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DOE OSTI2024

Wavelength modulation laser-induced fluorescence for plasma characterization

Laser-Induced Fluorescence (LIF) spectroscopy is an essential tool for probing ion and atom velocity distribution functions (VDFs) in complex plasmas. VDFs carry information about the kinetic properties of species that is critical for plasma characterization. Accurate interpretation of these functions is challenging due to factors such as multicomponent distributions, broadening effects, and background emissions. Our research investigates the use of Wavelength Modulation (WM) LIF to enhance the sensitivity of VDF measurements. Unlike standard Amplitude Modulation (AM) methods, WM–LIF measures the derivative of the LIF signal. This approach makes variations in VDF shape more pronounced. VDF measurements with WM–LIF were investigated with both numerical modeling and experimental measurements. The developed model enables the generation of both WM and AM signals, facilitating comparative analysis of fitting outcomes. Experiments were conducted in a weakly collisional argon plasma with magnetized electrons and non-magnetized ions. Measurements of the argon ion VDFs employed a narrow-band tunable diode laser, which scanned the 4p 4 D 7/2 –3d 4 F 9/2 transition centered at 664.553 nm in vacuum. A lock-in amplifier detected the second harmonic WM signal, which was generated by modulating the laser wavelength with an externally controlled piezo-driven mirror of the diode laser. Finally, our findings indicate that the WM–LIF signal is more sensitive to fitting parameters, allowing for better identification of VDF parameters such as the number of distribution components, their temperatures, and velocities. In addition, WM–LIF can serve as an independent method to verify AM measurements and is particularly beneficial in environments with substantial light noise or background emissions, such as those involving thermionic cathodes and reflective surfaces.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Design Optimization for Weighted Conduction Loss Minimization in a Dual-Active-Bridge-Based PV Microinverter

This manuscript presents a harmonic-superposition based frequency-domain approach for analysis and optimal design of a single-stage DAB-based DC-AC converter used in low-voltage DC to high voltage AC applications, such as PV microinverter. Specifically, two topological variations and correspondingly different modulation strategies involving up to four control variables (three phase shifts and switching frequency) are analyzed. Optimal trajectories of control variables are determined that result in minimized transformer RMS current at a given average power, while enforcing near-uniform ZVS. To make the design process holistic, an outer optimization loop is used to determine optimal values for the power transfer inductance (integrated as the transformer’s leakage inductance) and turns ratio, which minimize the weighted-average conduction loss contribution to the microinverter’s CEC efficiency. Based on the optimization analyses, a 400 W microinverter prototype is built and experimental results at one operating point are presented, achieving a measured efficiency of 92.8%.

14 SOLAR ENERGY↗

DOE OSTI2021

Analysis of Loss-of-Offsite-Power Events: Update

Loss-of-offsite power (LOOP) can have a negative impact on a nuclear power plant’s ability to achieve and maintain safe shutdown conditions. LOOP event frequencies and times required for subsequent restoration of offsite power are important inputs to plant probabilistic risk assessments. This report presents a statistical and engineering analysis of LOOP frequencies and durations at U.S. commercial nuclear power plants. The data used in this study were based on the operating experience during calendar years 1987–2020, while the most recent 15-year data (i.e., from 2006–2020) were used for most analyses in this report. LOOP events during critical operation that did not result in a reactor trip are not included. Frequencies and durations were determined for four LOOP event categories: plant-centered, switchyard-centered, grid-related, and weather related. Highly significant decreasing trends in the LOOP occurrence rates were identified for All-LOOPs during critical operation (p-value = 0.001) and switchyard-centered LOOPs during critical operation (p-value = 0.002) for the most recent 10-year period (2011–2020). Adverse trends in LOOP durations continue for switchyard-centered LOOPs (p-value = 0.005), All-LOOPs (p-value = 0.019), as well as All-LOOPs during shutdown operation (p-value = 0.003). Statistical tests show the LOOP counts are not uniformly distributed across the 12 months, and variation among the months exists for plant-centered LOOPs (p-value = 0.028), grid-related LOOPs (p-value = 0.021), All-LOOPs (p-value = 0.003), and All-LOOPs during critical operation (p-value = 0.008). The engineering analysis of LOOP data showed for the period of 2006–2020, the equipment failure events were dominated by failures of circuits and relay; human errors have been less frequent and occurred primarily in maintenance; and weather events were dominated by tornadoes and lightning.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Scale effects on core design, fuel costs, and spent fuel volume of pressurized water reactors

