Model-fitting Methods Research Articles

Experimental Investigation of the Effect of Microstructure on Coalbed Methane Adsorption Characteristics Affected by Chemical Solvents.

Coalbed methane (CBM) reservoir modification based on chemical solvent treatment could change the coal microstructure, which further affects the adsorption capacity and flow characteristics of this clean energy. Coal samples were extracted by tetrahydrofuran (THF), carbon disulfide (CS2), and hydrochloric acid (HCl). Low-pressure nitrogen adsorption, carbon dioxide adsorption, Fourier transform infrared spectroscopy, and methane isothermal adsorption test were adopted. The variations of pore structure and chemical composition in coal were evaluated by density functional theory, Barrett-Joyner-Halenda model, and peak fitting method, and their impacts on methane adsorption characteristics were studied. Results show that (1) the micropores less than 2 nm show a bimodal distribution. After acidification, micropore specific surface areas of coal samples I and II increase by 16.79% and 11.72%, respectively, while that of coal sample III-HCl decreases by 4.29% closely related to carbonate and silicate minerals in coal. Microporous specific surface areas of sample II-CS2 and III-CS2 affected by solvent rise by 4.28% and 4.17%, respectively. (2) Among the three original coal samples, the highest level of OH-OH hydrogen bonds content is observed. Solvents have a tendency to interact with -CH2 groups, which shorten the length of fat chains and increase the number of branched chains. THF tends to dissolve C-O-C groups and carbonyl C═O groups. Following CS2 treatment, samples II and III show 38.42% and 47.76% decrease in aromatic C═C area, respectively. (3) The methane adsorption capability in three coal samples is I > III > II. Except for sample I-HCl and sample III-THF, other coal samples have a lower methane adsorption capability than raw coal. Methane adsorption is reduced not just by a decrease in the number of micropores but also by aliphatic groups, aromatic structures, and oxygen-containing structures. Relevant results could deliver guiding significance for understanding methane adsorption and flow characteristics in coal after chemical solvent modification.

Analysis of the Pyrolysis Kinetics, Reaction Mechanisms, and By-Products of Rice Husk and Rice Straw via TG-FTIR and Py-GC/MS.

This study employed thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy (FTIR), and pyrolysis gas chromatography/mass spectrometry (Py-GC/MS) to characterize and provide insights into the pyrolysis behaviors and by-products of rice husk (RH) and rice straw (RS). The primary pyrolysis range is partitioned into three stages, designated as pseudo-hemicellulose, pseudo-cellulose, and pseudo-lignin pyrolysis, by an asymmetric bi-Gaussian function. The average activation energies of the three pseudo-components of RH were estimated by the Flynn-Wall-Ozawa and Starink methods to be 179.1 kJ/mol, 187.4 kJ/mol, and 239.3 kJ/mol, respectively. The corresponding values for RS were 171.8 kJ/mol, 185.8 kJ/mol, and 203.2 kJ/mol. The results of the model-fitting method indicated that the diffusion model is the most appropriate for describing the pseudo-hemicellulose reaction. The reaction of pseudo-cellulose and pseudo-lignin is most accurately described by a nucleation mechanism. An accelerated heating rate resulted in enhanced pyrolysis performance, with RS exhibiting superior performance to that of RH. RH produces 107 condensable pyrolysis by-products, with ketones, acids, and phenols representing the largest proportion; RS produces 135 species, with ketones, phenols, and alcohols as the main condensable by-products. These high-value added by-products have the potential to be utilized in a variety of applications within the agricultural, bioenergy, and chemical industries.

