13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Normalized distance, X The rate of atom density change, Di L G 0 0.2 0.4 0.6 0.8 1 -0.08 -0.06 -0.04 -0.02 0 Figure 7. Definition of disordered regions of super atoms Number of super atoms, N Length of disordered region of super atoms, L,G L(Direct) L(Verlet) G(Direct) G(Verlet) 10 100 1000 10000 0 0.1 0.2 0.3 0.4 0.5 Number of super atoms, N Length of disordered region of super atoms, L,G L(Direct) L(Verlet) G(Direct) G(Verlet) 10 100 1000 10000 0 0.1 0.2 0.3 0.4 0.5 Number of super atoms, N Length of disordered region of super atoms, L,G L(Direct) L(Verlet) G(Direct) G(Verlet) 10 100 1000 10000 0 0.1 0.2 0.3 0.4 0.5 (a) Condition 1 (b) Condition 2 (c) Condition 3 Figure 8. Plots of the length of disordered regions of super atoms vs. the number of super atoms on each condition 4. Considerations These fractal analyses show that self-similarity of the distribution of super atoms is considered to be held when N is larger than Nc (Nc = 250). Using this property and projection approach, it becomes possible to predict the actual arrangement of atoms. The region of analysis is assumed to be the average value of experimental values of trigger point for Ni-Cr-Mo-V steel, that is, 10 ~ 210 μm [10]. When actual distance between neighboring atoms is assumed to be 0.3 nm, the number of atom, N is considered to be 3×105. Based on Fig. 8, values of L and G at N = 3×105 were predicted as shown in Table 2. Table 2. Disordered region at N = 3.0×105 Direct method Verlet method Condition 1 Condition 2 Condition 3 Condition 1 Condition 2 Condition 3 L 0.238 0.384 0.0 0.211 0.359 0.0 G 0.203 0.062 0.398 0.183 0.055 0.420
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