The desire to improve the economic competitiveness and deployment pace of nuclear energy through modularization, manufacturing, and series production had led to the development of smaller size reactors. As the standard 17x17 fuel technology is mainly maintained in the pressurized water reactors (PWRs) category, this translates into a lower number of fuel assemblies in the core and sometimes a reduced fuel height. To assess the impact of such scale change in core design on fuel cycle cost and spent fuel volume, a scoping analysis tool is developed based on infinite lattice calculations, leakage, fuel management reduced models, and levelized unit cost of electricity (LCOE) estimate. As such, cost dynamics driven by fuel specific power, burnup, core leakage, feed, cycle length, fuel assembly height as well as uranium market data are captured with consistent set of assumptions and analysis methods. A selection of 5 reactor designs representative of leading PWR developers is assessed and compared. Pursuing higher specific powers and optimal burnups are highlighted as the main fuel cost reduction drivers, nevertheless, practical limitations and opportunities must be evaluated to establish the feasibility of such enhanced fuel operation. In consequence, a detailed core design is performed using SIMULATE3 code for 5 PWR variations including natural and forced coolant circulation modes, two reactor scales, power densities of 73, 112, and 123 kW/l and higher discharge burnups. Design and optimization are performed at the lattice level, for the reflector, and at the core loading level. Satisfactory steady-state operation including power distribution, coolant operating limits, and reactivity requirements are analyzed and reported in this paper. The fuel economics of the detailed core designs confirm the scoping analysis findings. Despite the unlocked power uprates in small PWRs, the achievable burnup for a given fuel specific power requires more enrichment and shorter fuel height results in higher fabrication costs per mass of fuel, which makes scaling down core size a more expensive endeavor on the fuel cycle front. Spent fuel volumes are reported for the PWRs designed in this paper. Furthermore, these volumes are driven by the core average discharge burnup regardless of the scale in consideration. Additional cost and core performance aspects related to heavy reflector gains, fuel-reflector substitution, and disposal cost policy in the U.S. are examined.

42 ENGINEERING↗

DOE OSTI2020

Comparison of equilibrium climate sensitivity estimates from slab ocean, 150-year, and longer simulations

We compare equilibrium climate sensitivity (ECS) estimates from pairs of long (= 800-year) control and abruptly quadrupled CO2 simulations with shorter (150, 300 year) coupled atmosphere-ocean simulations and Slab Ocean Models (SOM). Consistent with previous work, ECS estimates from shorter coupled simulations based on annual averages for years 1-150 underestimate those from SOM (-8% ± 13%) and long (-14% ± 8%) simulations. Analysis of only years 21-150 improved agreement with SOM (-2% ± 14%) and long (-8% ± 10%) estimates. Use of pentadal averages for years 51-150 results in improved agreement with long simulations (-4% ± 11%). While ECS estimates from current generation US models based on SOM and coupled annual averages of years 1-150 range from 2.6°C to 5.3°C, estimates based longer simulations of the same models range from 3.2°C to 7.0°C. Such variations between methods argues for caution in comparison and interpretation of ECS estimates across models.

Dunne, John P.↗

DOE OSTI2021

Absolute contrast estimation for soft X-ray photon fluctuation spectroscopy using a variational droplet model

Abstract X-ray photon fluctuation spectroscopy using a two-pulse mode at the Linac Coherent Light Source has great potential for the study of quantum fluctuations in materials as it allows for exploration of low-energy physics. However, the complexity of the data analysis and interpretation still prevent recovering real-time results during an experiment, and can even complicate post-analysis processes. This is particularly true for high-spatial resolution applications using CCDs with small pixels, which can decrease the photon mapping accuracy resulting from the large electron cloud generation at the detector. Droplet algorithms endeavor to restore accurate photon maps, but the results can be altered by their hyper-parameters. We present numerical modeling tools through extensive simulations that mimic previous x-ray photon fluctuation spectroscopy experiments. By modification of a fast droplet algorithm, our results demonstrate how to optimize the precise parameters that lift the intrinsic counting degeneracy impeding accuracy in extracting the speckle contrast. These results allow for an absolute determination of the summed contrast from multi-pulse x-ray speckle diffraction, the modus operandi by which the correlation time for spontaneous fluctuations can be measured.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Cuticular wax profiling of Populus trichocarpa and P. balsamifera reveals surface similarities with underlying differences

