Resonant planetary dynamics: Periodic orbits and long-term stability

Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet system shows complicated dynamics with mostly chaotic trajectories. We can determine possible stable configurations by computing resonant periodic trajectories of the general planar three body problem, which can be used for modeling a two-planet system. In this work, we review our model for both the planar and the spatial case. We present families of symmetric periodic trajectories in various resonances and study their linear horizontal and vertical stability. We show that around stable periodic orbits there exist regimes in phase space where regular evolution takes place. Unstable periodic orbits are associated with the existence of chaos and planetary destabilization.Comment: Proceedings of 10th HSTAM International Congress on Mechanics, Chania, Crete, Greece, 25-27 May, 201

Admissible predictive density estimation

Let $X|\mu\sim N_p(\mu,v_xI)$ and $Y|\mu\sim N_p(\mu,v_yI)$ be independent $p$-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on observing $X=x$, we consider the problem of estimating the true predictive density $p(y|\mu)$ of $Y$ under expected Kullback--Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang [Statistical Decision Theory and Related Topics (1982) III 205--230] are sufficient for a formal Bayes rule to be admissible.Comment: Published in at http://dx.doi.org/10.1214/07-AOS506 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Acoustics of tachyon Fermi gas

We consider a Fermi gas of free tachyons as a continuous medium and find whether it satisfies the causality condition. There is no stable tachyon matter with the particle density below critical value $n_T$ and the Fermi momentum $k_F<\sqrt{\frac 32}m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but the situation $P>E$ is not forbidden. Existence of shock waves in tachyon gas is also discussed. At low density $n_T<n<3.45n_T$ the tachyon matter remains stable but no shock wave do survive.Comment: 14 pages, 2 figures (color

Regional differences in store-operated Ca2+ entry in the epithelium of the intact human lens

An elevated level of Ca2+ is an important factor in cataract, yet precisely how Ca2+ enters the lens is unknown. Lens epithelial cells contain a range of G-protein–coupled receptors and receptor tyrosine kinases that induce increases in intracellular Ca2+. Receptor-associated Ca2+ influx is, therefore, likely to be an important route for Ca2+ influx to the lens. The authors investigated stimulated and passive Ca2+ influx in in situ human lens epithelium. Ca2+ changes in equatorial (E) and central anterior (CA) epithelial cells were monitored with the use of a Ca2+ indicator (Fluo4) and confocal microscopy. Gene expression was monitored by RT-PCR and immunoblotting. Adenosine triphosphate (ATP) induced Ca2+ responses that were smaller in CA than E. Ca2+ store depletion, using ATP (100 µM) or thapsigargin (1 µM), revealed greater relative store capacity and Ca2+ influx in E. Ca2+ influx was blocked by La3+ (0.5 µM) in both regions. Unstimulated Ca2+ influx was greater in E than CA. Greater expression of Orai1 and STIM1 was detected in E than in CA. Greater Ca2+ store capacity and Ca2+ influx in E compared with CA reflects underlying differences in proliferation and differentiation between the regions. The relatively small resting Ca2+ influx in CA epithelium suggests that store-operated Ca2+ entry (SOCE) is the main route of Ca2+ influx in these cells. Greater resting influx and SOCE in E cells suggests that these are a major route for Ca2+ influx into the lens. Increased expression of Orai1 and STIM1 in E could account for the differences in Ca2+ entry. Receptor activation will modulate Ca2+ influx, and inappropriate activity may contribute to cortical cataract

Spin phase diagram of the nu_e=4/11 composite fermion liquid

Spin polarization of the "second generation" nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is determined for GaAs structures of different width and electron concentration. Transition between the polarized and partially unpolarized states with distinct composite fermion correlations is predicted for realistic parameters.Comment: 5 pages, 3 figure

Exact Gravity Dual of a Gapless Superconductor

A model of an exact gravity dual of a gapless superconductor is presented in which the condensate is provided by a charged scalar field coupled to a bulk black hole of hyperbolic horizon in asymptotically AdS spacetime. Below a critical temperature, the black hole acquires its hair through a phase transition while an electromagnetic perturbation of the background Maxwell field determines the conductivity of the boundary theory.Comment: 21 pages, 8 figures, a section on the stability of the MTZ black hole is added, references are added, version to be published in JHE

The average X-ray/gamma-ray spectrum of radio-quiet Seyfert 1s

We have obtained the average 1--500 keV spectrum of radio-quiet Seyfert 1s using data from EXOSAT, Ginga, HEAO, and GRO/OSSE. The spectral fit to the combined average EXOSAT and OSSE data is fully consistent with that for Ginga and OSSE, confirming results from an earlier Ginga/OSSE sample. The average spectrum is well-fitted by a power-law X-ray continuum with an energy spectral index of $\alpha \simeq 0.9$ moderately absorbed by an ionized medium and with a Compton reflection component. A high-energy cutoff (or a break) in the the power-law component at a few hundred keV or more is required by the data. We also show that the corresponding average spectrum from HEAO A1 and A4 is fully compatible with that obtained from EXOSAT, Ginga and OSSE. These results confirm that the apparent discrepancy between the results of Ginga (with $\alpha \simeq 0.9$) and the previous results of EXOSAT and HEAO (with $\alpha \simeq 0.7$) is indeed due to ionized absorption and Compton reflection first taken into account for Ginga but not for the previous missions. Also, our results confirm that the Seyfert-1 spectra are on average cut off in gamma-rays at energies of at least a few hundred keV, not at $\sim 40$ keV (as suggested earlier by OSSE data alone). The average spectrum is compatible with emission from either an optically-thin relativistic thermal plasma in a disk corona, or with a nonthermal plasma with a power-law injection of relativistic electrons.Comment: 7 pages, 3 Postscript figures, MNRAS accepte