Pyrolysis kinetics and reaction mechanism of waste medical masks by sectional heating process

The COVID-19 epidemic has led to a significant upsurge in the accumulation of waste medical masks. This work focuses on the detailed examination of waste medical masks’ pyrolysis kinetic and reaction mechanism, employing a sectional heating process. The degradation properties were analyzed via thermal gravimetric analysis and pyrolysis reactor. The comprehensive kinetic process was studied using model-free and model-fitting methods, which determined the apparent activation energy and pre-exponential factor. The calculated average value for these parameters was 221.32 kJ/mol and 2.6 × 1014 min−1, respectively. The pyrolysis process was carried out at three distinct temperatures: 380, 470, and 490 ℃, corresponding to the initial peak degradation rate and final degradation temperatures determined by TGA results. The total yield of oil, gas and tar was 88.6 %, 11.3 % and 0.1 %, respectively. The identification and quantification of pyrolysis products were achieved through GC–MS and FTIR. It was observed that higher pyrolysis temperature facilitated the generation of alkanes and hydrocarbons with lower carbon chain lengths in oil products and propylene monomers in gas products. The dominant pyrolysis products in oil under 380 ℃, 470 ℃ and 490 ℃ were C20, C20 and C12 with the yield of 36.17 %, 48.96 % and 43.35 %, respectively. And the corresponding dominant products in gas all were propylene with the yield of 34.74 %, 53.02 % and 54.55 %, respectively. Furthermore, a reaction mechanism was postulated to elucidate the pyrolysis process under varying temperature conditions.

Degradation of poly (2-ethyl-2-oxazoline) prepared at lower temperature: a study of kinetics using thermal analysis and advanced predictive modeling

The thermal degradation kinetics of poly(2-ethyl-2-oxazoline) (PEOX) prepared under different pH conditions were studied. Kinetic assessment was conducted by analyzing the thermal degradation of PEOX. The kinetic parameters were estimated using model-free methods; including Friedman, OFW, KAS and Starink methods and model-fitting method; Combined kinetics (Ck). The investigation revealed that the activation energy of PEOX degradation exhibited variability when prepared under different pH conditions. During the process of conversion, the activation energy for PEOX thermal degradation showed an increase when synthesized under neutral conditions, while it remained consistent when synthesized under alkaline conditions. The synthesis of PEOX in an acidic medium led to a compromised thermal stability, as indicated by a gradual reduction in activation energy during its thermal degradation. By employing artificial neural network (ANN) and advanced classification regression tree (C&RT), the prediction of activation energy's evolution was conducted, taking into account pH, conversion, heating rate, and temperature. The predictive performance of the advanced C&RT model surpassed that of ANN in determining the activation energy of PEOX degradation at different pH levels for different heating rates.

Kinetic Analysis of Molten Oxide Reduction Using Bottom-Blown Hydrogen Injection

Hydrogen-based smelting reduction has received widespread attention as an important technology for realizing low-carbon development in hydrogen metallurgy. In this study, the thermodynamics of smelting reduction was firstly analyzed by using FactSage 8.1 thermodynamic software, on the basis of which smelting reduction experiments of iron oxides by using bottom-blown hydrogen were carried out. The experiments used oxidized pellets as experimental materials, and the effects of the reduction process were analyzed in terms of the reduction temperature, the reduction time, and the hydrogen flow rate. The experimental results show that under the experimental conditions of a temperature of 1550 °C and a hydrogen flow rate of 0.2 Nm3/h, the reduction rate of iron oxides in the process of reducing iron oxides by hydrogen is significantly faster in the first 10 min than after 10 min. The hydrogen utilization rate reached a maximum of 41.87%, then decreased continuously and finally maintained at about 20%. Using the method of model fitting, it was found that the hydrogen-based molten reduction conformed to the phase boundary reaction model (Gα=1−(1−α)1/2), the corresponding mechanism function is fα=2(1−α)1/2, where α stands for the reduction conversion, and the reaction rate constant k(T) is 2.37 × 10−4 s−1 under the experimental conditions.

SsVERDICT: Self-supervised VERDICT-MRI for enhanced prostate tumor characterization.

