Model-fitting Methods Research Articles

Pyrolysis characteristics and kinetics of lignin: effect of starting lignins

ABSTRACT To elucidate the impact of starting lignins on pyrolysis characteristics and kinetics of lignin, seven lignins were pyrolyzed on a thermogravimetric (TG) analyzer. Results show that hardwood lignins showed derivative thermogravimetric (DTG) curves with one weight loss peak, softwood lignin showed a curve with two weight loss peaks, while grass lignins showed curves with a main weight loss peak and a shoulder peak. The average apparent activation energy (Ea ) obtained with Starink model-free method varied greatly across the lignins. Prepared under mild conditions, the Ea values followed the order as grass lignin > hardwood lignin > softwood lignin. The most probable mechanism functions (MPMF) determined by Coats-Redfern model-fitting method also depended upon the lignins. This work shows that the slow pyrolysis behavior of lignin and the kinetic parameters are tightly related to its structure which depended greatly upon the biomass sources and isolation methods. More weak linkage structures, like β − O − 4 linkage, ferulates, and p-coumarates, could lead to the lower activation energy.

Pyrolysis Kinetic Properties of Thermal Insulation Waste Extruded Polystyrene by Multiple Thermal Analysis Methods

Extruded polystyrene (XPS) is a thermal insulation material extensively applied in building systems. It has attracted much attention because of outstanding thermal insulation performance, obvious flammability shortcoming and potential energy utilization. To establish the reaction mechanism of XPS’s pyrolysis, thermogravimetric experiments were performed at different heating rates in nitrogen, and multiple methods were employed to analyze the major kinetics of pyrolysis. More accurate kinetic parameters of XPS were estimated by four common model-free methods. Then, three model-fitting methods (including the Coats-Redfern, the iterative procedure and masterplots method) were used to establish the kinetic model. Since the kinetic models established by the above three model-fitting methods were not completely consistent based on different approximations, considering the effect of different approximates on the model, the reaction mechanism was further established by comparing the conversion rate based on the model-fitting methods corresponding to the possible reaction mechanisms. Finally, the accuracy of the above model-fitting methods and Particle Swarm Optimization (PSO) algorithm were compared. Results showed that the reaction function g(α) = (1 − α)−1 − 1 might be the most suitable to characterize the pyrolysis of XPS. The conversion rate calculated by masterplots and PSO methods could provide the best agreement with the experimental data.

An investigation on thermal behaviour of Sevelamer Carbonate and non-isothermal decarboxylation kinetics using TGA to obtain activation energy and pre-exponential factor

Sevelamer carbonate (SC) is a phosphate binder used to treat chronic kidney disease patients to remove excess phosphate. It is an insoluble drug and thus cannot be absorbed into the systemic circulation, so the in vivo bioequivalence studies cannot be performed. The USFDA, therefore, recommends in vitro phosphate binding tests and API-sameness tests to show the interchangeability of generic variants of the sevelamer carbonate tablets. The API-sameness mentions a variety of physicochemical characteristics including carbonate content. In this work, we studied the decarboxylation characteristics using thermal techniques (DSC & TGA). We have determined the activation energy and pre-exponential factor (Arrhenius parameters-Ea and A) that of the decarboxylation using nonisothermal kinetics of decarboxylation in combination with a well-accepted Coats-Redfern model-fitting method. A total of 13 different models were tested of solid-state reaction in which the second-order model suits best with an excellent correlation of 0.9926. The resultant values of the Ea and A are 25 kcal/mol and 1.23007 × 1012 Sec-1, respectively. The comparison of decarboxylation activation energy values may offer additional assurance on the API-sameness, in addition to comparing carbonate content alone.

Thermal, kinetic and thermodynamic study for co-pyrolysis of pine needles and styrofoam using thermogravimetric analysis

This study investigate the thermal decomposition behavior of pine needles (PN), styrofoam (SF) as well as their mixture at ratio of 1:1 (w/w), determine the kinetic and thermodynamic parameters for co-pyrolysis of PN and SF using thermogravimetric analysis (TGA) data. The co-pyrolysis experiments were performed in an inert environment (N2) at three variable heating rates of 5, 10 and 20 °C/min in TG analyzer from 35 to 850 °C. TGA outcomes represent that the thermal degradation of PN occurred in three stages, while SF degradation took place in a single stage and degradation of their mixture occurred in three stages. Model-free methods such as Ozawa-Flynn-Wall (OFW) and Kissinger-Akahira-Sunose (KAS) were employed to findout the activation energy (Ea) for co-pyrolysis of PN and SF. Moreover, the thermodynamic parameters (changes in enthalpy, Gibbs free energy and entropy) were also determined by OFW method. The pre-exponential factors were also evaluated by model-fitting (Coats-Redfern) method. The average of Ea for co-pyrolysis of PN and SF determined by KAS and OFW methods was 96.44 and 109.73 kJ/mol, respectively. The results of this study suggest that PN and SF mixture has potential to be used as a pyrolysis feedstocks.

