The Scattering Polarization of the Sr I 4607 \AA Line at the Diffraction Limit Resolution of a 1-m Telescope

One of the greatest challenges in solar and stellar physics in coming years will be to observe the Second Solar Spectrum with a spatial resolution significantly better than 1 arcsec. This type of scattering polarization observations would probably allow us to discover hitherto unknown aspects of the Sun's hidden magnetism. Here we report on some theoretical predictions for the photospheric line of Sr I at 4607 \AA, which we have obtained by solving the three-dimensional (3D) radiative transfer problem of scattering line polarization in a realistic hydrodynamical model of the solar photosphere. We have taken into account not only the anisotropy of the radiation field in the 3D medium and the Hanle effect of a tangled magnetic field, but also the symmetry breaking effects caused by the horizontal atmospheric inhomogeneities produced by the solar surface convection. Interestingly, the Q/I and U/I linear polarization signals of the emergent spectral line radiation have sizable values and fluctuations, even at the very center of the solar disk where we meet the forward scattering case. The ensuing small-scale patterns in Q/I and U/I turn out to be sensitive to the assumed magnetic field model, and are of great diagnostic value. We argue that it should be possible to observe them with the help of a 1-m telescope equipped with adaptive optics and a suitable polarimeter.Comment: Accepted for publication in The Astrophysical Journal Letters (12 pages and 2 color figures

Problems which are well-posed in a generalized sense with applications to the Einstein equations

In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory of systems which are well-posed in the generalized sense to establish the well-posedness of constraint preserving boundary conditions for this system when treated in second order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation.Comment: Final version to appear in Classical and Qunatum Gravit

FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation

AbstractVertebrate segmentation requires a molecular oscillator, the segmentation clock, acting in presomitic mesoderm (PSM) cells to set the pace at which segmental boundaries are laid down. However, the signals that position each boundary remain unclear. Here, we report that FGF8 which is expressed in the posterior PSM, generates a moving wavefront at which level both segment boundary position and axial identity become determined. Furthermore, by manipulating boundary position in the chick embryo, we show that Hox gene expression is maintained in the appropriately numbered somite rather than at an absolute axial position. These results implicate FGF8 in ensuring tight coordination of the segmentation process and spatiotemporal Hox gene activation

Markov Models of Statistical Multiplexing of Telephone Dialogue with Packet Switching

Existing methods of analysis of voice transmission by packet switching were designed mainly with respect to a Poisson stream of input packets, for which the probability of an active packet on each input port of the router is a constant value in time. This assumption is not always valid, since the formation of speech packets during a dialogue is a nonstationary process, in which case mathematical modeling becomes an effective method of analysis, through which necessary estimates of a network node being designed for packet transmission of speech may be obtained. This paper presents the result of analysis of mathematical models of Markov chain based speech packet sources vis-à-vis the peculiarities of telephone dialogue models. The derived models can be employed in the design and development of methods of statistical multiplexing of packet switching network nodes

Markov Models of Telephone Speech Dialogues

Analogue speech signals are the most natural form of communication among humans. The contemporary methods adopted for the analysis of voice transmission by packet switching were designed mainly with respect to a Poisson stream of input packets, for which the probability of an active packet on each input port of the router is a constant value in time. An assumption that is not always valid, since the formation of speech packets during a dialogue is a non-stationary process, in which case mathematical modeling becomes an effective method of analysis, through which necessary estimates of a network node being designed for packet transmission of speech may be obtained. This paper presents the result of analysis of mathematical models of Markov chain based speech packet sources vis-à-vis the peculiarities of telephone dialogue models. The derived models can be employed in the design and development of methods of statistical multiplexing of packet switching network nodes

Dependence of boundary lubrication on the misfit angle between the sliding surfaces

Using molecular dynamics based on Langevin equations with a coordinate- and velocity-dependent damping coefficient, we study the frictional properties of a thin layer of "soft" lubricant (where the interaction within the lubricant is weaker than the lubricant-substrate interaction) confined between two solids. At low driving velocities the system demonstrates stick-slip motion. The lubricant may or may not be melted during sliding, thus exhibiting either the "liquid sliding" (LS) or the "layer over layer sliding" (LoLS) regimes. The LoLS regime mainly operates at low sliding velocities. We investigate the dependence of friction properties on the misfit angle between the sliding surfaces and calculate the distribution of static frictional thresholds for a contact of polycrystalline surfaces.Comment: 8 pages, 11 figure

Gas-liquid critical parameters of asymmetric models of ionic fluids

The effects of size and charge asymmetry on the gas-liquid critical parameters of a primitive model (PM) of ionic fluids are studied within the framework of the statistical field theory based on the collective variables method. Recently, this approach has enabled us to obtain the correct trends of the both critical parameters of the equisize charge-asymmetric PM without assuming ionic association. In this paper we focus on the general case of an asymmetric PM characterized by the two parameters: hard-sphere diameter-, $\lambda=\sigma_{+}/\sigma_{-}$ and charge, $z=q_{+}/|q_{-}|$, ratios of the two ionic species. We derive an explicit expression for the chemical potential conjugate to the order parameter which includes the effects of correlations up to the third order. Based on this expression we consider the three versions of PM: a monovalent size-asymmetric PM ($\lambda\neq 1$, $z=1$), an equisize charge-asymmetric PM ($\lambda=1$, $z\neq 1$) and a size- and charge-asymmetric PM ($\lambda\neq 1$, $z=2$). Similar to simulations, our theory predicts that the critical temperature and the critical density decrease with the increase of size asymmetry. Regarding the effects of charge asymmetry, we obtain the correct trend of the critical temperature with $z$, while the trend of the critical density obtained in this approximation is inconsistent with simulations, as well as with our previous results found in the higher-order approximation. We expect that the consideration of the higher-order correlations will lead to the correct trend of the critical density with charge asymmetry.Comment: 23 pages, 6 figure