

PENNSYLVANIAN HETEROCONCHIA (MOLLUSCA, BIVALVIA) FROM THE PIAUI FORMATION, PARNAIBA BASIN, BRAZIL

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Permian bivalves of the Taciba Formation, Itarare group, Parana basin, and their biostratigraphic significance

A small and poorly diversified bivalve fauna from Taciba Formation, Itarare Group, Parana Basin (State of Santa Catarina, Mafra Municipality), is described in this paper for the first time, based on new findings. The fauna is recorded in a 30 cm thick interval of fine sandstone locally at the top of Taciba Formation, in the Butia quarry. The studied fossil-bearing sand-stone bed is a marine intercalation recording a brief eustatic rise in sea-level, probably following glacier retreat and climate amelioration at the end of a broad glacial scenario. The fauna is mainly dominated by productid brachiopods, which are not described here, and rare mollusk shells (bivalves and gastropods). Two bivalve species were identified: Myonia argentinensis (Harrington, 1955), and Aviculopecten multiscalptus (Thomas, 1928). The presence of Myonia argentinensis is note-worthy since this species is also present in the Baitaca assemblage found in marine siltstones (Baitaca assemblage) of the Rio do Sul Formation, cropping out at the Teixeira Soares region, Parana State. This species is also recorded in the bivalve fauna from the Bonete Formation, Pillahinco Group, Sauce Grande Basin, Buenos Aires Province, in Argentina. Hence, the marine bivalves of the Taciba Formation are associated with the transgressive event that characterizes the Eurydesma fauna, indicating a Late Asselian-Sakmarian age for the bivalve fauna. Presence of the Myonia argentinensis megadesmid species reinforces the Gondwanic nature of the studied fauna.

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schrodinger equation and a variational method it is shown that (3 + 1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.

Extra dimensions at the CERN LHC via mini-black holes: Effective Kerr-Newman brane-world effects

We solve Einstein equations on the brane to derive the exact form of the brane-world-corrected perturbations in Kerr-Newman singularities, using Randall-Sundrum and Arkani-Hamed-Dimopoulos-Dvali (ADD) models. It is a consequence of such models that Kerr-Newman mini-black holes can be produced in LHC. We use this approach to derive a normalized correction for the Schwarzschild Myers-Perry radius of a static (4+n)-dimensional mini-black hole, using more realistic approaches arising from Kerr-Newman mini-black hole analysis. Besides, we prove that there are four Kerr-Newman black hole horizons in the brane-world scenario we use, although only the outer horizon is relevant in the physical measurable processes. Parton cross sections in LHC and Hawking temperature are also investigated as functions of Planck mass (in the LHC range 1-10 TeV), mini-black hole mass, and the number of large extra dimensions in brane-world large extra-dimensional scenarios. In this case a more realistic brane-effect-corrected formalism can achieve more precisely the effective extra-dimensional Planck mass and the number of large extra dimensions-in the Arkani-Hamed-Dimopoulos-Dvali model-or the size of the warped extra dimension-in Randall-Sundrum formalism.

Kinematics of a spacetime with an infinite cosmological constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant L is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When Lambda --> infinity, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c --> infinity. is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.

The quadratic spinor Lagrangian, axial torsion current and generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field-Weyl, Majorana, flagpole, or flag-dipole spinor fields-yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.