## 3 Result  
### Three-Dimensional and Two-Dimensional Mapping of Amount of PM Remaining  
Figure 7 shows the dependence of the regeneration condition. The \(x\)-axis shows the activation energy. The \(y\)-axis shows the exhaust gas temperature. The \(z\)-axis shows the remaining PM per unit deposited, including the space. The PM sedimentation quantities showing the relationships of the remaining amounts are (Figure 7a-d) 1 g, 10 g, 20 g, and 30 g. The remaining amount of PM according to each condition is shown in the field; when the remaining amount of PM is large, it is shown in red, and when the remaining amount is small, it is in blue.  
Figure 8 shows that when the amount of PM deposited is as low as 1 g, the amount of PM remaining is low when the activation energy is low (Figure 8a). For \(E\) = 90 and 100 kJ/mol, the amount of remaining PM is 0.5 g or less even at 600 \({}^{\circ}\)C. On the other hand, when the activation energy is 120 kJ/mol or more, the residual amount of PM is 0.5 g or more. However, when the temperature becomes 700 \({}^{\circ}\)C or more, the remaining amount of PM in all conditions becomes 0.5 g or less. Similarly, when the PM deposition amount is 10 g, the remaining amount of PM when the activation energy is low (Figure 8b). When the activation energy is 90 kJ/mol at 650 \({}^{\circ}\)C or higher, the remaining amount of PM becomes 0.5 g or less. However, when the activation energy is 120 kJ/mol, the residual amount of PM does not become 0.5 g or less unless the condition is 750 \({}^{\circ}\)C or higher. The behavior is almost the same when the activation energy is 140 kJ/mol or more. When the amount of PM deposited is as large as 20 g or 30 g, the condition becomes more severe (Figure 8c,d). When the activation energy is \(E\) = 90, the remaining amount of PM becomes 0.5 g or less at 650 \({}^{\circ}\)C or higher. However, it has been found that about 700 \({}^{\circ}\)C is required when the activation energy is 100 kJ/mol, and about 800 \({}^{\circ}\)C is required when the activation energy is 120 kJ/mol. In addition, in the case of low temperature, the remaining amount of PM was very large, 10 g or more. This is because the action of the catalyst supported on the DPF is effective only for the PM in direct contact. In the case of a large amount of PM, all of the PM is not in direct contact with the catalyst. When the amount of PM deposited is large, most of the PM becomes a reaction in the gas phase. Thus, the higher the temperature, the better  
the combustion rate of the PM. Conversely, when the amount of PM deposited is small, the catalyst and most PM come into contact. In this case, the combustion efficiency of the PM is good when the activation energy of the catalyst is low even at a low temperature. In other words, we found that the catalyst is effective when the amount of PM deposited is small.  
These results can evaluate the activities of the catalysts used to the fullest extent, for example, when the conditions are \(E\) = 120 kJ/mol, \(T\) = 800 \({}^{\circ}\)C, and the amount of PM deposited = 20 g. In order to lower the exhaust temperature by 100 \({}^{\circ}\)C compared with the catalyst-free catalyst, it is more effective to select a catalyst with an activation energy of less than 100 kJ/mol. Using the 3D map and 2D map proposed by us, we can investigate the activity of the catalyzer and the remaining amount of PM-burned gas that is provided by the exhaust gas temperature.  
Figure 7: The left side of (**a–d**) shows the dependence of regeneration conditions on the DPF with the catalyst. The \(x\)-axis shows the activation energy. The \(y\)-axis shows the exhaust gas temperature. The \(z\)-axis shows the remaining PM per unit deposited, including the space. The PM deposition amounts 1 g, 10 g, 15 g, and 20 g in relation to (**a,b,c,d**).