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Asymptotic behaviour of time averages for non-ergodic Gaussian processes
In this work, we study the behaviour of time-averages for stationary (non-ageing), but ergodicity-breaking Gaussian processes using their representation in Fourier space. We provide explicit formulae for various time-averaged quantities, such as mean square displacement, density, and analyse the behaviour of time-averaged characteristic function, which gives insight into rich memory structure of the studied processes. Moreover, we show applications of the ergodic criteria in Fourier space, determining the ergodicity of the generalised Langevin equation’s solutions. - Highlights: Ergodic criteria for Gaussian models which use Fourier transform are provided. Smooth, field Hamiltonian models are ergodic, discrete models are non-ergodic. Fractal Fourier structure can induce recurring correlations and non-mixing. Non-ergodic models exhibit non-linear dynamics and complex constants of motion. This non-linearity can be studied using time-averaged characteristic function.
Turbulence-induced bias in time-averaged laser absorption tomography of correlated concentration and temperature fields with a first-order correction
The influence of correlated scalar fluctuations on time-averaged laser absorption tomography measurements of temperature and species in a piloted turbulent premixed flame was examined using a coupled spectroscopic and fluid-dynamic analysis. To understand bias associated with turbulence, spatio-temporally resolved temperature and species mole fraction profiles predicted by large eddy simulations (LES) were used to synthetically generate time-resolved line-of-sight absorption measurements at short time scales (microsecond) to reflect the unsteady nature of a canonical jet burner across various transverse measurement planes. Inversion methods were employed on the time-averaged line-of-sight data to produce radially-resolved temperature and mole fraction profiles, analogous to those produced by laser absorption tomography performed on a time-averaged axisymmetric flowfield. It is shown that bias in the measurements compared to true time-averaged scalar fields is a function primarily of temperature dependence in absorptivity and non-zero correlation between temperature and species concentration scalars. Finally, a first-order correction to tomography measurements is proposed to account for the bias based on estimated correlations and the known spectroscopic parameters of the probed absorption transitions.
Langmuir probe measurements in a time-fluctuating-highly ionized non-equilibrium cutting arc: Analysis of the electron retarding part of the time-averaged current-voltage characteristic of the probe
This work describes the application of Langmuir probe diagnostics to the measurement of the electron temperature in a time-fluctuating-highly ionized, non-equilibrium cutting arc. The electron retarding part of the time-averaged current-voltage characteristic of the probe was analysed, assuming that the standard exponential expression describing the electron current to the probe in collision-free plasmas can be applied under the investigated conditions. A procedure is described which allows the determination of the errors introduced in time-averaged probe data due to small-amplitude plasma fluctuations. It was found that the experimental points can be gathered into two well defined groups allowing defining two quite different averaged electron temperature values. In the low-current region the averaged characteristic was not significantly disturbed by the fluctuations and can reliably be used to obtain the actual value of the averaged electron temperature. In particular, an averaged electron temperature of 0.98 ± 0.07 eV (= 11400 ± 800 K) was found for the central core of the arc (30 A) at 3.5 mm downstream from the nozzle exit. This average included not only a time-average over the time fluctuations but also a spatial-average along the probe collecting length. The fitting of the high-current region of the characteristic using such electron temperature value together with the corrections given by the fluctuation analysis showed a relevant departure of local thermal equilibrium in the arc core.
Thermal motion in proteins: Large effects on the time-averaged interaction energies
As a consequence of thermal motion, inter-atomic distances in proteins fluctuate strongly around their average values, and hence, also interaction energies (i.e. the pair-potentials evaluated at the fluctuating distances) are not constant in time but exhibit pronounced fluctuations. These fluctuations cause that time-averaged interaction energies do generally not coincide with the energy values obtained by evaluating the pair-potentials at the average distances. More precisely, time-averaged interaction energies behave typically smoother in terms of the average distance than the corresponding pair-potentials. This averaging effect is referred to as the thermal smoothing effect. Here, we estimate the strength of the thermal smoothing effect on the Lennard-Jones pair-potential for globular proteins at ambient conditions using x-ray diffraction and simulation data of a representative set of proteins. For specific atom species, we find a significant smoothing effect where the time-averaged interaction energy of a single atom pair can differ by various tens of cal/mol from the Lennard-Jones potential at the average distance. Importantly, we observe a dependency of the effect on the local environment of the involved atoms. The effect is typically weaker for bulky backbone atoms in beta sheets than for side-chain atoms belonging to other secondary structure on the surface of the protein. The results of this work have important practical implications for protein software relying on free energy expressions. We show that the accuracy of free energy expressions can largely be increased by introducing environment specific Lennard-Jones parameters accounting for the fact that the typical thermal motion of protein atoms depends strongly on their local environment.