Cuticular waxes are a mixture of hydrophobic components protecting plant tissues from the environment. Populus trichocarpa and P. balsamifera are closely-related tree species with broad North American distribution; however, variation in their cuticular wax composition across their range remained poorly understood. To address this gap, stem and leaf waxes from both species across three developmental stages were profiled by gas chromatography-mass spectrometry. A core set of compounds shared across tissues, accessions, and developmental stages was detected, as well as tissue- or species-specific constituents such as phenolics and alkenes. Phenolic-derived compounds were more prevalent at early stages of development compared to the predominantly aliphatic composition of mature tissues. Moreover, early stage leaves also showed enhanced protection from desiccation and oxidative stress in a subset of accessions. Alkenes, found exclusively in leaves, segregated the poplar accessions into alkene-producing and alkene-lacking phenotypes. GWAS analysis of 174 P. trichocarpa accessions identified a region on chromosome 10 containing a tandem cluster of ketoacyl CoA synthases associated with alkene accumulation in P. trichocarpa , which was not significantly associated in 133 P. balsamifera individuals examined. These findings reveal dynamic, developmentally regulated, and species-specific variation in poplar wax profiles. Understanding these chemical traits offers new opportunities to develop Populus varieties with enhanced environmental resilience and adaptive potential.

GWAS↗

DOE OSTI2021

Incorporating historical data and past analyses for improved tensile property prediction of 9% Cr steel

Data-driven analytical clustering and visualization techniques were applied to the dataset of 9% Cr experimental alloy data generated through the eXtremeMAT project. Techniques and results were compared with the resulting clusters obtained through similar analytical techniques on previous and reduced versions of the dataset. The principal components were generated in order to reduce the dimensionality of the complex dataset and to visualize the underlying trends in the data. Partitioning around medoids was performed on the resulting principal components to determine relevant clusters. Domain knowledge labels were further applied to the principal components to compare the labels with the trends identified through the clustering methods. The resulting clusters show the addition of the new data into the dataset, and show where alignment between the domain knowledge labels and partitioning around medoids (PAM) clusters show where the labels are appropriate. The clusters can be used to compare the tensile properties of the alloys, and to reduce the variation in the dataset.

Alloy design, Mechanical Properties, data analysis↗

DOE OSTI2022

Variational quantum state eigensolver

Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The variational quantum eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we address the case when the matrix is a density matrix ρ. We introduce the variational quantum state eigensolver (VQSE), which is analogous to VQE in that it variationally learns the largest eigenvalues of ρ as well as a gate sequence V that prepares the corresponding eigenvectors. VQSE exploits the connection between diagonalization and majorization to define a cost function C=Tr(ρ~H) where H is a non-degenerate Hamiltonian. Due to Schur-concavity, C is minimized when ρ~=VρV† is diagonal in the eigenbasis of H. VQSE only requires a single copy of ρ (only n qubits) per iteration of the VQSE algorithm, making it amenable for near-term implementation. We heuristically demonstrate two applications of VQSE: (1) Principal component analysis, and (2) Error mitigation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

What explains the year-to-year variation in growing season timing of boreal black spruce forests?