Demonstrating and assessing self-supervised machine-learning fitting of the VERDICT (vascular, extracellular and restricted diffusion for cytometry in tumors) model for prostate cancer. We derive a self-supervised neural network for fitting VERDICT (ssVERDICT) that estimates parameter maps without training data. We compare the performance of ssVERDICT to two established baseline methods for fitting diffusion MRI models: conventional nonlinear least squares and supervised deep learning. We do this quantitatively on simulated data by comparing the Pearson's correlation coefficient, mean-squared error, bias, and variance with respect to the simulated ground truth. We also calculate in vivo parameter maps on a cohort of 20 prostate cancer patients and compare the methods' performance in discriminating benign from cancerous tissue via Wilcoxon's signed-rank test. In simulations, ssVERDICT outperforms the baseline methods (nonlinear least squares and supervised deep learning) in estimating all the parameters from the VERDICT prostate model in terms of Pearson's correlation coefficient, bias, and mean-squared error. In vivo, ssVERDICT shows stronger lesion conspicuity across all parameter maps, and improves discrimination between benign and cancerous tissue over the baseline methods. ssVERDICT significantly outperforms state-of-the-art methods for VERDICT model fitting and shows, for the first time, fitting of a detailed multicompartment biophysical diffusion MRI model with machine learning without the requirement of explicit training labels.

Estimation of Forest Growing Stock Volume with Synthetic Aperture Radar: A Comparison of Model-Fitting Methods

Satellite-based estimation of forest variables including forest biomass relies on model-based approaches since forest biomass cannot be directly measured from space. Such models require ground reference data to adapt to the local forest structure and acquired satellite data. For wide-area mapping, such reference data are too sparse to train the biomass retrieval model and approaches for calibrating that are independent from training data are sought. In this study, we compare the performance of one such calibration approach with the traditional regression modelling using reference measurements. The performance was evaluated at four sites representative of the major forest biomes in Europe focusing on growing stock volume (GSV) prediction from time series of C-band Sentinel-1 and Advanced Land Observing Satellite Phased Array L-band Synthetic Aperture Radar (ALOS-2 PALSAR-2) backscatter measurements. The retrieval model was based on a Water Cloud Model (WCM) and integrated two forest structural functions. The WCM trained with plot inventory GSV values or calibrated with the aid of auxiliary data products correctly reproduced the trend between SAR backscatter and GSV measurements across all sites. The WCM-predicted backscatter was within the range of measurements for a given GSV level with average model residuals being smaller than the range of the observations. The accuracy of the GSV estimated with the calibrated WCM was close to the accuracy obtained with the trained WCM. The difference in terms of root mean square error (RMSE) was less than 5% units. This study demonstrates that it is possible to predict biomass without providing reference measurements for model training provided that the modelling scheme is physically based and the calibration is well set and understood.

Pyrolysis kinetic analysis of molten bioplastics based on the combination of real-time characterization and Guassian deconvolution: Case study of poly(lactic acid) materials

Pyrolysis remains a promising method for the utilization of biogradable plastics. However, the kinetics and mechanisms of molten polymer pyrolysis are not well understood, and the effect of additives (mainly inorganic nucleating agents) on the reaction pathway has not been widely explored. In this work, we conducted a method using the thermogravimetric analysis-Fourier transform infrared spectrometry (TG-FTIR) combined with a model-fitting method, instead of a traditional method subjectively selecting a reaction model. The FTIR curves provided information for sub-reaction determination, and the detailed parameters were determined using Gaussian deconvolution. The calculation results revealed that the whole process of poly(latic acid) (PLA) pyrolysis is the random nucleation and nuclei growth model. The introduction of inorganic nucleating agents provided nuclei for PLA decomposition, decreasing the initial activation energy (E) from approximately 136 kJ·mol−1 to 88 and 79 kJ·mol−1 at a conversion rate of 0.01. However, the nucleating agent could hinder the generation of nuclei from PLA ontology, which led to the increase of E value after the nucleating agents were occupied.

