Coupled Bose-Einstein condensate: Collapse for attractive interaction

The collapse of trapped Boson-Einstein condensate (BEC) of atoms in states 1 and 2 was studied. When the interaction among the atoms in state i was attractive the component i of the condensate experienced collapse. When the interaction between an atom in state 1 and state 2 was attractive both components experienced collapse. The time-dependant Gross-Pitaevski (GP) equation was used to study the time evolution of the collapse. There was an alternate growth and decay in the number of particles experiencing collapse.

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Morphological aspects of the capybara stomach (Hydrochaeris hydrochaeris): Gross and microscopic structure

The digestive system of the capybara has been investigated because of its coprofagia habits, important for their absorptive activity. These species present differences in terms of gastrointestinal morphological characters when compared with other rodents. Macroscopiclly, the stomach of the capybara is constituted of the following parts: cardiac, pyloric, body, fundic and gastric diverticulum. It presents two curvatures, one big and another small. Externally, the presence of gastric bands (tenias) is observed. With regards to the volumetric view, the gastric capacity varies from 850 to 2010 ml, with an average of 1498.57 ml. So, the stomach of this animal can be classified as a simple stomach, in the format of a curved sack and similar to an inverted letter 'J'. The gastric mucous membrane presents a surface filled by numerous tortuous gastric folds and longitudinally distributed along all its extension. The mucous tunic also possesses recesses located among the successive gastric folds, which were denoted as gastric parts with numerous openings described as gastric pits. In the cardiac part, a glandular epithelium with cardiac glands is noticed containing a lot of parietal and mucous neck cells. The fundic part, body and gastric diverticulum contain proper gastric glands with main, parietal and mucous neck cells. Finally, the pyloric part has pyloric glands with two cellular types, mucous neck and parietal cells.

Additional observations on the gross morphology and microstructure of Baccaconularia Hughes, Gunderson et Weedon, 2000, a Cambrian (Furongian) conulariid from the north-central USA

Baccaconularia Hughes, Gunderson et Weedon, 2000, from the Furongian Series (Cambrian System) of the north-central USA, has been interpreted as a conulariid cnidarian, based on a suite of gross morphological similarities shared only with other post-Cambrian genera currently assigned to this group. Closely spaced, squarish to subrectangular facial nodes of Baccaconularia are aligned in distinct longitudinal files. Nodes also display a subtler, more or less rectilinear transverse alignment, though this pattern commonly is disrupted by offset parallel to the longitudinal files. In their shape and pattern of arrangement, the nodes of Baccaconularia are most similar to the squarish to elongate nodes of Pseudoconularia Bouček, 1939. Longitudinal node files of Baccaconularia may also be compared with the longitudinal facial ridges of Conularia cambria Walcott, 1890 from the Furongian of Wisconsin. Apical angles of Baccaconularia range from approximately 13° to 14.5°. Scanning electron imaging of B. cf. robinsoni shows that its thin, phosphatic skeleton is finely lamellar, with the thickness of individual lamellae measuring approximately 1 μm. The skeleton also exhibits microscopic circular pores and crater-like pits that range from approximately 5 to 10 μm in diameter. These pores and pits are similar in size, geometry, areal density and pattern of arrangement to those of many post-Cambrian conulariids. Microscopic circular pores are documented here for the first time in the genus Archaeoconularia Bouček, 1939 from the Upper Ordovician of the Czech Republic. Although the origin of the pores and pits is open to alternative interpretations, the discovery of these features and fine lamination in Baccaconularia strengthens the argument that this genus is a Cambrian conulariid. © 2006 Nanjing Institute of Geology and Palaeontology, CAS.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

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

Antinucleon spectra in the Dirac equation with scalar and vector Wood-Saxon potentials

We analyze here the spin and pseudospin symmetry for the antinucleon spectra solving the Dirac equation with scalar and vector Wood-Saxon potentials. In relativistic nuclear mean field theories where these potentials have large magnitudes and opposite signs we show that contrary to the nucleon case where pseudospin interaction is never very small and cannot be treated perturbatively, for antinucleon systems this interaction is perturbative and an exact pseudospin symmetry is possible. This result manifests the relativistic nature of the nuclear pseudospin symmetry. © 2009 American Institute of Physics.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

Stability of the null solution of the equation ẋ(t) = -a(t)x(t) + b(t)x([t])

The asymptotic stability of the null solution of the equation ẋ(t) = -a(t)x(t)+b(t)x([t]) with argument [t], where [t] designates the greatest integer function, is studied by means of dichotomic maps. © 2010 Academic Publications.

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.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

Peru: integration, sectoral specialization and synchronization with international gross domestic product cycles

Includes bibliography

A simple derivation of the Lindblad equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Spin and pseudospin symmetries of the Dirac equation with confining central potentials

We derive the node structure of the radial functions which are solutions of the Dirac equation with scalar S and vector V confining central potentials, in the conditions of exact spin or pseudospin symmetry, i.e., when one has V=±S+C, where C is a constant. We show that the node structure for exact spin symmetry is the same as the one for central potentials which go to zero at infinity but for exact pseudospin symmetry the structure is reversed. We obtain the important result that it is possible to have positive energy bound solutions in exact pseudospin symmetry conditions for confining potentials of any shape, including naturally those used in hadron physics, from nuclear to quark models. Since this does not occur for potentials going to zero at large distances, which are used in nuclear relativistic mean-field potentials or in the atomic nucleus, this shows the decisive importance of the asymptotic behavior of the scalar and vector central potentials on the onset of pseudospin symmetry and on the node structure of the radial functions. Finally, we show that these results are still valid for negative energy bound solutions for antifermions. © 2013 American Physical Society.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.