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Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: a comparison study with detrended fluctuation analysis and wavelet leaders

In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter {\mu} = 0.15. We find that the SF underestimates scaling exponent when q > 3. The Hilbert method provides a slight underestimation when q > 5. However, both DFA and WL overestimate the scaling exponents when q > 5. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Relambda \simeq 250. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents {\xi}{\theta}(q) quite close to the one for longitudinal velocity.Comment: 13 pages, 10 figure

Turbulent transport of material particles: An experimental study of finite size effects

We use an acoustic Lagrangian tracking technique, particularly adapted to measurements in open flows, and a versatile material particles generator (in the form of soap bubbles with adjustable size and density) to characterize Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow of air. We vary the size of the particles in a range corresponding to turbulent inertial scales and explore how the turbulent forcing experienced by the particles depends on their size. We show that, while the global shape of the intermittent acceleration probability density function does not depend significantly on particle size, the acceleration variance of the particles decreases as they become larger in agreement with the classical scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow

A dissipative random velocity field for fully developed fluid turbulence

We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter $\gamma$ that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions), including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter $\gamma$ and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion in power of $\gamma$ shows that energy transfers, at leading order, indeed take place, justifying the dissipative nature of this random field.Comment: 38 pages, 5 figure

Development of a Low-Lift Chiller Controller and Simplified Precooling Control Algorithm - Final Report

KGS Buildings LLC (KGS) and Pacific Northwest National Laboratory (PNNL) have developed a simplified control algorithm and prototype low-lift chiller controller suitable for model-predictive control in a demonstration project of low-lift cooling. Low-lift cooling is a highly efficient cooling strategy conceived to enable low or net-zero energy buildings. A low-lift cooling system consists of a high efficiency low-lift chiller, radiant cooling, thermal storage, and model-predictive control to pre-cool thermal storage overnight on an optimal cooling rate trajectory. We call the properly integrated and controlled combination of these elements a low-lift cooling system (LLCS). This document is the final report for that project

Spatially-Resolved Spectra of the "Teacup" AGN: Tracing the History of a Dying Quasar

The Sloan Digital Sky Survey (SDSS) Galaxy Zoo project has revealed a number of spectacular galaxies possessing Extended Emission-Line Regions (EELRs), the most famous being Hanny's Voorwerp galaxy. We present another EELR object discovered in the SDSS endeavor: the Teacup Active Galactic Nucleus (AGN), nicknamed for its EELR, which has a handle like structure protruding 15 kpc into the northeast quadrant of the galaxy. We analyze physical conditions of this galaxy with long-slit ground based spectroscopy from Lowell, Lick, and KPNO observatories. With the Lowell 1.8m Perkin's telescope we took multiple observations at different offset positions, allowing us to recover spatially resolved spectra across the galaxy. Line diagnostics indicate the ionized gas is photoionized primarily by the AGN. Additionally we are able to derive the hydrogen density from the [S II] 6716/6731 ratio. We generated two-component photoionization models for each spatially resolved Lowell spectrum. These models allow us to calculate the AGN bolometric luminosity seen by the gas at different radii from the nuclear center of the Teacup. Our results show a drop in bolometric luminosity by more than two orders of magnitude from the EELR to the nucleus, suggesting that the AGN has decreased in luminosity by this amount in a continuous fashion over 46,000 years, supporting the case for a dying AGN in this galaxy independent of any IR based evidence. We demonstrate that spatially resolved photoionization modeling could be applied to EELRs to investigate long time scale variability.Comment: 38 pages, 11 figures, accepted for publication in the Astrophysical Journa