Magnesiothermic reduction kinetics of UF4

The most popular method for production of metallic uranium is by magnesiothermic reduction of UF4. Efficient production of good quality uranium metal chunk in the reaction vessel requires multiple parameter constraints. To theoretically optimize these process parameters, many basic properties, i.e. particle size, heat dissipation, packing density, heating rate, kinetic parameters of reaction, etc., are required. There was lack of information on kinetic parameters of this reaction; therefore, kinetic triplets of UF4 and magnesium metal reaction were determined by non-isothermal DTA method, at 5–20 K min−1 heating rates. The analysis of data was done by model-less methods and model-fitting methods. It was found that the reaction takes place through two parallel competitive mechanisms, bulk diffusion and first-order nucleation and growth of reaction sites, and the corresponding kinetic parameters, frequency factors and activation energies, were 440 min−1, 43.9 kJ mol−1, 420 min−1 and 49.03 kJ mol−1, respectively.

Overview of the Whole Heart and Heart Chamber Segmentation Methods.

Preservation and improvement of heart and vessel health is the primary motivation behind cardiovascular disease (CVD) research. Development of advanced imaging techniques can improve our understanding of disease physiology and serve as a monitor for disease progression. Various image processing approaches have been proposed to extract parameters of cardiac shape and function from different cardiac imaging modalities with an overall intention of providing full cardiac analysis. Due to differences in image modalities, the selection of an appropriate segmentation algorithm may be a challenging task. This paper presents a comprehensive and critical overview of research on the whole heart, bi-ventricles and left atrium segmentation methods from computed tomography (CT), magnetic resonance (MRI) and echocardiography (echo) imaging. The paper aims to: (1) summarize the considerable challenges of cardiac image segmentation, (2) provide the comparison of the segmentation methods, (3) classify significant contributions in the field and (4) critically review approaches in terms of their performance and accuracy. The methods described are classified based on the used segmentation approach into (1) edge-based segmentation methods, (2) model-fitting segmentation methods and (3) machine and deep learning segmentation methods and are further split based on the targeted cardiac structure. Edge-based methods are mostly developed as semi-automatic and allow end-user interaction, which provides physicians with extra control over the final segmentation. Model-fitting methods are very robust and resistant to the high variability in image contrast and overall image quality. Nevertheless, they are often time-consuming and require appropriate models with prior knowledge. While the emerging deep learning segmentation approaches provide unprecedented performance in some specific scenarios and under the appropriate training, their performance highly depends on the data quality and the amount and the accuracy of provided annotations.

Comparative kinetic analysis of total hypericin extraction from Hypericum perforatum flowers carried out under simultaneous external physical field and cooling reaction system operational conditions

The comparative kinetic analysis of total hypericin (TH) extraction from the pre-extracted flowers of Hypericum perforatum carried out under simultaneous external physical field and cooling reaction system operational conditions (SEPFC) was performed. The kinetics curves of TH extraction in SEPFC were measured in the temperature range from T=298 to 328K. It was proved that presence of ultrasonic and microwave field cause increasing of the extraction rate compared to conventional isothermal extraction. The possibility of describing the kinetics of TH extraction in SEPFC with empirical (Elovich's model) and physically-based (film-theory model) were explored. The kinetic complexity of the process was examined with the differential isoconversional method. By applying the model-fitting method the proper kinetic model of TH extraction in SEPFC was found: [1−(1−α)(1/3)]2=kM·t. The values of the extraction rate constant (kM), activation energy (Ea) and pre-exponential factor (lnA) of TH extraction were calculated. The effect of ultrasonic and microwave field on (a) kM; (b) Ea and (c) lnA of TH extraction was determined. The model mechanism of activation of hypericin molecule for extraction in SEPFC conditions was proposed. The values of wave number of resonant vibrations, vibration quantum number and anharmonicity parameter for the TH extraction are obtained.

