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

State-Space Interpretation of Model Predictive Control

A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through general first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC)

Hall response of interacting bosonic atoms in strong gauge fields: from condensed to FQH states

Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional-quantum-Hall-type states [M. Popp, B. Paredes, and J. I. Cirac, Phys. Rev. A 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [ L. J. LeBlanc, K. Jimenez-Garcia, R. A. Williams, M. C. Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Proc. Natl. Acad. Sci. USA 109, 10811 (2012)] and we analyze the role played by vortex states in the Hall response.Comment: 10 pages, 7 figure

HD 85567: A Herbig B[e] star or an interacting B[e] binary

Context. HD 85567 is an enigmatic object exhibiting the B[e] phenomenon, i.e. an infrared excess and forbidden emission lines in the optical. The object's evolutionary status is uncertain and there are conflicting claims that it is either a young stellar object or an evolved, interacting binary. Aims. To elucidate the reason for the B[e] behaviour of HD 85567, we have observed it with the VLTI and AMBER. Methods. Our observations were conducted in the K-band with moderate spectral resolution (R~1500, i.e. 200 km/s). The spectrum of HD 85567 exhibits Br gamma and CO overtone bandhead emission. The interferometric data obtained consist of spectrally dispersed visibilities, closure phases and differential phases across these spectral features and the K-band continuum. Results. The closure phase observations do not reveal evidence of asymmetry. The apparent size of HD 85567 in the K-band was determined by fitting the visibilities with a ring model. The best fitting radius, 0.8 +/- 0.3 AU, is relatively small making HD 85567 undersized in comparison to the size-luminosity relationship based on YSOs of low and intermediate luminosity. This has previously been found to be the case for luminous YSOs, and it has been proposed that this is due to the presence of an optically thick gaseous disc. We demonstrate that the differential phase observations over the CO bandhead emission are indeed consistent with the presence of a compact (~1 AU) gaseous disc interior to the dust sublimation radius. Conclusions. The observations reveal no sign of binarity. However, the data do indicate the presence of a gaseous disc interior to the dust sublimation radius. We conclude that the data are consistent with the hypothesis that HD 85567 is a YSO with an optically thick gaseous disc within a larger dust disc that is being photo-evaporated from the outer edge.Comment: Accepted for publication in A &