Amplified climate warming in high latitudes is expected to affect growing season timing of the vast boreal biome. It is unclear whether the presence of permafrost (perennially frozen ground) might have an influence on changes in growing season timing. Here, this study examined how different environmental variables explained, either directly or indirectly, the variation in growing season timing of boreal forest stands with and without permafrost. We expected that environmental variables explaining the variation in growing season timing differed or had different explanatory power depending on permafrost presence or absence. The growing season was delineated from daily gross primary productivity (GPP) time series derived from 40 site-year data of net ecosystem carbon dioxide exchange measured with eddy covariance techniques over five black spruce (Picea mariana [Mill.])-dominated boreal forest stands in North America. In permafrost-free forest stands, a combination of start in canopy ‘green-up’ in spring and the timing of air and soil temperature increasing above freezing explained the start-of-season (SOS GPP ). Results from commonality analysis and structural equation modeling suggest that canopy ‘green-up’ and air temperature directly affected SOS GPP in permafrost-free forest stands. In addition, soil temperature acted as mediator for an indirect effect of air temperature on SOS GPP . In contrast, none of the environmental variables, or their combination, explained the variation in SOS GPP in forest stands with permafrost. The explanatory power of environmental variables was more consistent regarding the end-of-season (EOS GPP ). In both, forest stands with and without permafrost, EOS GPP was directly explained by mean soil water content in the fall and the first day of continuous snowpack formation. A better understanding how environmental variables control SOS GPP and EOS GPP in forest stands with and without permafrost will help to refine parameterizations of the boreal biome in Earth system models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The relation between quasars’ optical spectra and variability

Abstract Brightness variation is an essential feature of quasars, but its mechanism and relationship to other physical quantities are not understood well. We aimed to find the relationship between the optical variability and spectral features to reveal the regularity behind the random variation. It is known that a quasar’s Fe ii/Hβ flux ratio and equivalent width of [O iii]5007 are negatively correlated; this is called Eigenvector 1. In this work, we visualized the relationship between the position on this Eigenvector 1 (EV1) plane and how the brightness of the quasars had changed after ∼10 yr. We conducted three analyses, using a different quasar sample in each. The first analysis showed the relation between the quasars’ distributions on the EV1 plane and how much they had changed brightness, using 13438 Sloan Digital Sky Survey quasars. This result shows how brightness changes later are clearly related to the position on the EV1 plane. In the second analysis, we plotted the sources reported as “changing-look quasars” (or “changing-state quasars”) on the EV1 plane. This result shows that the position on the EV1 plane corresponds to the activity level of each source, and the bright or dim states of them are distributed on the opposite sides divided by the typical quasar distribution. In the third analysis, we examined the transition vectors on the EV1 plane using sources with multiple-epoch spectra. This result shows that the brightening and dimming sources move on a similar path and they reach a position corresponding to the opposite activity level. We also found this trend is opposite to the empirical rule that $R_{\rm {Fe\, \small {II}}}$ positively correlated with the Eddington ratio, which has been proposed based on the trends of a large number of quasars. From all these analyses, it is indicated that quasars tend to oscillate between both sides of the distribution ridge on the EV1 plane; each of them corresponds to a dim state and a bright state. This trend in optical variation suggests that significant brightness changes, such as changing-look quasars, are expected to repeat.

Astronomy & Astrophysics↗

DOE OSTI2021

An analysis of Bayesian estimates for missing higher orders in perturbative calculations

With current high precision collider data, the reliable estimation of theoretical uncertainties due to missing higher orders (MHOs) in perturbation theory has become a pressing issue for collider phenomenology. Traditionally, the size of the MHOs is estimated through scale variation, a simple but ad hoc method without probabilistic interpretation. Bayesian approaches provide a compelling alternative to estimate the size of the MHOs, but it is not clear how to interpret the perturbative scales, like the factorisation and renormalisation scales, in a Bayesian framework. Recently, it was proposed that the scales can be incorporated as hidden parameters into a Bayesian model. In this paper, we thoroughly scrutinise Bayesian approaches to MHO estimation and systematically study the performance of different models on an extensive set of high-order calculations. We extend the framework in two significant ways. First, we define a new model that allows for asymmetric probability distributions. Second, we introduce a prescription to incorporate information on perturbative scales without interpreting them as hidden model parameters. We clarify how the two scale prescriptions bias the result towards specific scale choice, and we discuss and compare different Bayesian MHO estimates among themselves and to the traditional scale variation approach. Finally, we provide a practical prescription of how existing perturbative results at the standard scale variation points can be converted to 68%/95% credibility intervals in the Bayesian approach using the new public code MiHO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Quantitative assessment of the influence of external magnetic field on clustering of nano-Fe3O4 particles in cementitious paste