Evaluation of the Validity of Model-Fitting and Model-Free Methods for Kinetic Analysis of Nonisothermal Pyrolysis of Siberian Fir Bark

The kinetic parameters of the pyrolysis of Siberian fir bark were estimated by thermogravimetric analysis. The thermochemical conversion of the bark biomass was performed at heating rates of 5, 10, and 20 deg/min in an inert (argon) medium. The results of thermogravimetric and differential thermogravimetric analyses were studied by model-fitting (Arrhenius and Coats–Redfern) and model-free (Friedman and Ozawa–Flynn–Wall) kinetic methods. The most reliable values of the activation energy were obtained by the model-free Ozawa–Flynn–Wall and Friedman methods (159 and 156 kJ/mol, respectively). It was shown that using these kinetic models enables one to determine more accurate temperature ranges of decomposition of biomass components under pyrolysis conditions.

Pyrolysis of Mixed Plastic Waste: I. Kinetic Study.

Plastic wastes have become one of the biggest global environmental issues and thus recycling such massive quantities is targeted. Low-density polyethylene (LDPE), high-density polyethylene (HDPE), polypropylene (PP), and polystyrene (PS) are considered among the main types of plastic wastes. Since pyrolysis is one of the most promising recycling techniques, this work aims to build knowledge on the co-pyrolysis of mixed polymers using two model-fitting (Criado and Coats–Redfern) methods. Seventeen co-pyrolysis tests using a thermogravimetric analyzer (TGA) at 60 K/min for different mixed compositions of LDPE, HDPE, PP, and PS were conducted. It was observed that the pyrolysis of the pure polymer samples occurs at different temperature ranges in the following order: PS < PP < LDPE < HDPE. However, compared to pure polymer samples, the co-pyrolysis of all-polymer mixtures was delayed. In addition, the synergistic effect on the co-pyrolysis of polymer blends was reported. The Master plot of the Criado model was used to determine the most suitable reaction mechanism. Then, the Coats–Redfern model was used to efficiently obtain the kinetic parameters (R2 ≥ 97.83%) and the obtained values of the activation energy of different polymer blends were ranging from 104 to 260 kJ/mol. Furthermore, the most controlling reaction mechanisms were in the following orders: First order reaction (F1), Contracting sphere (R3), and then Contracting cylinder (R2).

Isothermal decomposition and mechanism of N-guanylurea dinitramide

The isothermal decomposition of a new material with high energy, namely N-guanylurea dinitramide (FOX-12), was studied by a self-established isothermal decomposition gas metering device. The gas pressure versus time curves of the isothermal decomposition of FOX-12 were obtained at temperature intervals within 120 °C and 170 °C. An extremely long lag phase and acceleration period were found in the decomposition process of FOX-12. The kinetic parameters of FOX-12 were obtained by the Arrhenius equation and model-fitting method. Results of the two methods were consistent, and the activation energy of the acceleration period was smaller than that of the lag phase. With an average Ea of 159.4 kJ mol−1 and lnA of 34.74 s−1 were obtained at the lag phase, whereas an average Ea of 125.6 kJ mol−1 and lnA of 26.97 s−1 were noted at the acceleration period. The model-fitting method further proved that isothermal decomposition at 120–160 °C conformed to no. 28 corresponding to the reaction order n = 1/4, whether at the lag phase or acceleration period. The time required for decomposition was estimated to be 9.8 years when the extent of reaction reached 0.1% at ambient temperature (25 °C). The residual phase after FOX-12 decomposition was analyzed by Fourier transform infrared spectroscopy, and gases were analyzed by gas chromatography, and the possible decomposition process was proposed.

Kinetic study of microwave enhanced mercury desorption for the regeneration of spent activated carbon supported mercuric chloride catalysts

A novel microwave enhanced mercury desorption process was proposed for the regeneration of the spent activated carbon supported mercuric chloride catalysts. The mercury species desorption kinetics were investigated in detail by TG experiments, the overall apparent activation energy of 128.4 kJ/mol, the main reaction activation energy of 95.84 kJ/mol and the adsorption energy of 32.56 kJ/mol were confirmed with the combination of the model-free method and the DMol3 DFT module of Materials Studio package. The thermal desorption of HgCl2 and Hg2Cl2 were mainly between 473 K and 670 K, and the dominant mechanism for the desorption process was determined as second-order-model by the model-fitting method and the Z(α) master-plot method. Furthermore, the microwave enhancement degree of 26.36% was proved by the microwave heating experiment for the mercury desorption within 1500 s at 673 K, and the mercury content was significantly reduced from 19500 mg/kg to 149 mg/kg, which met the requirement of US land disposal restrictions (<260 mg/kg). Moreover, the preliminary activation of the spent activated carbon after microwave heating was demonstrated from the results of XRD, SEM and nitrogen adsorption analysis. Meanwhile, the HgCl2 solution with the concentration of 40–50 g/L could be effectively prepared by the water leaching of the condensate of mercury species, which could be used to regenerate the catalyst by soaking adsorption with activated carbon after microwave heating. Finally, a novel microwave enhanced mercury desorption process was proposed, which can synchronous realize the harmless and recovery of the spent activated carbon supported mercuric chloride catalysts.

