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At least 757 records · Page 42

Investigations of correlation and coherence in turbulence from a large-eddy simulation

Abstract. Microscale flow descriptions are often given in terms of mean quantities, turbulent kinetic energy, and/or stresses. Those metrics, while valuable, give limited information about turbulent eddies and coherent turbulent structures. This work investigates the structure of an atmospheric boundary layer using coherence and correlation in space and time with a range of separation distances. We calculate spatial correlations over entire planes of velocity fluctuations, from which we can evaluate the correlation along different directions at different spacings. Similarly, coherence of the three velocity components over separations in the three directions is also investigated. We apply these analyses to a mesoscale–microscale coupled scenario with time-varying conditions and examine nuances in spatial correlations that are often overlooked. Through these analyses and results, this work highlights important differences observed in terms of coherence when comparing large-eddy simulation data to simpler models and suggests ways to improve these simpler models. We note that such differences are important for disciplines like wind energy structural dynamic analysis, in which blade loading and fatigue depend strongly on the structure of the turbulence. We emphasize the additional wealth of data that can be provided by typical atmospheric boundary layer large-eddy simulation when correlation and coherence analysis is included, and we also state the limitations of large-eddy simulation data, which inherently truncate the smaller scales of turbulence.

17 WIND ENERGY↗

Cross-correlating Cosmic IR and X-ray Background Fluctuations: Evidence of Significant Black Hole Populations Among the CIB Sources

In order to understand the nature of the sources producing the recently uncovered cosmic infrared background (CIB) fluctuations, we study cross-correlations between the fluctuations in the source-subtracted CIB from Spitzer/IRAC data and the unresolved cosmic X-ray background from deep Chandra observations. Our study uses data from the EGS/AEGIS field, where both data sets cover an approx = 8' x 45' region of the sky. Our measurement is the cross-power spectrum between the IR and X-ray data. The cross-power signal between the IRAC maps at 3.6 micron and 4.5 micron and the Chandra [0.5-2] keV data has been detected, at angular scales approx >20'', with an overall significance of approx = 3.8 sigma and approx. = 5.6 sigma, respectively. At the same time we find no evidence of significant cross-correlations at the harder Chandra bands. The cross-correlation signal is produced by individual IR sources with 3.6 micron and 4.5 micron magnitudes m(sub AB) approx. > 25-26 and [0.5-2] keV X-ray fluxes << 7 × 10(exp -177 erg sq. cm/ s. We determine that at least 15%-25% of the large scale power of the CIB fluctuations is correlated with the spatial power spectrum of the X-ray fluctuations. If this correlation is attributed to emission from accretion processes at both IR and X-ray wavelengths, this implies a much higher fraction of accreting black holes than among the known populations. We discuss the various possible origins for the cross-power signal and show that neither local foregrounds nor the known remaining normal galaxies and active galactic nuclei can reproduce the measurements. These observational results are an important new constraint on theoretical modeling of the near-IR CIB fluctuations. local foregrounds, nor the known remaining normal galaxies and active galactic nuclei (AGN) can reproduce the measurements. These observational results are an important new constraint on theoretical modeling of the near-IR CIB fluctuations

Cosmic X-ray Background (CXB)↗

Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories

International Conference on Envronmental Systems (ICES), Seattle WA NCTS 20964-15. The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earths magnetosphere as a laboratory tostudy the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10-4 Pa (10-6 torr)and the surrounding temperature achieving -180 C. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperatureversus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDAFLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 C of the test data using the standard deviation and mean deviation error calculation. Individual temperature error goal is to be within 5 C and the heater power goal is to be within 5 of test data. The results of the model correlation are discussed and the effect of some material and interface parameters on the temperature profiles are presented.

Thermal↗

Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories

The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earth's magnetosphere as a laboratory to study the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10 (sup -4) pascals (10 (sup -6) torr) and the surrounding temperature achieving -180 degrees Centigrade. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperature versus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDA/FLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 degrees Centigrade of the test data using the standard deviation and mean deviation error calculation. Individual temperature error goal is to be within 5 degrees Centigrade and the heater power goal is to be within 5 percent of test data. The results of the model correlation are discussed and the effect of some material and interface parameters on the temperature profiles are presented.