In view of active rheology control of cementitious materials, nano-Fe{sub 3}O{sub 4} can be added as responsive particles. Following the concept of magnetorheological fluids, it is assumed that magnetic nanoparticles will form chains or clusters in cementitious paste following magnetic field lines. A quantitative experimental validation of this assumption is presented herein. The clustering of nano-Fe{sub 3}O{sub 4} particles under magnetic fields is studied by mapping iron (Fe) element distribution in cementitious paste using energy dispersive X-ray spectroscopy. By means of image analysis, the Fe-element patterns are quantified by the deviation of Fe-elements in a unit area from the mean value expected in case of a uniform distribution, as expressed by coefficient of variation (COV). The magneto-rheological responses of cementitious pastes are evaluated using small amplitude oscillatory shear technique. Results show that the magneto-rheological effect exhibits a linear relationship with the relative change of COV, providing a quantitative validation of magnetic clustering in cementitious paste.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Ultrasonic Elastography for Nondestructive Evaluation of Dissimilar Material Joints

Dissimilar material joints or multilayered metals have become inevitable in the manufacturing industry due to the increasing demand for multifunctional materials with variable mechanical, thermal, or electrical characteristics in a single assembly. Lattice mismatch of materials at the interface of dissimilar materials leads to inferior mechanical characteristics. In particular, the mismatch in elastic properties indicated by a large initial elastic deformation is critical to determine the extent of variation in stress. However, nanoindentation, the most common and accepted technique to measure elastic modulus, is destructive, time-consuming, and can only examine mechanical properties within a limited area. A non-invasive elastographic mapping technique evaluates the mechanical properties using ultrasonic elastography to study incompressibility. The dissimilar joint between steel and copper was obtained via friction stir welding. The variation of the stress developed at the welded joint of the two different metals was evaluated from the dynamic bulk modulus map. A tensile test of the involved workpiece confirmed a good agreement with our analysis based on the dynamic bulk modulus elastographic mapping results. This study provides a rapid and non-invasive technique for the bulk metallurgic elastic modulus inspection to overcome the limitations of conventional methods.

Jin, Yuqi↗

DOE OSTI2022

Correlation between thickness dependent nanoscale structural chemistry and superconducting properties of ultrathin epitaxial NbN films

NbN-based superconductors have attracted interest for superconducting circuits, quantum computation and high frequency devices. The superconducting properties of NbN films are predominately reliant on the microstructure, therefore, an atomic-level understanding of the structure-chemistry is required to achieve high quality epitaxial NbN films. Here, in this study, the thickness-dependent superconducting properties of NbN films (5, 10, and 50 nm) within NbN/AlN/Al 2 O 3 heterostructures are investigated. NbN and AlN were epitaxially grown by an industrial scale physical vapor deposition technique. The role of nanoscale chemistry on the ultrathin NbN superconducting film is investigated at the atomic level for the first time via atom probe tomography, providing three-dimensional atomic distribution, chemical homogeneity, effect of impurities, specially, in secondary phase formations and interfacial abruptness. The NbN film with 5 nm of thickness demonstrates a superconducting transition temperature of 11.2 K as compared to 50 nm NbN films with a transition temperature of 15.3 K. These thickness dependent variation of superconducting properties are associated with the chemical inhomogeneity in terms of in-plane N:Nb distribution, secondary phase formations and NbN/AlN interfacial abruptness as a function of the NbN films thicknesses. The analysis depicts the interplay between the surface/interface and the superconducting properties of ultrathin NbN films. These results provide insights on material design and growth that will enable the development of optimized superconducting NbN films for quantum devices.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Sol-gel derived silicate-phosphate glass SiO 2 –P 2 O 5 –CaO–TiO 2 : The effect of titanium isopropoxide on porosity and thermomechanical stability

