New global stability estimates for the Gel'fand-Calderon inverse problem

We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172]

General Statistical properties of the CMB Polarization field

The distribution of the polarization of the Cosmic Microwave Background (CMB) in the sky is determined by the hypothesis of random Gaussian distribution of the primordial density perturbations. This hypotheses is well motivated by the inflationary cosmology. Therefore, the test of consistency of the statistical properties of the CMB polarization field with the Gaussianity of primordial density fluctuations is a realistic way to study the nature of primordial inhomogeneities in the Universe. This paper contains the theoretical predictions of the general statistical properties of the CMB polarization field. All results obtained under assumption of the Gaussian nature of the signal. We pay the special attention to the following two problems. First, the classification and statistics of the singular points of the polarization field where polarization is equal to zero. Second, the topology of contours of the value of the degree of polarization. We have investigated the percolation properties for the zones of ``strong'' and ``weak'' polarization. We also have calculated Minkowski functionals for the CMB polarization field. All results are analytical.Comment: Latex, 22 pages, including 5 figure

Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton

The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a chi^2 that is large at the 95% level for all scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 sigma. On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap

Power filtration of CMB observational data

We propose a power filter Gp for linear reconstruction of the CMB signal from observational maps. This Gp filter preserves the power spectrum of the CMB signal in contrast to the Wiener filter which diminishes the power spectrum of the reconstructed CMB signal. We demonstrate how peak statistics and a cluster analysis can be used to estimate the probability of the presence of a CMB signal in observational records. The efficiency of the Gp filter is demonstrated on a toy model of an observational record consisting of a CMB signal and noise in the form of foreground point sources.Comment: 17 pages; 4 figures; submitted to International Journal of Modern Physic

Time machines: the Principle of Self-Consistency as a consequence of the Principle of Minimal Action

We consider the action principle to derive the classical, non-relativistic motion of a self-interacting particle in a 4-D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves. For the case of a `hard-sphere' self-interaction potential we show that the only possible trajectories (for a particle with fixed initial and final positions and which traverses the wormhole once) minimizing the classical action are those which are globally self-consistent, and that the `Principle of self-consistency' (originally introduced by Novikov) is thus a natural consequence of the `Principle of minimal action.'Comment: 26 pages, plain latex; modified version includes extra constraint for collinear collision case and other minor misprints correction

Squeezars: Tidally powered stars orbiting a massive black hole

We propose that there exists a class of transient sources, "squeezars", which are stars caught in highly eccentric orbits around a massive (m<10^8 Mo) black hole (MBH), whose atypically high luminosity (up to a significant fraction of their Eddington luminosity) is powered by tidal interactions with the MBH. Their existence follows from the presence of a mass sink, the MBH, in the galactic center, which drives a flow of stars into nearly radial orbits to replace those it has destroyed. We consider two limits for the stellar response to tidal heating: surface heating with radiative cooling ("hot squeezars") and bulk heating with adiabatic expansion ("cold squeezars"), and calculate the evolution of the squeezar orbit, size, luminosity and effective temperature. The squeezar formation rate is only ~0.05 that of tidal disruption flares, but squeezar lifetimes are many orders of magnitude longer, and so future observations of squeezars in nearby galaxies can probe the tidal process that feeds MBHs and the effects of extreme tides on stars. The mean number of squeezars orbiting the Galactic MBH is estimated at 0.1-1.Comment: ApJ Lett. accepted. 4 pp. 1 fi

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

CMB anisotropies due to cosmological magnetosonic waves

We study scalar mode perturbations (magnetosonic waves) induced by a helical stochastic cosmological magnetic field and derive analytically the corresponding cosmic microwave background (CMB) temperature and polarization anisotropy angular power spectra. We show that the presence of a stochastic magnetic field, or an homogeneous magnetic field, influences the acoustic oscillation pattern of the CMB anisotropy power spectrum, effectively acting as a reduction of the baryon fraction. We find that the scalar magnetic energy density perturbation contribution to the CMB temperature anisotropy is small compared to the contribution to the CMB $E$-polarization anisotropy.Comment: 17 pages, references added, version accepted for publication in Phys. Rev.