A Discrete-Time Average Model Based Predictive Control for Quasi-Z-Source Inverter
A discrete-time average model-based predictive control (DTA-MPC) is proposed for a quasi-Z-source inverter (qZSI). As a single-stage inverter topology, the qZSI regulates the dc-link voltage and the ac output voltage through the shoot-through (ST) duty cycle and the modulation index. Several feedback strategies have been dedicated to produce these two control variables, among which the most popular are the proportional–integral (PI)-based control and the conventional model-predictive control (MPC). However, in the former, there are tradeoffs between fast response and stability; the latter is robust, but at the cost of high calculation burden and variable switching frequency. Moreover, they require an elaborated design or fine tuning of controller parameters. The proposed DTA-MPC predicts future behaviors of the ST duty cycle and modulation signals, based on the established discrete-time average model of the quasi-Z-source (qZS) inductor current, the qZS capacitor voltage, and load currents. The prediction actions are applied to the qZSI modulator in the next sampling instant, without the need of other controller parameters’ design. A constant switching frequency and significantly reduced computations are achieved with high performance. Transient responses and steady-state accuracy of the qZSI system under the proposed DTA-MPC are investigated and compared with the PI-based control and the conventional MPC. Simulation and experimental results verify the effectiveness of the proposed approach for the qZSI.
Quantifying the uncertainty introduced by discretization and time-averaging in two-fluid model predictions
The two-fluid model (TFM) has become a tool for the design and troubleshooting of industrial fluidized bed reactors. To use TFM for scale up with confidence, the uncertainty in its predictions must be quantified. Here, we study two sources of uncertainty: discretization and time-averaging. First, we show that successive grid refinement may not yield grid-independent transient quantities, including cross-section–averaged quantities. Successive grid refinement would yield grid-independent time-averaged quantities on sufficiently fine grids. A Richardson extrapolation can then be used to estimate the discretization error, and the grid convergence index gives an estimate of the uncertainty. Richardson extrapolation may not work for industrial-scale simulations that use coarse grids. We present an alternative method for coarse grids and assess its ability to estimate the discretization error. Second, we assess two methods (autocorrelation and binning) and find that the autocorrelation method is more reliable for estimating the uncertainty introduced by time-averaging TFM data.
TIME-AVERAGE-BASED METHODS FOR MULTI-ANGULAR SCALE ANALYSIS OF COSMIC-RAY DATA
Over the past decade, a number of experiments dealt with the problem of measuring the arrival direction distribution of cosmic rays, looking for information on the propagation mechanisms and the identification of their sources. Any deviation from the isotropy may be regarded to as a signature of unforeseen or unknown phenomena, mostly if well localized in the sky and occurring at low rigidity. It induced experimenters to search for excesses down to angular scales as narrow as 10 Degree-Sign , disclosing the issue of properly filtering contributions from wider structures. A solution commonly envisaged was based on time-average methods to determine the reference value of cosmic-ray flux. Such techniques are nearly insensitive to signals wider than the time window in use, thus allowing us to focus the analysis on medium- and small-scale signals. Nonetheless, the signal often cannot be excluded in the calculation of the reference value, which induces systematic errors. The use of time-average methods recently revealed important discoveries about the medium-scale cosmic-ray anisotropy, present both in the northern and southern hemispheres. It is known that the excess (or deficit) is observed as less intense than in reality and that fake deficit zones are rendered around true excesses because of the absolute lack of knowledge a priori of which signal is true and which is not. This work is an attempt to critically review the use of time-average-based methods for observing extended features in the cosmic-ray arrival distribution pattern.
Passive magnetic bearing systems stabilizer/bearing utilizing time-averaging of a periodic magnetic field
A high-stiffness stabilizer/bearings for passive magnetic bearing systems is provide where the key to its operation resides in the fact that when the frequency of variation of the repelling forces of the periodic magnet array is large compared to the reciprocal of the growth time of the unstable motion, the rotating system will feel only the time-averaged value of the force. When the time-averaged value of the force is radially repelling by the choice of the geometry of the periodic magnet array, the Earnshaw-related unstable hit motion that would occur at zero rotational speed is suppressed when the system is rotating at operating speeds.
Accuracy of the time-averaged ponderomotive approximation for laser-plasma accelerator modeling
Reliable modeling of laser-plasma accelerators, where a short and intense laser pulse propagates in an underdense plasma over long distances, is a computationally challenging task. This is due to the great disparity among the scales involved in the modeling, ranging from the micrometer scale of the laser wavelength to, for instance, the meter scale of the laser-plasma interaction length for a multi-GeV-class laser-plasma accelerator. To reduce such imbalance, the time-averaged ponderomotive approximation may be used, where the plasma particle dynamics is analytically averaged over the laser frequency, and only spatiotemporal scales associated with the laser envelope are retained in the calculations, resulting in significant computational savings. Here, we characterize the accuracy and robustness of the time-averaged ponderomotive approximation for a range of laser parameters of interest for present and future laser-plasma accelerators, and we show that the error introduced by the averaging process is small in all relevant cases.