Despite of several decades lasting extensive research of bioactive and bioresorbable glasses the systematic parametrization and determination of the key factors affecting porosity and thermomechanical characteristics still remains challenging. Here, we present silica-phosphate glasses, with the composition 70SiO 2 - 20P 2 O 5 - (10-x)CaO-xTiO 2 (mol%; x = 0, 2.5, 5, and 7.5), prepared by sol -gel method and reinforced by titanium dioxide via titanium isopropoxide (TTIP) incorporation which demonstrated tunable variation of porosity from micro-to macro -region and superb mechanical integrity during the calcination process. The presence of 7.5 mol% TiO 2 promotes dimensional stability up to 1000°C as investigated by thermomechanical analysis. The XRD showed the dominant presence of silicon phosphate [Si(P 2 O 7 )], titanium phosphate [Ti(P 2 O 7 )] and calcium phosphates [β-Ca(P 2 O 6 ) and γ- Ca 2 (P 2 O 7 )]. The effect of TiO 2 doping on the multiscale morphology and porosity was investigated by means of SEM, MIP, μCT, N 2 adsorption and USAXS/SAXS. Increasing TiO 2 content leads to the formation of open porosity up to 70vol% and drives the formation of a refined interconnected macroporosity of 2-30 μm. In contrast, mesoporosity with a dominance of 3-6nm pores decreases in all samples with increasing TiO 2 content. USAXS/SAXS revealed an increase in primary particle size with increasing TiO 2 content which is in good agreement with the nitrogen physisorption analysis showing that microporosity decreases with increasing TiO2 content.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Modelling dust transport in DIII-D with DTOKS-Upgrade

Comprehensive upgrades to the dust transport code Dust in TOKamaks (DTOKS) that extend the plasma-dust interaction model are presented and compared with recent measurements of dust transport in DIII-D. Simulations incorporating variation in physical properties of graphite dust with temperature and size in a stationary plasma background suggest a substantial decrease in lifetimes due principally to thermal expansion. The trajectories of 53 dust grains identified from analysis of visible camera data taken across two similar shots were used to measure the dust particle velocity distributions. Dust tracks terminated mostly at the outer divertor strike point having a mean observation time of 2.1 ± 0.4 ms. Stochastic modelling of 200 graphite dust particles in the DIII-D tokamak performed with DTOKS-U using plasma simulations generated by OEDGE found similar behaviour, with particles ablating rapidly after acquiring a positive charge in the region close to the outer strike point, creating an acute source of neutral carbon atoms. The simulated mean lifetime, 11 ± 2 ms, showed approximate agreement with experimental observation when corrected by accounting for dust visibility and ignoring the longest trajectories 1.5 ± 0.2 ms. Synthetic diagnostic data generated from coupling the results of DTOKS-U with the visualisation software Calcam offers a powerful new tool for validation of simulations and predictive calculations of dust dynamics.

Physics↗

DOE OSTI2020

Imaging systematics and clustering of DESI main targets

ABSTRACT We evaluate the impact of imaging systematics on the clustering of luminous red galaxies (LRG), emission-line galaxies (ELG), and quasars (QSO) targeted for the upcoming Dark Energy Spectroscopic Instrument (DESI) survey. Using Data Release 7 of the DECam Legacy Survey, we study the effects of astrophysical foregrounds, stellar contamination, differences between north galactic cap and south galactic cap measurements, and variations in imaging depth, stellar density, galactic extinction, seeing, airmass, sky brightness, and exposure time before presenting survey masks and weights to mitigate these effects. With our sanitized samples in hand, we conduct a preliminary analysis of the clustering amplitude and evolution of the DESI main targets. From measurements of the angular correlation functions, we determine power law fits $r_0 = 7.78 \pm 0.26\, h^{-1}$Mpc, γ = 1.98 ± 0.02 for LRGs and $r_0 = 5.45 \pm 0.1\, h^{-1}$Mpc, γ = 1.54 ± 0.01 for ELGs. Additionally, from the angular power spectra, we measure the linear biases and model the scale-dependent biases in the weakly non-linear regime. Both sets of clustering measurements show good agreement with survey requirements for LRGs and ELGs, attesting that these samples will enable DESI to achieve precise cosmological constraints. We also present clustering as a function of magnitude, use cross-correlations with external spectroscopy to infer dN/dz and measure clustering as a function of luminosity, and probe higher order clustering statistics through counts-in-cells moments.

79 ASTRONOMY AND ASTROPHYSICS↗