Correlation↗

Validation of Universal Cryogenic Flow Boiling Correlations in Thermal Desktop for Liquid Helium

Understanding two-phase cryogenic propellant behavior is key to enabling technologies for future spaceflight missions. Developing accurate models of two-phase flow phenomena, particularly in the current work, flow boiling in the heating configuration, is relevant to the propellant transfer process both in 1-g and microgravity. Currently there is a need for more accurate, direct cryogenic data anchored models for various boiling phenomena. Recently, universal correlations for cryogens flowing in heated tubes have been developed for a wide variety of fluids, thermodynamic conditions, and various regimes across the boiling curve, and have been patched to provide a smooth, continuous predictive curve. This paper describes implementation and validation of these correlations into Thermal Desktop to improve predictive performance, with a focus on liquid helium. Results from Thermal Desktop using both the built-in and new correlations are validated against a historical dataset of flow boiling experiments in the heating configuration using liquid helium. Based on results, the new correlations show a substantial improvement over the original built-in flow boiling correlations in Thermal Desktop in predicting the wall temperature as a function of preponderant parameters for this quantum fluid at temperatures greater than the lambda temperature, T λ = 2.17K.

cryogenic propellant transfer↗

Model Correlation and Thermal Analysis of xEMU Boot at Lunar South Pole Temperatures

The National Aeronautics and Space Administration (NASA) Artemis program plans to send astronauts to the lunar south pole, a region of the moon that is colder than previous lunar missions and low earth orbit operations. The spacesuit boots that will be used on these missions will be directly impacted by these extremely cold temperatures (down to ~50 K). To assess the performance of the Exploration Extravehicular Mobility Unit (xEMU) lunar boot in these extreme temperatures, the boot was tested at the Jet Propulsion Lab (JPL) in the Cryogenic Ice Transfer, Acquisition Development, and Excavation Laboratory (CITADEL) thermal vacuum (TVAC) chamber. This data was used to correlate thermal models to predict operational performance of the boots on the lunar south pole. This paper documents the data analysis, thermal boot model correlation, and operational predictions conducted using data from the xEMU TVAC test. Data from the test series was used to determine expected thermal conductances within the boot and between the boot and environment. These conductances were used to correlate a Thermal Desktop model of the xEMU boot across 10 different test points which varied external temperature, internal boot ventilation flowrate, and contact pressure. The correlated model was then used to predict operational performance in the lunar south pole. While the predictions indicate promising evidence for performance of the boots at the 100K test point, there is still substantial uncertainty in performance, particularly at the 48K test point. The results of this test series and model correlation stress the importance of improved testing for characterizing the expected thermal resistance between the outside of the boot and the lunar surface.

thermal analysis↗

Model Correlation and Thermal Analysis of xEMU Boot at Lunar South Pole Temperatures

The National Aeronautics and Space Administration (NASA) Artemis program plans to send astronauts to the lunar south pole, a region of the moon that is colder than previous lunar missions and low earth orbit operations. The spacesuit boots that will be used on these missions will be directly impacted by these extremely cold temperatures (down to ~50 K). To assess the performance of the Exploration Extravehicular Mobility Unit (xEMU) lunar boot in these extreme temperatures, the boot was tested at the Jet Propulsion Lab (JPL) in the Cryogenic Ice Transfer, Acquisition Development, and Excavation Laboratory (CITADEL) thermal vacuum (TVAC) chamber. This data was used to correlate thermal models to predict operational performance of the boots on the lunar south pole. This paper documents the data analysis, thermal boot model correlation, and operational predictions conducted using data from the xEMU TVAC test. Data from the test series was used to determine expected thermal conductances within the boot and between the boot and environment. These conductances were used to correlate a Thermal Desktop model of the xEMU boot across 10 different test points which varied external temperature, internal boot ventilation flowrate, and contact pressure. The correlated model was then used to predict operational performance in the lunar south pole. While the predictions indicate promising evidence for performance of the boots at the 100K test point, there is still substantial uncertainty in performance, particularly at the 48K test point. The results of this test series and model correlation stress the importance of improved testing for characterizing the expected thermal resistance between the outside of the boot and the lunar surface.

