Information Technology Reference
In-Depth Information
1000
800
600
400
200
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Time Steps
Fig. 3.4
The result of diffusion process with the initial value of
u
0
3.6.2 Results for Diffusion
According to the settings of the simulation, we can implement the program under
1,024 possible initial conditions. Since the number of links of
u
i
tends to decrease as
i
becomes large, we pick up a typical result of initial value of
u
i
for
i
¼
0
;
128
;
256
;
384
;
512
;
640
;
768
;
896 and 1
,
024.
Figure
3.4
shows the case of diffusion process with the initial value of
u
0
, which
is the same initial condition of Fig.
3.3
except for the scaling of axis of time steps.
The population grows in the earlier time steps, and reaches the saturation point at
t
1
,
012.
Figure
3.5
shows the case of diffusion process with the initial value of
u
128
. The
population remains 9 or below until the quantum leap of 9-50 at time step 1,030.
The quantum leaps also occur at time step 2,050 (23-259) and 3,073 (564-713).
The population reaches the saturation point at time step 4,085.
Figure
3.6
shows the case of diffusion process with the initial value of
u
256
. The
population remains 1 until the small quantum leap of 1-16 at time step 79. The
critical quantum leaps are observed at time step 5,126 (110-149), 6,146 (201-229)
and 7,169 (654-713). The population reaches the saturation point at time step
8,181.
Figure
3.7
shows the case of diffusion process with the initial value of
u
384
. The
population remains 10 or below until the critical quantum leap of 10-69 at time step
1,025. There is only one quantum leap in the result. The population reach the
saturation point at time step 2,037.
¼
