Green and short preparation of CeO₂ nanoparticles with large specific surface area from rare earth extraction (CeCl₃) was successfully achieved by spray pyrolysis (SP). In this method, a precursor solution is first prepared by mixing CeCl₃, C₆H₈O, and H₂O in the requisite quantities. Subsequently, the precursor consisting of a mixture of CeO₂ and C was obtained by SP method by using the precursor solution. Finally, the calcination at 500 °C~800 °C in air for two hours to transform the precursor to CeO₂ nanoparticles. Thermodynamic analysis and experimental studies were performed to determine the optimal SP temperature and citric acid amount. The results indicated that the maximum specific surface area (59.72 m²/g) of CeO₂ nanoparticles were obtained when the SP temperature was 650 °C and the molar ratio of citric acid to CeCl₃ was 1.5.

MILD oxy-fuel combustion has become the subject of study as it can improve the combustion efficiency and reducing the emission of harmful gases. However, there are few researches on the vortex motion of Oxy-fuel combustion, and there is no clear definition for the application of gas vortex. In this paper, based on the experimental and simulation data of the heating furnace, the distribution of eddy motion was analyzed from aspects of the turbulent vortex formation, formation, and movement of the vortex. In this paper, the vortex structure of the furnace is analyzed by using the Q criterion, ${\lambda }_2$ method, and $\mathrm{\Omega }$ method. We found that both Q criterion, ${\lambda }_2$ criterion, and $\mathrm{\Omega }$ method could identify the vortex structure in the furnace, but $\mathrm{\Omega }$ method could identify the vortex structure that could not be identified by the other two methods. $\mathrm{\Omega }$ could display more vortex structures and could identify both weak and strong vertices, with stronger recognition ability.

Hyperparameter tuning is crucial in the development of machine learning models. This study introduces the nonlinear shrinking factor and the Cauchy mutation mechanism to improve the Dujiangyan Irrigation System Optimization (DISO), proposing the improved Dujiangyan Irrigation System Optimization algorithm (IDISO) for hyperparameter tuning in machine learning. The optimization capabilities and convergence performance of IDISO were validated on 87 CEC2017 benchmark functions of varying dimensions and nine real-world engineering problems, demonstrating that it significantly outperforms DISO in terms of convergence speed and accuracy, and ranks first in overall performance among the seventeen advanced metaheuristic algorithms being compared. To construct a robust and generalizable prediction model for hydrochar element characteristics, this study utilized IDISO and DISO algorithms to fine-tune the parameters of the XGBoost model. The experimental results show that the IDISO-XGBoost model achieved an average prediction performance of 0.95, which represents a 4% improvement over the DISO-XGBoost model. These results indicate that the IDISO algorithm has significant potential and value in practical applications.

Molten salt electrolysis stands as an indispensable technique for the production of rare earth metals, where the judicious distribution of the electric field within the electrolytic cell is paramount for ensuring the seamless operation of the electrolysis process. This study introduces a pioneering approach by integrating the Nernst-Planck equation with the Butler-Volmer equation, thereby devising a holographic electric field model tailored for the electrolysis of the NdF3-LiF molten salt system. The paper presents pioneering experimental measurements concerning the potential distribution and voltage drop characteristics within a 6kA rare earth electrolytic cell, elucidating the interplay between decomposition voltage and current density, which substantiates the model's precision. Our findings unveil that, under operational conditions of 4010 amperes, the 6kA electrolytic cell incurs a total voltage drop of 6.3 volts, delineating a melt voltage drop of 4.43 volts, an ohmic voltage drop of 0.248 volts, and an interfacial voltage drop of 1.622 volts at the electrode-electrolyte junction. The discrepancy in error is confined to within 0.3% of the actual measured voltage of 6.28 volts.The simulation outcomes from the holographic electric field model have been confirmed to precisely and comprehensively reflect the characteristics of the electric field distribution during the rare earth molten salt electrolysis process, offering valuable theoretical insights for practical manufacturing applications.