xEMU↗

Upper subcritical calculations based on correlated data - 14427

The American National Standards Institute and American Nuclear Society standard for Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations defines the upper subcritical limit (USL) as 'a limit on the calculated k-effective value established to ensure that conditions calculated to be subcritical will actually be subcritical'. Often, USL calculations are based on statistical techniques that infer information about a nuclear system of interest from a set of known/well-characterized similar systems. The work in this paper is part of an active area of research to investigate the way traditional trending analysis is used in the nuclear industry, and in particular, the research is assessing the impact of the underlying assumption that the experimental data being analyzed for USL calculations are statistically independent. In contrast, the multiple experiments typically used for USL calculations can be correlated because they are often performed at the same facilities using the same materials and measurement techniques. This paper addresses this issue by providing a set of statistical inference methods to calculate the bias and bias uncertainty based on the underlying assumption that the experimental data are correlated. Methods to quantify these correlations are the subject of a companion paper and will not be discussed here. The newly proposed USL methodology is based on the assumption that the integral experiments selected for use in the establishment of the USL are sufficiently applicable and that experimental correlations are known. Under the assumption of uncorrelated data, the new methods collapse directly to familiar USL equations currently used. We will demonstrate our proposed methods on real data and compare them to calculations of currently used methods such as USLSTATS and NUREG/CR-6698. Lastly, we will also demonstrate the effect experiment correlations can have on USL calculations. (authors)

42 ENGINEERING↗

Verification of the Uniformly-Ordered Binary Decision Algorithm in Correlated-Benchmark Whisper Calculations

Whisper is a nuclear criticality safety code package that aids analysts in validation exercises by computing upper subcritical limits (USL) for applications of interest. To obtain statistically meaningful, significant, and conservative USLs, the analyst must ensure that Whisper selects a sufficient number of benchmarks that are neutronically similar to the application. Many of the available benchmarks are correlated but are currently treated as independent, leading to an artificially small sample size, as their individual information contributions will be overestimated. To aid the analyst in obtaining a sufficient sample size, prior work [2] demonstrated application of the Uniformly-Ordered Binary Decision (UOBD) algorithm in adjusting benchmark weights to account for benchmark correlations. This work provides verification of the Whisper implementation and considers the impact of updated benchmark correlations compared to those available previously. We demonstrate that the UOBD algorithm performs as expected with an analytic example. With HEU-SOL-THERM-001 cases 1 through 10 as the applications, we compare the USLs computed with benchmark correlations available in the Whisper 1.1 release only to those computed with additional benchmark correlations from DICE 2023 and demonstrate substantive differences.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Angular Correlations of Gamma Rays from Fission Product Solution

Fission products from photon-induced fission are routinely used at Idaho National Laboratory as part of nuclear forensics activities. Typically, the focus is on fission products with relatively large fission yields (Ba-140, Mo-99, etc.). The nuclear data associated with the well-known isotopes have small uncertainties, and many have well-known angular correlations between emitted gamma-rays, if applicable. However, for isotopes with smaller fission yields or less intense gamma-ray emission intensities, the nuclear decay schemes and gamma-ray emission intensities may be less well-known. The Germanium Rotational Measurements for Angular Correlation (GeRMAC) system was designed to use two high-purity germanium (HPGe) detectors in a coincidence counting set-up but allows one of the HPGe detectors to rotate at a constant distance from a radioactive source, changing the relative angle between the two HPGe detectors. Angular correlations can then be determined from the relative photopeak areas between two gamma-rays emitted as part of the same nuclear decay. By recording the HPGe spectra in list mode, the angular correlations of gamma-rays emitted from complex sources, consisting of multiple isotopes, can be measured simultaneously and the individual isotope emissions can be isolated. Using the GeRMAC system, a multi-isotope fission product source, produced with photon-induced fission of U-238, was measured using a single rotational arc (180 degrees) to obtain the angular correlation between gamma-rays emitted by the large number of fission products contained in the solution with an angular accuracy of 1 degree. In particular, La-140 (38 gamma rays) and Nd-147 (26 gamma rays) are of interest to the nuclear forensics community.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

Predictions for energy correlators probing substructure of groomed heavy quark jets

We develop an effective field theory (EFT) framework to perform an analytic calculation for energy correlator observables computed on groomed heavy-quark jets. A soft-drop grooming algorithm is applied to a jet initiated by a massive quark to minimize soft contamination effects such as pile-up and multi-parton interactions. We specifically consider the two-particle energy correlator as an initial application of this EFT framework to compute heavy quark jet substructure. We find that there are different regimes for the event shapes, depending on the size of the measured correlator observable, that require the use of different EFT formulations, in which the quark mass and grooming parameters may be relevant or not. We use the EFT to resum large logarithms in the energy correlator observable in terms of the momentum of a reconstructed heavy hadron to NLL' accuracy and subsequently match it to a full QCD O(α s ) cross section, which we also compute. We compare our predictions to simulations in Pythia for e + e – collisions. We find a good agreement with partonic simulations, as well as hadronic ones with an appropriate shape function used to describe nonperturbative effects and the heavy quark hadron decay turned off. We also predict the scaling behavior for the leading nonperturbative power correction due to hadronization. Consequently, we can give a prediction for the energy correlator distribution at the level of the reconstructed heavy hadron. This work provides a general framework for the analysis of heavy quark jet substructure observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The study of the core–valence and core–core correlation effects on the radiative properties along the magnesium isoelectronic sequence

