## 4 Summary and Conclusions  
We investigated the processes of PM deposition and oxidation within a DPF using a catalyst through numerical calculations. Both 3D and 2D mapping were employed to visualize the results. This study analyzed the remaining PM amount and pressure loss in the DPF under varying activation energies and exhaust gas temperatures for different catalysts. Based on these findings, the correlation between exhaust gas temperature and activation energy for PM combustion catalysts was mapped and is outlined below.  
1. The relationship between the exhaust gas temperature and the activation energy for the PM combustion catalyst was mapped. These results can evaluate the activities of the catalysts used to the fullest extent. We suggest that the optimum conditions may differ depending on the PM combustion catalyst used.
2. When the amount of PM deposited is low, the catalytic reaction plays a more significant role. To maximize catalyst efficiency, it is preferable to perform regeneration with a smaller PM accumulation. Conversely, when the PM deposition exceeds approximately 20 g, gas-phase reactions become more dominant than direct catalytic contact. Additionally, the results indicate that pressure loss increases regardless of activation energy when a large amount of PM is present. To minimize pressure loss even under high PM accumulation, maintaining the exhaust gas temperature within a range of  
Figure 12: The dependence of the remaining PM amount on activation energy after 5400 s of regeneration at an exhaust gas temperature of 700 \({}^{\circ}\)C. The red line corresponds to a PM deposition of 1 g, the blue line represents 10 g, the green line indicates 20 g, and the yellow line denotes 30 g.  
Figure 13: The relationship between activation energy and the remaining PM amount after 5400 s of regeneration at an exhaust gas temperature of 800 \({}^{\circ}\)C. The red line represents a PM deposition of 1 g, the blue line corresponds to 10 g, the green line indicates 20 g, and the yellow line denotes 30 g.  
700 to 750 \({}^{\circ}\)C is recommended. Furthermore, it was observed that when a catalyst is applied, regeneration time at elevated temperatures (above 650 \({}^{\circ}\)C) can be reduced.
3. The study also revealed that lower activation energy enhances PM combustion efficiency at high exhaust gas temperatures. This suggests that higher temperatures expand the effective range of catalytic activity. A threshold for catalytic efficiency was identified between activation energies of 100 and 120 kJ/mol.  
By utilizing the 3D and 2D mapping techniques developed in this study, the catalytic activity and the remaining PM after combustion can be evaluated as a function of exhaust gas temperature. The results provide valuable insights for optimizing the design of DPF systems incorporating catalysts.  
Conceptualization, M.N., K.Y. and M.O.; Methodology, M.N., K.Y. and M.O.; Software, K.Y.; Formal analysis, M.N.; Writing--original draft, M.N.; Writing--review & editing, M.N. and M.O.; Visualization, M.N.; Supervision, M.N. and M.O. All authors have read and agreed to the published version of the manuscript.  
This work was supported by JSPS KAKENHI, Grant Number 20K04325, and the Creation of Life Innovation Materials for Interdisciplinary and International Researcher Development of the MEXT.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
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