Temperature- and heating rate-dependent pyrolysis mechanisms and emissions of Chinese medicine residues and numerical reconstruction and optimization of their non-linear dynamics

The study bases on the pyrolysis characteristic, kinetic, and thermodynamic parameters and evolved gas analysis to quantity Chinese medicine residues (CMR) and uses artificial neural network (ANN) to reconstruct and jointly optimize pyrolysis. The main weightlessness interval of CMR is between 150 and 600 °C including organic matter decomposition. Four model-free methods and one model-fitting method were provided to find function mechanisms and kinetic parameters show it existing kinetic compensation through pyrolysis. TG-FTIR finds the gases and functional groups included CO2, CO, H2O, CH4, CO, CC, and C–O. And the main pyrolytic products were detected included esters, phenols and acids et al. 9-octadecenoic acid (z)-, methyl ester as one of the high quality products was in the highest proportion about 53.75%. The temperature-, heating rate-, and their non-linear dynamics of the multiple pyrolysis response surfaces were reconstructed and jointly optimized using an artificial neural network algorithm. Finally, the study is helpful for Chinese medicine residues high-value utilization.

Improved traceable measurement of the reflected step pressure in shock tube with the compensation of shock wave attenuation

Shock tube is an exceptional valuable facility that can produce approximately ideal step pressure from the reflected shock wave for the dynamic characterization of pressure sensors in aerospace industry. However, the traceable measurement accuracy of the reflected step pressure (RSP) is limited by the inevitable attenuation of the incident shock wave (ISW), leading to the dynamic characterization results with large error. This paper proposes an improved method for achieving high-accuracy traceable measurement of RSP in shock tube with the compensation of shock wave attenuation. The traceable measurement model of RSP relates to the ISW velocity is established firstly based on shock tube theory. To compensate the ISW velocity attenuation, a distributed measurement combined with a non-equidistant fractional-order grey (NFOG) method is implemented to establish ISW velocity model in consideration of the nonlinear, small-sample and non-equidistant features of the velocity sequence obtained by multiple sensors. Meantime, an ergodic optimization method based on a similarity index is adopted to estimate the optimal fractional-order in NFOG. With ISW velocity model, the velocity at the end-wall of shock tube is predicted and then more reliable RSP result is achieved with the traceable measurement model. Four experiments under different shock wave conditions are carried out to verify the proposed method. Results show that NFOG is able to establish the velocity model effectively, and the modeling error is less than that of the non-equidistant grey model and least square fitting methods. Furthermore, the traceable measurement accuracy of RSP by the proposed method is improved significantly than existing methods according to the investigation of pressure sensor sensitivity in both dynamic and static conditions.

On Nonlinear Regression for Trends in Split-Belt Treadmill Training.

Single and double exponential models fitted to step length symmetry series are used to evaluate the timecourse of adaptation and de-adaptation in instrumented split-belt treadmill tasks. Whilst the nonlinear regression literature has developed substantially over time, the split-belt treadmill training literature has not been fully utilising the fruits of these developments. In this research area, the current methods of model fitting and evaluation have three significant limitations: (i) optimisation algorithms that are used for model fitting require a good initial guess for regression parameters; (ii) the coefficient of determination () is used for comparing and evaluating models, yet it is considered to be an inadequate measure of fit for nonlinear regression; and, (iii) inference is based on comparison of the confidence intervals for the regression parameters that are obtained under the untested assumption that the nonlinear model has a good linear approximation. In this research, we propose a transformed set of parameters with a common language interpretation that is relevant to split-belt treadmill training for both the single and double exponential models. We propose parameter bounds for the exponential models which allow the use of particle swarm optimisation for model fitting without an initial guess for the regression parameters. For model evaluation and comparison, we propose the use of residual plots and Akaike’s information criterion (AIC). A method for obtaining confidence intervals that does not require the assumption of a good linear approximation is also suggested. A set of MATLAB (MathWorks, Inc., Natick, MA, USA) functions developed in order to apply these methods are also presented. Single and double exponential models are fitted to both the group-averaged and participant step length symmetry series in an experimental dataset generating new insights into split-belt treadmill training. The proposed methods may be useful for research involving analysis of gait symmetry with instrumented split-belt treadmills. Moreover, the demonstration of the suggested statistical methods on an experimental dataset may help the uptake of these methods by a wider community of researchers that are interested in timecourse of motor training.