Synthesizing Landsat images using time series model-fitting methods for China’s coastal areas against sparse and irregular observations

ABSTRACT Long historical records and free accessibility have made Landsat data valuable for time-series analysis. However, Landsat time-series analysis is restricted for coastal areas due to the lack of sufficient numbers of clear images. The generation of synthetic Landsat images using model-fitting methods is accepted as an effective means of overcoming this problem. But for coastal areas, available observations are typically sparse and irregular, leading to ill-fitted models that distort synthetic Landsat images. In this study, we propose a linear harmonic model with different orders and implement it on an annual basis to generate synthetic Landsat images based on the Google Earth Engine (GEE) platform. First, we incorporated the available observations from adjacent years and filtered them by season to address the problems of data sparsity and irregularity. Then, we combined the threshold segmentation and ridge regression approaches to address the fake cloud problem, which sometimes contaminates synthetic Landsat images in summer. All cloud-free real Landsat images from five typical sites along China’s coasts during 1986–2020 were used to evaluate the accuracy and robustness of the synthetic Landsat images generated using our proposed methods. The principal results are as follows: (1) the R2 value of the linear harmonic model averaged across different Landsat bands and land cover types was 0.640, and the model was especially successful in simulating the surface reflectance in near NIR bands in forest and grassland areas; (2) 81.1% of the synthetic Landsat images covered by fake clouds were effectively restored, and there was the particular need to remove fake clouds for the synthetic Landsat images at low latitudes; (3) The mean absolute error for our synthetic Landsat images was 0.015, with the rate of 0.124; this was achieved under the clear-sky probability of only 36% and the average number of annual observations below 9, indicating a good performance. Compared with the continuous change detection and classification (CCDC) and seasonal median composite (SMC) methods, our proposed method offers advantages in both the accuracy and integrity of synthetic Landsat images. Our proposed method for synthesizing images also has potential for application to global coastal areas and other satellite datasets.

Kinetic research of red mud waste oxidative pyrolysis and comparison under different atmospheres

Red mud, as a solid waste with high alkalinity, had a detrimental impact on the environment and required urgent attention. Currently, the mass processing and consumption of red mud were typically conducted under thermal conditions, so it was essential to gain a comprehensive understanding of the oxidative pyrolysis process. The thermogravimetric experiments were conducted at multiple heating rates in air and exhibited three obvious stages. The activation energy and reaction mechanism of three oxidative pyrolysis stages were explored using model-free and model-fitting methods, revealing the activation energies of 162.2, 265.8, 214.1 kJ/mol and the most suitable reaction mechanisms of g(α)=[-ln(1-α)]³, g(α)=1-(1-α)1/⁴, g(α)=[-ln(1-α)]1/2 for each stage, respectively. Furthermore, the estimated kinetic parameters and reaction mechanisms were applied to extra heating rate to verify the accuracy. More important, the effect of air on the pyrolysis process of red mud was examined by comparing the results with those obtained from pure nitrogen pyrolysis. The obtained oxidative pyrolysis characteristics of red mud could provide valuable insights of its co-pyrolysis or combustion for resources recycling.

Pyrolysis characteristics and kinetic analysis of coating pitch derived from ethylene tar using model-free and model-fitting methods

This work conducted the pyrolysis of coating pitch derived from the ethylene tar through thermogravimetry analysis. The thermogravimetry-mass spectrometry and solid-state 13C nuclear magnetic resonance spectroscopy were performed to correlate the structural characteristics with the pyrolysis behavior. Meanwhile, the pyrolysis kinetics were estimated with model-free and model-fitting methods. The TG-DTG results showed that the pyrolysis process was generally divided into drying, fast pyrolysis, and polycondensation stages, accompanied by the decomposition of active functional groups like the aliphatic carbons bonded to oxygen (falO), the pyrolysis of relatively stable groups like the non-protonated aromatic carbon (faH), and the condensation of high bonding-energy aromatic structure like aromatic bridgehead carbon (faB). The activation energy obtained from model-free analysis ranged from 78.12 to 150.92 kJ/mol with the increasing conversion, indicating the pyrolysis process as a multi-step reaction mechanism. Furthermore, the reaction model A1/3 (gα=[−ln(1−α)]3) was identified as the most suitable model for the pyrolysis of coating pitch in the conversion range of 0.25–0.8. The modeling values matched well with the experimental data, indicating the accuracy and feasibility of the results.

