Porto Oscillation Code (POSC)

The Porto Oscillation Code (POSC) has been developed in 1995 and improved over the years, with the main goal of calculating linear adiabatic oscillations for models of solar-type stars. It has also been used to estimate the frequencies and eigenfunctions of stars from the pre-main sequence up to the sub-giant phase, having a mass between 0.8 and 4 solar masses. The code solves the linearised perturbation equations of adiabatic pulsations for an equilibrium model using a second order numerical integration method. The possibility of using Richardson extrapolation is implemented. Several options for the surface boundary condition can be used. In this work we briefly review the key ingredients of the calculations, namely the equations, the numerical scheme and the output.Comment: Accepted for publication in Astrophysics and Space Science

Atoms in double-delta-kicked periodic potentials: Chaos with long-range correlations

We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization

2δ2\delta-Kicked Quantum Rotors: Localization and `Critical' Statistics

The quantum dynamics of atoms subjected to pairs of closely-spaced $\delta$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$\delta$-kicked system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase-space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances which approximate the `critical statistics' relation $\Sigma_2(L) \simeq \chi L \approx {1/2}(1-\nu) L$, where $\nu \approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $\nu \approx 0.75$ exponent is analyzed.Comment: 4 pages, 3 fig

Effect of FSH on testicular morphology and spermatogenesis in gonadotrophin-deficient hypogonadal mice lacking androgen receptors

Follicle stimulating hormone (FSH) and androgen act to stimulate and maintain spermatogenesis. FSH acts directly on the Sertoli cells to stimulate germ cell number and acts indirectly to increase androgen production by the Leydig cells. In order to differentiate between the direct effects of FSH on spermatogenesis and those mediated indirectly through androgen action we have crossed hypogonadal (hpg) mice which lack gonadotrophins with mice lacking androgen receptors (AR) either ubiquitously (ARKO) or specifically on the Sertoli cells (SCARKO). These hpg.ARKO and hpg.SCARKO mice were treated with recombinant FSH for 7 days and testicular morphology and cell numbers assessed. In untreated hpg and hpg.SCARKO mice germ cell development was limited and did not progress beyond the pachytene stage. In hpg.ARKO mice testes were smaller with fewer Sertoli cells and germ cells compared to hpg mice. Treatment with FSH had no effect on Sertoli cell number but significantly increased germ cell numbers in all groups. In hpg mice FSH increased numbers of spermatogonia and spermatocytes and induced round spermatid formation. In hpg.SCARKO and hpg.ARKO mice, in contrast, only spermatogonial and spermatocyte numbers were increased with no formation of spermatids. Leydig cell numbers were increased by FSH in hpg and hpg.SCARKO mice but not in hpg.ARKO mice. Results show that in rodents 1) FSH acts to stimulate spermatogenesis through an increase in spermatogonial number and subsequent entry of these cells into meiosis, 2) FSH has no direct effect on the completion of meiosis and 3) FSH effects on Leydig cell number are mediated through interstitial ARs

Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

In this paper, we show that every quasiorder $R$ induces a Nelson algebra $\mathbb{RS}$ such that the underlying rough set lattice $RS$ is algebraic. We note that $\mathbb{RS}$ is a three-valued {\L}ukasiewicz algebra if and only if $R$ is an equivalence. Our main result says that if $\mathbb{A}$ is a Nelson algebra defined on an algebraic lattice, then there exists a set $U$ and a quasiorder $R$ on $U$ such that $\mathbb{A} \cong \mathbb{RS}$.Comment: 16 page