We investigated the effect of core–valence and core–core correlations on the energy levels and transition probabilities along the Mg isoelectronic sequence from Si{sup 2+} to U{sup 80+}. In order to attain a certain accuracy for the atomic structure we considered configurations obtained by electron promotions from the n=3 up to n=7 valence shells. Core–valence and core–core correlations are systematically included in the model by allowing single and double electron promotions from the n=2 core up to the n=6 and n=5 shells with l≤4 and l≤2, respectively. The present results contain the energy of the levels arising from the valence configurations along with oscillator strengths and radiative rates corresponding to E1, M1, E2, M2 transitions between states arising from 3l3l{sup ′} with l,l{sup ′}≤2 and 3snl{sup ′′} with n≤7 and l{sup ′′}≤4 configurations. We conclude the data accuracy trend along the magnesium isoelectronic sequence as a result of the detailed study of the correlation effects on the radiative properties. The core–valence correlations generally improve both energy and radiative rate values, while the core–core correlations mostly give better oscillator strengths but may slightly increase the energy deviations. The calculations have been performed by employing the fully relativistic model-potential Flexible Atomic Code.

74 ATOMIC AND MOLECULAR PHYSICS↗

Reassessment of the nonlocality of correlation boxes

Correlation boxes are hypothetical systems usually designed to produce the maximal algebraic violation of a Bell inequality, beyond the quantum bound and without superluminal signalling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states, as the spin singlet, has been regarded as a demonstration that the former are more nonlocal than the latter. By applying an alternative, consistent measure of nonlocality to a family of correlation boxes, we show that this conclusion is not necessarily true. Complementarily, we define a class of systems displaying subquantum correlations which, nevertheless, are more nonlocal than the singlet state, showing that the extent of the numeric violation of an inequality may have little to do with the degree of nonlocality, especially in the case of correlation boxes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Enhancement of frequency estimation by spatially correlated environments

In metrological tasks, employing entanglement can quantitatively improve the precision of parameter estimation. However, susceptibility of the entanglement to decoherence fades this capability in the realistic metrology and limits ultimate quantum improvement. One of the most destructive decoherence-type noise is uncorrelated Markovian noise which commutes with the parameter-encoding Hamiltonian and is modeled as a semigroup dynamics, for which the quantum improvement is constrained to a constant factor. It has been shown (Chin et al., 2012) that when the noisy time evolution is governed by a local and non-semigroup dynamics (e.g., induced by an uncorrelated non-Markovian dephasing), emerging the Zeno regime at short times can result in the Zeno scaling in the precision. Here, by considering the impact of the correlated noise in metrology, we show that spatially correlated environments which lead to a nonlocal and non-semigroup dynamics can improve the precision of a noisy frequency measurement beyond the Zeno scaling. In particular, it is demonstrated that one can find decoherence-free subspaces and subsequently achieve the Heisenberg precision scaling for an approximated dynamics induced by spatially correlated environments. - Highlights: • Here, the impact of correlated noise in metrology is studied. • We have focused on spatially correlated environments. • We show that such environments can result in precision beyond the Zeno scaling. • In particular, we find decoherence-free subspaces. • This leads to achieving the Heisenberg precision scaling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Correlation of spatio-temporal characteristics of intestinal inflammation with IL-17 in a rat model of hypoganglionosis