Kinetic studies on the catalyzed and un-catalyzed pyrolysis of mixed HDPE and PP (75:25 wt%) plastic waste using a combination of model-fitting and model-free methods

Kinetic studies on the catalyzed and un-catalyzed pyrolysis of mixed HDPE and PP (75:25 wt%) plastic waste using a combination of model-fitting and model-free methods

A spatiotemporal shape model fitting method for within-season crop phenology detection

Crop phenological information must be reliably acquired earlier in the growing season to benefit agricultural management. Although the popular shape model fitting (SMF) method and its various improved versions (e.g., SMF by the Separate phenological stage, SMF-S) have been successfully applied to after-season crop phenology detection, these existing methods cannot be applied to within-season crop phenology detection. This discrepancy arises due to the fact that, in the within-season scenario, phenological stages can beyond the defined cut-off time. Consequently, enhancing the alignment of the vegetation index (VI) curve segments prior to the cut-off time does not necessarily guarantee accurate within-season phenological detection. To resolve this issue, a new method named spatiotemporal shape model fitting (STSMF) was developed. STSMF does not seek to optimize the local curve matching between the target pixel and the shape model; instead, it determines similar local VI trajectories in the neighboring pixels of previous years. The within-season phenology of the target pixel was thus estimated from the corresponding phenological stage of the determined local VI trajectories. When compared with ground phenology observations, STSMF outperformed the existing SMF and SMF-S which were modified for the within-season scenario (SMFws and SMFSws) with the smallest mean absolute differences (MAE) between observed phenological stages and their corresponding model estimates. The MAE values averaged over all phenological stages for STSMF, SMFSws, and SMFws were 9.8, 12.4, and 27.1 days at winter wheat stations; 8.4, 14.9, and 55.3 days at corn stations; and 7.9, 12.4, and 64.6 days at soybean stations, respectively. Intercomparisons between after-season and within-season regional phenology maps also demonstrated the superior performance of STSMF (e.g., correlation coefficients for STSMF and SMFSws are 0.89 and 0.80 at the maturity stage of winter wheat). Furthermore, the performance of STSMF was less affected by the detection time and the determination of shape models. In conclusion, the straightforward, effective, and stable nature of STSMF makes it suitable for within-season detection of agronomic phenological stages.

Isothermal pyrolysis of discarded bakelite: Kinetics analysis and batch pyrolysis studies

Plastic is widely used, leading to an increase in plastic waste in the environment and resulting in pollution. Plastic waste can currently be managed differently and reduced by converting it into useful products via different methods. The extensive use of thermosetting polymers such as bakelite, which are nonrecyclable, has led to an increase in bakelite scrap and pollution. Therefore, minimizing pollution due to such waste requires sustainable, modern, eco-friendly, and economical recycling technology and the upgrading of existing recycling technology. This work reports the recycling of discarded bakelite through pyrolysis and a kinetic study of the isothermal pyrolysis of bakelite via model fitting methods as well as product analyses. Therefore, isothermal degradation experiments for discarded bakelite were carried out at different temperatures (300, 350, 400, 450, and 500 °C) for 2 h. The isothermal degradation of bakelite follows the D1-diffusion model fitting method, with an activation energy (Ea) of 17.178 kJ/mol and an Arrhenius constant (A) of 0.095 min−1. The kinetic information provided throughout the research will aid in the development of an appropriate reactor for the valorization of discarded bakelite. Batch pyrolysis of bakelite gives the highest yield of 39.12% pyrolytic waxy oil at 450 °C. The presence of components such as alkanes, cycloalkenes, alkenes, alcohols, ethers, and aromatic compounds in the pyrolytic waxy oil and residue was confirmed by FTIR and GC‒MS analysis.