Pyrolytic conversion of halophyte (Tetraena coccinea)

Pyrolytic conversion of Tetraena coccinea, a halophilic plant widely found along the coastal belt of the Saudi Arabian Red Sea, was investigated for its bio-energy potential. The kinetic triplets of pyrolysis were estimated from model-free and model-fitting methods using the conversion data obtained under non-isothermal conditions. Activation energies estimated from model-free methods such as Friedman, Flynn-Wall-Ozawa (FWO), and Vyazovkin methods were 96.40 (±14.98), 84.50 (±13.89), and 65.32 (±12.38) kJ/mol, respectively. Combined kinetics and master-plot considering a single-step reaction indicated third (F3) or fourth order (F4) reaction as the most probable mechanism. The differential thermogravimetric profile indicated complex conversion in the active pyrolysis zone. Two subzones in the active pyrolysis region were investigated using the Coats-Redfern method. From 20 to 55% conversion, F4 or diffusion 3-D (D3) reaction were the most probable mechanisms, whereas, during 55–80%, the probability of the F4 reaction mechanism was the most likely. ΔH, ΔG, and ΔS indicated that the conversion process was endothermic and non-spontaneous throughout the conversion range.

Characterization, thermal and kinetic analysis of Pinusroxburghii

Uttarakhand has the maximum potential of pine of about 20 lakh tonnes/year including reserved forests and van panchayat which makes pine needle an abundant resource. The analysis of the pine needles reveals it a potential biomass feedstock for gasification to produce electricity. This manuscript deals with the combustion study of Pine needles (Pinusroxburghii) biomass using a thermogravimetric analyzer to investigate the thermal degradation behavior and kinetic parameters. The pine needles were heated in the presence of air at four different heating rates 5, 10, 25 and 50 °C/min, and the degradation phenomenon was studied. From the proximate and ultimate analysis of pine needles, it was observed that the biomass could be a potential feedstock for gasification. The TG-DTG curves revealed that the main decomposition was between 190 and 450 °C with the release of 80–84% volatiles. It was observed that as the heating rate increases, the maximum decomposition temperature also increases and the peak shifts to the right. The obtained thermal data were used to calculate the kinetic parameters using Kissinger–Akharia–Sunose, Ozawa-Flynn-Wall, Friedman and Kissinger. The average values obtained from the above methods are 190.74, 190.75, 199.48 and 172 kJ/mol and 2.749 × 1022, 5.13 × 1022, 4.21 × 1021 and 4.14 × 106/min, respectively. The model fitting method and Coats–Redfern method were used to determine the kinetic triplet (A, E and n). The above model-free methods and model fitting methods predicts the progress of gasification at different positions along the reactor. Considering proximate analysis and heating value, pine needles could be considered as a potential feedstock for energy production through gasification process. The estimated results help as a source to understand the thermal degradation of biomass during the gasification process and be used to design the systems.

Kinetic analysis of CO2 gasification of biochar and anthracite based on integral isoconversional nonlinear method

AbstractThe nonisothermal thermogravimetric analysis was implemented for gasification of sawdust char (SD-char), wheat straw char (WS-char), rice husk char (RH-char), bamboo char (BB-char) and anthracite coal (AC) in the presence of CO2. The dependence of activation energy upon conversion for different biochars and AC was obtained by the integral isoconversional nonlinear (NL-INT) method which is a model-free method. Based on the activation energy values from the NL-INT method, a model-fitting method called random pore model (RPM) was used to estimate the kinetic parameters including the preexponential factor and pore structure parameter from the experimental data. The results are shown that the gasification reactivity of different samples from high to low can be sorted as that of WS-char, SD-char, BB-char, RH-char and AC. In the early stage of gasification, the activation energy values of biochars increase generally with an increase in the conversion degree, whereas the value of AC decreases. Thereafter, the activation energy values remain almost unchanged when the conversion is up to some extent. When the conversion degree varies between about 0.3 and 0.9, these carbon materials can be sorted in the order of average activation energy from low to high as WS-char, SD-char, AC, RH-char and BB-char, respectively, 134.3, 143.8, 168.5, 184.8 and 193.0 kJ/mol. It is shown that a complex multistep mechanism occurs in the initial stage of gasification, while a single-step gasification mechanism exists in the rest of the gasification process. The RPM is suitable for describing the gasification of biomass chars and AC except the initial gasification. Additionally, it is found that the kinetic compensation effect (KCE) still exists in the gasification reactions of biochars and AC. However, the AC deviates markedly from the KCE curve. This may be caused by the similarity of carbonaceous structure of biochars and the difference in reactivity between biochars and AC.

