Kalikow-type decomposition for multicolor infinite range particle systems

We consider a particle system on $\mathbb{Z}^d$ with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an algorithm to obtain an explicit construction of a coupling attaining Ornstein's $\bar{d}$-distance for two ordered Ising probability measures.Comment: Published in at http://dx.doi.org/10.1214/12-AAP882 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Convergence of statistical moments of particle density time series in scrape-off layer plasmas

Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a fixed shape, an exponential distribution of waiting times and amplitudes represents the radial motion of blob-like structures. With an analytic formulation of the process at hand, we derive expressions for the mean-squared error on estimators of sample mean and sample variance as a function of sample length, sampling frequency, and the parameters of the stochastic process. % Employing that the probability distribution function of a particularly relevant shot noise process is given by the gamma distribution, we derive estimators for sample skewness and kurtosis, and expressions for the mean-squared error on these estimators. Numerically generated synthetic time series are used to verify the proposed estimators, the sample length dependency of their mean-squared errors, and their performance. We find that estimators for sample skewness and kurtosis based on the gamma distribution are more precise and more accurate than common estimators based on the method of moments.Comment: 31 pages, 10 figure

Exact and approximate symmetries for light propagation equations with higher order nonlinearity

For the first time exact analytical solutions to the eikonal equations in (1+1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit analytical expression for the self-focusing position, where the intensity tends to infinity, is found. Based on an approximated Lie symmetry group, solutions to the eikonal equations with arbitrary nonlinear refractive index are constructed. Comparison between exact and approximate solutions is presented. Approximate solutions to the nonlinear Schrodinger equation in (1+2) dimensions with arbitrary refractive index and initial intensity distribution are obtained. A particular case of refractive index consisting of Kerr refraction and multiphoton ionization is considered. It is demonstrated that the beam collapse can take place not only at the beam axis but also in an off-axis ring region around it. An analytical condition distinguishing these two cases is obtained and explicit formula for the self-focusing position is presented.Comment: 25 pages, 5 figure

The spectroscopic orbits and the geometrical configuration of the symbiotic binary AR Pavonis

We analyze optical and near infrared spectra of intermediate and high resolution of the eclipsing symbiotic system AR Pavonis. We have obtained the radial velocity curves for the red and the hot component from the M-giant absorption lines and from the wings of Halpha, H and He II4686 emission profiles, respectively. From the orbital elements we have derived the masses, Mgiant=2.5 and Mhot =1.0 solar masses, for the red giant and the hot component, respectively. We also present and discuss radial velocity patterns in the blue cF absorption spectrum as well as various emission lines. In particular, we confirm that the blue absorption lines are associated with the hot component. The radial velocity curve of the blue absorption system, however, does not track the hot companion's orbital motion in a straightforward way, and its departures from an expected circular orbit are particularly strong when the hot component is active. We suggest that the cF-type absorption system is formed in material streaming from the giant presumably in a region where the stream encounters an accretion disk or an extended envelope around the hot component. The broad emission wings originate from the inner accretion disk or the envelope around the hot star.We also suggest that the central absorption in H profiles is formed in a neutral portion of the cool giant's wind which is strongly concentrated towards the orbital plane. The nebula in AR Pav seems to be bounded by significant amount of neutral material in the orbital plane. The forbidden emission lines are probably formed in low density ionized regions extended in polar directions and/or the wind-wind interaction zone.Comment: 12 pages, 5 figures, accepted by A&