Thermal decomposition kinetics and storage life prediction of nitramine propellants with different energetic plasticizers based on model-fitting method

The research on the thermal decomposition of propellant is critical to determining its safe storage life. The thermogravimetry (TG) testing of nitramine propellants plasticized by nitroglycerin (NG), glycidyl azide polymer (GAP), 2,2-dinitropropanol hexanoate (DNPH), and N-butyl-2-nitratoethylnitramine (BuNENA) was performed under non-isothermal circumstances. The thermal decomposition mechanism of propellant was then analyzed using the model-fitting method, and the storage life was predicted based on the mechanism. The results show that when heated to the same mass loss, the temperature of GAP-NC-RDX, BuNENA-NC-RDX, and DNPH-NC-RDX is higher than that of NG-NC-RDX. GAP-NC-RDX, BuNENA-NC-RDX, and DNPH-NC-RDX propellants have superior thermal stability to that of NG-NC-RDX. The kinetic mechanism functions and equations of the propellants were calculated, and multi-step reaction models of the thermal decomposition were built. The major thermal decomposition mechanism of nitramine propellants was discovered to be composite autocatalytic decomposition (Kamal-Sourour equation), which means that the reaction of reactants and the reaction catalyzed by products occur in tandem. The decomposition depth of propellants increases as the temperature rises during the same storage time. The storage lifetimes of GAP-NC-RDX, BuNENA-NC-RDX, DNPH-NC-RDX, and NG-NC-RDX propellants at 288 K are 28.71 years, 24.49 years, 18.34 years, and 16.33 years, respectively. The inclusion of GAP, DNPH, and BuNENA in the formulation improves the storage life of propellant more than NG. This study offers an attractive strategy for analyzing the decomposition mechanism of propellant with a multi-step decomposition reaction and forecasting its storage life.

Computational analysis of GCaMP fluorescence data in neuronal activity

The background and motivation of our research is to explore how to use computational methods to analyze GCaMP fluorescence data. GCaMP is a genetically encoded calcium indicator that can be used to observe the activity of thousands of neurons simultaneously using modern fluorescence imaging techniques. Our research includes the application of principles such as basic signal processing, statistical inference, hypothesis testing, and graph theory to help understand raw GCaMP fluorescence data recorded from awake, behavioral mice. The data set includes GCaMP fluorescence trace and correlation coefficient matrix among neurons. Our methods include high-pass filtering, Gaussian mixture model fitting and online active set method peak inference (oasis). By analyzing the correlation between neurons, we can understand the connection and centrality between neurons.

Thermokinetic study of tannery sludge using combustion and pyrolysis process through non-isothermal thermogravimetric analysis

Sludge from the tannery is produced in enormous amount. This work has investigated the thermal analysis behaviour of the tannery sludge by use of the thermogravimetric analysis (TGA). The TGA experiments is carried out in both air and nitrogen environment at the varied heating rates of 5, 10, 20 and 40 °C/min from the temperature range of 30–900 °C. In the assessment of kinetic parameters, the model fitting (Combined kinetics) method was employed. It was investigated that thermal degradation of the tannery sludge sample occurred in three stages. Majorly the conversions were observed in stage II for both in air and nitrogen environment. The activation energy (Ea) value for the combustion is 165.9 kJ/mol while for the pyrolysis the Ea value is obtained as 65.2 kJ/mol from the conversion range between 0.2 and 0.8 which is a promising approximation supported by a strong R2 value of 0.9719 and 0.93 for combustion and pyrolysis respectively. It is estimated from the master plots that six ideal models A1/2, A1/3, A1/4, F3, F4 and D5 were probably in approximation with the linear fitted data for both air and nitrogen. Various thermodynamic parameters which include the ΔH, ΔG and ΔS are also complimented that indicates the formation of activated complex and non-spontaneity of the reaction. The detailed thermokinetic study of the tannery sludge in combustion and pyrolysis offers a novel approach to understanding how this waste material decomposes under different temperature conditions. This holistic perspective contributes valuable insights into waste management practices, environmental impacts, resource recovery, and process optimization within the leather industry. Furthermore, the optimization of leather production processes on a large scale can minimize waste generation and enhance energy efficiency, strengthening the competitiveness and sustainability of the leather industry.