Computing the Time-Averaged Nuclide Inventory Using the Chebyshev Rational Approximation Method
Here, the Chebyshev Rational Approximation Method (CRAM) algorithm has become the method of choice for modern nuclear depletion calculations. A simple modification of the CRAM yields not only depleted nuclide amounts but also time-averaged nuclide amounts, with little additional calculation cost.
Modeling laser-wakefield accelerators using the time-averaged ponderomotive approximation in a Lorentz boosted frame
Future, high-fidelity simulations of multi-GeV-class laser Wakefield accelerators (LWFAs) will need to model the propagation of high-intensity laser drivers over meter-scale plasmas with high spatial and temporal resolutions, thus requiring high amounts of computational resources. Various techniques have been devised over the years to reduce the computational cost of such simulations, including the time-averaged ponderomotive approximation, and the use of the Lorentz boosted frame technique. In this paper we discuss the combination of these two computational techniques, highlighting the resulting significant reduction in the computational cost of LWFA simulations and the limitations of this approach. The combination of the two techniques can potentially become essential for the modeling of a multi-TeV, LWFA-based collider.
Clear-Sky Detection Using Time-Averaged, Tilted-Plane Data
A method is presented to detect clear-sky periods for plane-of-array, time-averaged irradiance data that is based on the algorithm originally described by Reno and Hansen. We show this new method improves the state-of-the-art by providing accurate detection at longer data intervals, and by detecting clear periods in plane-of-array data, which is novel. We illustrate how accurate determination of clear-sky conditions helps to eliminate data noise and bias in the assessment of long-term performance of PV plants.
Time-Averaged "Slow" Carbon Dioxide Flux Data from wind and gas files, with additional diagnostic data: 22m samples (a1-level)
Time-Averaged "Slow" Carbon Dioxide Flux Data from wind and gas files, with additional diagnostic data: 22m samples
Time-Averaged "Slow" Carbon Dioxide Flux Data from wind and gas files, with additional diagnostic data: 40m samples (a1-level)
Time-Averaged "Slow" Carbon Dioxide Flux Data from wind and gas files, with additional diagnostic data: 40m samples
Time-Averaged "Slow" Carbon Dioxide Flux Data from wind and gas files, with additional diagnostic data: 45m samples (a1-level)
Time-Averaged "Slow" Carbon Dioxide Flux Data from wind and gas files, with additional diagnostic data: 45m samples
Quantitative time-averaged gas and liquid distributions using x-ray fluorescence and radiography in atomizing sprays
A method for quantitative measurements of gas and liquid distributions is demonstrated using simultaneous x-ray fluorescence and radiography of both phases in an atomizing coaxial spray. Synchrotron radiation at 10.1 keV from the Advanced Photon Source at Argonne National Laboratory is used for x-ray fluorescence of argon gas and two tracer elements seeded into the liquid stream. Simultaneous time-resolved x-ray radiography combined with time-averaged dual-tracer fluorescence measurements enabled corrections for reabsorption of x-ray fluorescence photons for accurate, line-of-sight averaged measurements of the distribution of the gas and liquid phases originating from the atomizing nozzle.
Time-averaged Spray Analysis in the Near-field Using Broadband and Narrowband X-ray Measurements
The characterization of a spray in the near-field region is challenging because of its high optical density in this region. X-ray based techniques, with weak scatter and strong penetration properties, can provide better characterization than optical assessment techniques in this region. Here, the effects of various operating parameters on the optical depth (defined as the accumulated liquid thickness in the beam path times the X-ray attenuation coefficient) and spray profile of an atomizing spray in the near-field region are evaluated based on time-averaged X-ray analysis techniques. Controlling parameters in the spray structure include swirl ratio, liquid phase Reynolds number, and gas phase Reynolds number. Data from the broadband X-ray radiographs obtained using a tube source at Iowa State University and from focused beam measurements at the Advanced Photon Source at Argonne National Laboratory are compared. The X-ray tube source at Iowa State University was operated at two different energy levels, which reveals that the X-ray tube source energy influenced the magnitude of the optical depth but did not change the shape of the distribution. For the no swirl condition, gas flow rate and liquid flow rate had opposite effects on the spray profile, where the spray widens as the gas flow rate increases and narrows as the liquid flow rate increases. As the swirl ratio increases from 0 to 1, the spray widens and then narrows. Furthermore, the critical swirl ratio at which the spray reaches its widest spread differs at different flow conditions.