Numerical Simulation of Convection-Diffusion Phenomena by Four Inverse-Quadratic-RBF Domain-Meshfree Schemes

The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection-diffusion problems numerically and to choose the optimal shape parameter of radial basis functions. The modified numerical scheme is tested on a benchmark problem with varying shape parameters. The root mean square error and maximum error are used to validate the accuracy and efficiency of the method. The proposed method can be a good alternative to the radial basis function collocation method to improve accuracy and results.

In this study, an ultrasound-assisted extraction (UAE) method combined with ion chromatography (IC) was developed, optimized and validated for the determination of benzoate in Northern Thai green chili dip. Four extraction variables were optimized using response surface methodology (RSM) based on a Box–Behnken design (BBD). The optimal conditions were a sample mass of 5.0 g, water volume of 20.0 mL, extraction temperature of 70 °C, and extraction time of 20 min. The validated method showed good linearity in the range of 0.5 to 100 mg L⁻¹, limits of detection (LOD) and quantification (LOQ) of 0.305 and 1.070 mg L⁻¹, respectively, precision in the range of 0.31 to 6.37% (%RSD, n = 11), and spiked recovery in the range of 85.50 to 107.80%, all of which were within the acceptable criteria. The AGREE score of the developed method was 0.45, which was higher than that of the conventional LLE-HPLC-UV method (0.27) due to the use of only deionized water as the extracting solvent and no generation of organic waste. The developed method was sensitive, validated, and environmentally friendly, and was successfully applied to the determination of benzoate in traditional condiment products. The proposed method may serve as an alternative approach for routine food analysis and quality control.

It is known that all RBF-based meshfree methods suffer from a lack of reliable judgment on the choice of shape parameter, appearing in most of the RBFs. Many attempts on providing promisingly useful information on how to define this parameter have been made during the part years. Nevertheless, it is known that it is practically impossible to have one form of parameter that yields reasonable results for all kinds of problems. In this work, we aim to complete three important tasks. Firstly, we apply the methodology of RBF-collocation method, one of the classical form of meshfree/meshless schemes to PDEs with nonlinear nature. Secondly, several forms of variable Multiquadric shape parameters proposed and those available in literature have been gathered and applied to the same type of PDEs. Lastly, we propose a new form of shape parameter under the form of inverse-multiquadric type of RBF. In order to justify the quality of our proposed variable, all forms gathered from the literature are applied to the same PDEs, and all the results are compared against one another. The information gathered and presented in this work shall be useful for the future users in making decision and will provide useful guide to further invent another potential shape adaptive approaches as well.

Torrefaction has emerged as a promising thermochemical pretreatment to enhance the fuel properties of agricultural biomass, yet predicting product characteristics remains challenging due to feedstock variability. This study developed and compared four machine learning (ML) models, support vector regression (SVR), artificial neural network (ANN), gradient boosting machine (GBM), and random forest (RF), to predict the higher heating value (HHV), mass yield (MY), and energy yield (EY) of torrefied biomass. A comprehensive dataset comprising 117 experimental samples from 11 biomass types torrefied at 200–280°C for 20–60 min was utilized. Input variables included the contents of proximate composition (ash, fixed carbon, and volatile matter), ultimate composition (C, H, N, O, S), and process conditions (temperature and residence time). SHapley Additive exPlanations (SHAP) analysis revealed that torrefaction temperature was the most influential parameter, followed by volatile matter and ash content. Results demonstrated that GBM consistently outperformed the other models, achieving an acceptably high coefficient of determination, with minimal prediction errors across different input configurations. Notably, simple proximate‐analysis data provided performance comparable to that of more detailed and instrument‐intensive ultimate analysis (UL), highlighting the practical value of GBM for operators handling diverse biomass feedstocks with limited access to specialized analytical instruments.