Highlights: • Concomitant expression of C-RP, TNF-, and IL-17 in HD-like animal model induced by benzalkonium chloride. • Their expression maintained the highest level at Day 21. • IL-17 may be involved in spatio-temporal inflammation. Interleukin 17 expression is increased in children with Hirschsprung disease, which is characterized by intestinal inflammation. This study designed to exploit the characteristics of intestinal inflammation and examine the correlation of interleukin 17 in this process of hypoganglionosis model established by benzalkonium chloride treatment. Colon sections from female rats were treated with benzalkonium chloride to induce hypoganglionosis or with saline alone as a sham control. C-reactive protein and tumor necrosis factor- were used as markers of inflammation. Expression of C-reactive protein, tumor necrosis factor-, and interleukin 17 was assessed in colon tissue and blood serum on days 7, 14 and 21 after treatment. The correlation between C-reactive protein, tumor necrosis factor-, and interleukin 17 expression was estimated using the Spearman's rank-correlation coefficient. C-reactive protein, tumor necrosis factor-, and interleukin 17 were strongly expressed in submucosa and mucosa layers and serum from treated animals. The expression of C-reactive protein, tumor necrosis factor-, and interleukin 17 maintained the highest level at Day 21. Only C-reactive protein and tumor necrosis factor- expression was increased in control animals and only on day 7. Spearman's rank correlation coefficient was significant in C-reactive protein, tumor necrosis factor-, and interleukin 17 at Day 7, 14 and 21. Concomitant upregulation of C-reactive protein, tumor necrosis factor-, and interleukin 17 and significant positive correlations between C-reactive protein, tumor necrosis factor-, and interleukin 17 may imply that interleukin 17 is involved in spatio-temporal inflammation induced by benzalkonium chloride.

60 APPLIED LIFE SCIENCES↗

Investigating the correlation of biomass recalcitrance with pyrolysis oil using poplar as the feedstock

Pyrolysis of five poplar samples with differing degrees of recalcitrance was performed; the correlations between the poplar enzymatic hydrolysis glucose yields and the physicochemical properties of pyrolysis product were studied in this work. Sugar release of five poplar samples varied from 48.1 to 112.3 mg/g for glucose, and 12.0 to 32.4 mg/g for xylose. The yield of pyrolysis products was calculated and the molecular weight distribution of pyrolysis oils was measured by GPC, ranging from 268 to 289 g/mol for its weight-average molecular weight. GC–MS analysis of the bio-oil exhibited a strong correlation between biomass recalcitrance and guaiacyl-type structures in bio-oils. The correlation between biomass recalcitrance and the ratio of syringyl-to-guaiacyl-type-related structures was also assessed. The results from quantitative 31 P NMR indicated some correlation between biomass recalcitrance and the guaiacyl hydroxyl groups in bio-oils. These conclusions illustrate correlations and differences between converting biomass to biofuels via the biological and thermal platform.

09 BIOMASS FUELS↗

An efficient correlation for heat and mass transfer effectiveness in tumble-type clothes dryer drums

A heat and mass transfer effectiveness definition relevant to clothes dryers is developed in this work. A correlation is presented for determining the effectiveness of heat and mass transfer in a horizontal-axis, tumble-type clothes dryer drum with axial airflow. The correlation is a function of four measurable quantities: air mass flow rate, cloth mass, air mass in the drum, and the fall time experienced by a cloth falling the full height (i.e. diameter) of the drum. The Buckingham Pi Theorem is applied to the problem in order to derive dimensionless terms upon which the effectiveness depends. Empirical data from several dryers are used to derive an empirical correlation as a function of the dimensionless variables. Three cloth types were investigated, and a separate empirical correlation is proposed for each. Accordingly, the drum effectiveness concept and the correlation presented provide a new, more accurate, computationally efficient, and readily implemented framework for modeling and simulating clothes dryers. It is relevant to conventional gas and electric clothes drying appliances, vapor compression heat pump dryers, and thermoelectric heat pump clothes dryers. Along with appropriate empirical inputs, the framework is extensible to any thermal-evaporative cloth drying systems, including radial-flow horizontal axis tumble drying drums.

42 ENGINEERING↗

A review of coal heating value correlations with application to coal char, tar, and other fuels

Accurately measuring a fuel’s heating value is one of the first steps in the classification of a new fuel. Heating values are widely used in coal combustion research and are becoming more useful in other fuel types as well. Many different empirical correlations to predict heating values based on primary organic (CHONS) elemental composition are found in the literature, many of which were originally created to predict heating values of parent coal, and some of which have been extended for biomass. However, no correlations exist for heating values of coal chars and tars. Thirteen literature heating value correlations (10 model forms with 13 unique sets of coefficients) were evaluated for their predictive accuracy of a wide variety of fuel types, including 353 coals. This comparative analysis showed that the predictive capabilities of many of these literature models are very similar for coal-based fuels, with good correlation of coal char heating values. Correlation of coal tar heating values was hampered by the lack of heating value data. The choice of which model to use becomes more important for biomass fuels as well as for more unique fuel types like propellants and explosives, municipal solid waste, etc. Finally, the best model forms for each fuel type are suggested based on several statistical measures of fit.

01 COAL, LIGNITE, AND PEAT↗