Rational approximation and arithmetic progressions

A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a metrical and a non-metrical point of view and, on the other hand, from an asymptotic and also a uniform point of view. The principal novelty is a Khintchine type theorem for uniform approximation in this context. Some applications of this theory are also discussed

The Neutron Stars Census

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin--down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, $\gtrsim 200-300$ ${\rm km s^{-1}},$ corresponding to a velocity dispersion $\sigma_V\gtrsim 125-190$ km s$^{-1}$. The same conclusion is reached for both a constant magnetic field ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Such high velocities are consistent with those derived from radio pulsar observations. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to less than 1%.Comment: 13 pages, 6 PostScript figures, accepted to Ap

Null Energy Condition Violation and Classical Stability in the Bianchi I Metric

The stability of isotropic cosmological solutions in the Bianchi I model is considered. We prove that the stability of isotropic solutions in the Bianchi I metric for a positive Hubble parameter follows from their stability in the Friedmann-Robertson-Walker metric. This result is applied to models inspired by string field theory, which violate the null energy condition. Examples of stable isotropic solutions are presented. We also consider the k-essence model and analyse the stability of solutions of the form $\Phi(t)=t$.Comment: 27 pages, references added, accepted for publication in Phys. Rev.

Resonance-Enhanced Two-Photon Ionization (RETPI) of SiII and an Anomalous, Variable Intensity of the 1892A SiIII] Line in the Weigelt Blobs of Eta Carinae

The Si III] 1892A intercombination line shows an anomalously high intensity in spectra of the radiation-rich Weigelt blobs in the vicinity of Eta Carinae. The line disappears during the 100 days long spectral events occurring every 5.5 years. The aim is to investigate whether resonance-enhanced two-photon ionization (RETPI) is a plausible excitation mechanism for the Si III] 1892A line. The possible intensity enhancement of the 1892A line is investigated as regards quasi-resonant intermediate energy levels of Si II. The RETPI mechanism is effective on SiII in the radiation-rich Weigelt blobs where the two excitation steps are provided by the two intense hydrogen lines Ly alpha and Ly gammaComment: 4 pages, Accepted for publication in A&

Synthetic Mudscapes: Human Interventions in Deltaic Land Building

In order to defend infrastructure, economy, and settlement in Southeast Louisiana, we must construct new land to mitigate increasing risk. Links between urban environments and economic drivers have constrained the dynamic delta landscape for generations, now threatening to undermine the ecological fitness of the entire region. Static methods of measuring, controlling, and valuing land fail in an environment that is constantly in flux; change and indeterminacy are denied by traditional inhabitation. Multiple land building practices reintroduce deltaic fluctuation and strategic deposition of fertile material to form the foundations of a multi-layered defence strategy. Manufactured marshlands reduce exposure to storm surge further inland. Virtual monitoring and communication networks inform design decisions and land use becomes determined by its ecological health. Mudscapes at the threshold of land and water place new value on former wastelands. The social, economic, and ecological evolution of the region are defended by an expanded web of growing land

Time variations of the narrow FeII and HI spectral emission lines from the close vicinity of Eta Carinae during the spectral event of 2003

The spectrum of Eta Carinae and its ejecta shows slow variations over a period of 5.5 years. However, the spectrum changes drastically on a time scale of days once every period called the 'spectral event'. We report on variations in the narrow emission line spectrum of gas condensations (the Weigelt blobs) close to the central star during a spectral event. The rapid changes in the stellar radiation field illuminating the blobs make the blobs a natural astrophysical laboratory to study atomic photoprocesses. The different responses of the HI Paschen lines, fluorescent lines and forbidden [FeII] lines allow us to identify the processes and estimate physical conditions in the blobs. This paper is based on observations from the Pico dos Dias Observatory (LNA/Brazil) during the previous event in June 2003.Comment: Accepted for publication in A&

Transmission of correlated electrons through sharp domain walls in magnetic nanowires: a renormalization group approach

The transmission of correlated electrons through a domain wall in a ferromagnetic one dimensional system is studied theoretically in the limit of a domain wall width smaller or comparable to the electron Fermi wavelength. The domain wall gives rise to both potential and spin dependent scattering of the charge carriers. Using a poor man's renormalization group approach for the electron-electron interactions, we obtain the low temperature behavior of the reflection and transmission coefficients. The results show that the low-temperature conductance is governed by the electron correlations, which may suppress charge transport without suppressing spin current. The results may account for a huge magnetoresistance associated with a domain wall in ballistic nanocontacs.Comment: 13 pages, 6 figure

A stellar flare during the transit of the extrasolar planet OGLE-TR-10b

We report a stellar flare occurring during a transit of the exoplanet OGLE-TR-10b, an event not previously reported in the literature. This reduces the observed transit depth, particularly in the u'-band, but flaring could also be significant in other bands and could lead to incorrect planetary parameters. We suggest that OGLE-TR-10a is an active planet-hosting star and has an unusually high X-ray luminosity

Spin ordering quantum transitions of superconductors in a magnetic field

We argue that recent neutron scattering measurements by Lake et. al. (Science 291, 1759 (2001)) of the spin excitation spectrum of LSCO in a magnetic field can be understood in terms of proximity to a phase with co-existing superconductivity and spin density wave order. We present a general theory for such quantum transitions, and argue that their low energy spin fluctuations are controlled by a singular correction from the superflow kinetic energy, acting in the region outside the vortex cores. We propose numerous experimental tests of our theory.Comment: 4 pages, 3 eps fig