Isothermal and Non-Isothermal Reduction Behaviors of Iron Ore Compacts in Pure Hydrogen Atmosphere and Kinetic Analysis

This study examines the isothermal and non-isothermal reduction behaviors of iron ore compacts in a pure hydrogen atmosphere and compares the results obtained during the reduction process by CO. The different phases accompanying the reduction reactions were identified using X-ray diffraction (XRD) and its morphology was microscopically examined. In isothermal experiments, temperature plays a significant role in the reduction process. At any given temperature, the reduction rate during the initial stages is higher than that during the final stages. The reduction rate in H2 atmosphere was faster than in CO gas. The comparison of activation energy values suggested that reduction with H2 is more efficient than with CO. At the same temperature, the time required to achieve a certain degree of reduction was lower when using H2 gas than CO atmosphere. In non-isothermal tests, the heating rate has a significant effect on the reduction rate and reduction extent. At the same heating rate, the degree of reduction was higher in H2 atmosphere than in CO gas. Based on experimental data, the parameters of reaction kinetics were deduced by application of model-free and model-fitting methods. The reduction in H2 atmosphere was controlled by nucleation model (Avrami-Erofeev model), while the CO reduction reaction was controlled by gas diffusion.

Combustion characteristics, kinetics and thermodynamics of Pinus Sylvestris pine needle via non-isothermal thermogravimetry coupled with model-free and model-fitting methods

The combustion characteristics of Pinus Sylvestris pine needle are studied employing thermogravimetric analysis in air. Kinetic and thermodynamic analyses are performed using two model-free methods and one model-fitting method. Results indicate that two peaks and two shoulders occur in the variations of reaction rate with conversion rate. The maximum and average values of reaction rate decrease with heating rate. The combustion process can be divided into three stages with the thresholds of conversion rate α = 0.15 and 0.75. The average values of activation energy/pre-exponential factor for stage 1 (0 = α ≤ 0.15), stage 2 (0.15 < α < 0.75), stage 3 (0.75 = α ≤ 1) and the entire combustion process are 163.18 kJ/mol/9.55 × 109 min-1, 166.46 kJ/mol/2.13 × 109 min-1, 132.09 kJ/mol/5.67 × 106 min-1 and 156.89 kJ/mol/3.89 × 109 min-1, respectively. The reaction model characterizing stage 1, 2 and 3 is A1/3, A1/4 and F3, respectively. The obtained kinetic parameters can be used to acceptably predict the conversion rate data. The variations of the change in enthalpy (ΔH), Gibbs free energy (ΔG) and entropy (ΔS) with α indicate that more favorable reactions occur and more homogeneous or well-ordered products are generated with the progressing of combustion. Besides, the average values of ΔH, ΔG and ΔS vary little with heating rate.

Shear measurement bias

We present a study of the dependencies of shear bias on simulation (input) and measured (output) parameters, noise, point-spread function anisotropy, pixel size, and the model bias coming from two different and independent galaxy shape estimators. We used simulated images from GALSIM based on the GREAT3 control-space-constant branch, and we measured shear bias from a model-fitting method (GFIT) and a moment-based method (Kaiser-Squires-Broadhurst). We show the bias dependencies found on input and output parameters for both methods, and we identify the main dependencies and causes. Most of the results are consistent between the two estimators, an interesting result given the differences of the methods. We also find important dependences on orientation and morphology properties such as flux, size, and ellipticity. We show that noise and pixelization play an important role in the bias dependencies on the output properties and galaxy orientation. We show some examples of model bias that produce a bias dependence on the Sérsic index n as well as a different shear bias between galaxies consisting of a single Sérsic profile and galaxies with a disc and a bulge. We also see an important coupling between several properties on the bias dependences. Because of this, we need to study several measured properties simultaneously in order to properly understand the nature of shear bias. This paper serves as a first step towards a companion paper that describes a machine learning approach to modelling shear bias as a complex function of many observed properties.