Aggregation of data from multiple recording stations for extreme wind analysis and prediction

Accurate, reliable and robust techniques for the probabilistic estimation of extreme wind speeds are essential for the design of structures for wind loading. Aggregating gust wind data from various stations with similar, homogeneous wind climates into a ‘superstation’ for hazard analysis has been employed since the 1980′s to reduce the effects of sampling errors. A concern that has been raised recently is that prediction biases may arise from such aggregation, when the data exhibit non-homogeneity due to inevitable short data lengths or imperfect homogeneity of the wind climates. By Monte Carlo simulation, we show that superstation aggregation is an unbiased technique for high recurrence level estimations when an appropriate fitting method is used, and the apparent biases are dependent on the method used for fitting the hazard model. To ensure homogeneity, we introduce a de–trending technique for minimizing any biases in the aggregated wind data. Four model-fitting methods for superstation analysis are compared, and shown that the introduced de-trending method is effective for eliminating the biases due to sampling errors and non-homogeneity.

Kinetic assessment of pulp mill-derived lime mud calcination in high CO2 atmosphere

The chemical pulping of biomass involves the recycling of calcium through the calcination of lime mud, which is mostly comprised of calcium carbonate (CaCO3). Lime mud decomposes under elevated temperatures to generate calcium oxide (CaO) and carbon dioxide (CO2), the kinetics of which are strongly influenced by the CO2 partial pressure and temperature. Oxy-fuel combustion and electrified lime kilns for lime mud calcination are intriguing methods to decarbonize this highly polluting operation within the biomass pulping industry. However, the high CO2 concentration in oxy-fuel and electrified calcination processes alters the kinetics and overall reactivity of lime mud. For the first time, a model-fitting method is used to determine the kinetic parameters for lime mud calcination under a wide range of temperatures (550 °C–1250 °C) and under different concentrations of CO2 (0 %, 15 %, 50 %, and 90 %). A kinetic model is developed that accurately predicts the reaction rates as a function of temperature and CO2 concentration. The apparent activation of energy for lime mud calcination is elevated under a high CO2 environment. Relative to inert gas (N2, Ar), the temperature window for calcination is much smaller under high CO2 environments. The presence of Na in lime mud does not seem to affect calcination under a high CO2 environment. Finally, particle size variation does not have a significant effect on calcination under a high CO2 environment.

The value of generalized linear mixed models for data analysis in the plant sciences

Modern data analysis typically involves the fitting of a statistical model to data, which includes estimating the model parameters and their precision (standard errors) and testing hypotheses based on the parameter estimates. Linear mixed models (LMMs) fitted through likelihood methods have been the foundation for data analysis for well over a quarter of a century. These models allow the researcher to simultaneously consider fixed (e.g., treatment) and random (e.g., block and location) effects on the response variables and account for the correlation of observations, when it is assumed that the response variable has a normal distribution. Analysis of variance (ANOVA), which was developed about a century ago, can be considered a special case of the use of an LMM. A wide diversity of experimental and treatment designs, as well as correlations of the response variable, can be handled using these types of models. Many response variables are not normally distributed, of course, such as discrete variables that may or may not be expressed as a percentage (e.g., counts of insects or diseased plants) and continuous variables with asymmetrical distributions (e.g., survival time). As expansions of LMMs, generalized linear mixed models (GLMMs) can be used to analyze the data arising from several non-normal statistical distributions, including the discrete binomial, Poisson, and negative binomial, as well as the continuous gamma and beta. A GLMM allows the data analyst to better match the model to the data rather than to force the data to match a specific model. The increase in computer memory and processing speed, together with the development of user-friendly software and the progress in statistical theory and methodology, has made it practical for non-statisticians to use GLMMs since the late 2000s. The switch from LMMs to GLMMs is deceptive, however, as there are several major issues that must be thought about or judged when using a GLMM, which are mostly resolved for routine analyses with LMMs. These include the consideration of conditional versus marginal distributions and means, overdispersion (for discrete data), the model-fitting method [e.g., maximum likelihood (integral approximation), restricted pseudo-likelihood, and quasi-likelihood], and the choice of link function to relate the mean to the fixed and random effects. The issues are explained conceptually with different model formulations and subsequently with an example involving the percentage of diseased plants in a field study with wheat, as well as with simulated data, starting with a LMM and transitioning to a GLMM. A brief synopsis of the published GLMM-based analyses in the plant agricultural literature is presented to give readers a sense of the range of applications of this approach to data analysis.