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Such a computing mode of grain growth is in good agreement with practical situations of ceramic grain growth.
Moreover, each process gets an exclusive ID (rank), numbered from 0 at the beginning of running an MPI program.
After growth times exceed 400, the total number of atoms is nearly kept at a stable level.
Sp = Ts/Tp (1) fp = Sp/p (2) where p is the number of nodes, Tp is the time in a PC cluster and Ts is the time in a single PC.
Thus, with an increasing number of PCs, the evolution of grain growth is greatly accelerated and the time for the parallel simulation is significantly reduced.

The grain size is enlarged with increasing Bi addition; while the number and size of the pores are decrease.
Further increase in Bi addition up to 1 mol % (S3) leads to the following; slight increase in the grain size, the average size of the white batches decreases, while the number of these batches increases.
In case of higher Bi content S2, S3 the probability of reaction (1) decreases to avoid large number of the negatively charged V"zn and instability of the grain, while the probability of the following reaction (2) increases.
The decrease of Eo is attributed to the decrease in the number of grain boundaries as a result of increasing the grain size Fig. 2.
Consequently the decrease in the number and size of the pores with Bi addition means decrease in the amount of the liberated oxygen, so probability of reaction (1) and the number of V"Zn.

However, the intensity of shear texture components decreased with increasing number of ECAR passages.
Observations by TEM and EBSD revealed that the degree of misorientations within the deformed grains increased with increasing number of ECAR passages.
The annealed sheets comprising of ultra-fine grains were successfully produced in the samples deformed by a large number of ECAR passages.
The new isolated grains developed frequently at prior grain boundaries.
With increasing number of ECAR passages, the further decrease in grain size was not pronounced.

As presented in Fig. 3, the number of δ phase decreases with increasing Mo addition in the range of 2.80% - 4.00%, while the Mo-bearing phase increases in the range of 5.50% - 7.50% Mo addition.
Compared with Fig. 3(c) and (d), the grain does not grow in both alloys at 1000°C, as shown in Fig. 5(a) and (c), and the number of Mo-bearing phase decreases obviously in 5.50% Mo alloy but decreases slightly in 7.50% Mo alloy.
Though the number of the Mo-bearing phase significantly reduces in 7.50% Mo alloy after solution treatment at 1050°C, the grain size changes little, as shown in Fig. 5(d).
When the temperature is raised to 980°C, the number of δ precipitates declines and the pinning force reduces during the grain boundary migration.
The number of Mo-bearing phase reduces gradually in the 5.50% Mo alloy, as shown in Fig. 3(c) and Fig. 5(a), as the solution temperature is 1000°C.

However, for the case of the thin film sample, the larger number of triple junctions allowed a more detailed analysis to be performed.
The resultant system of linear equations for all the triple junctions in the dataset is solved using a statistical multiscale method, described in detail elsewhere.[4-7] For the cube-textured Al foil, the number of triple junctions analyzed was 297.
This reduced the number of triple junctions analyzed from 8694 to 7367.
Table 1 - Annealing time, mean grain size (equivalent circular diameter), standard deviation in grain size, and number of grains measured for 100 nm-thick Al films annealed at 400 °C.
Support from the MRSEC program of the National Science Foundation under award number DMR-0079996 is gratefully acknowledged.

�umerical Models and Results Observation of Grain Boundary.
In order to investigate the transition of the number of lattice defects during the deformation, the number of atoms with centro-symmetry parameter greater than 0.25 for each entire model region is plotted in Fig. 5.
Although large variation of the number of defects is observed, we can detect the several regions showing the almost constant number of defects after 100000step (after the plastic deformation).
While the number of defects in the model 2 - 4 increases more smoothly than model 1.
Change of the Number of Defects

A number of deformation microstructure maps are developed to aid the discussion.
There are now a large number of research groups and approaches [1-24].
Having said this it must be noted that a number of factors intervene to cause the grain size in reality to exceed the values of those predicted from simple analyses such as those presented here.
Figure 3 shows the time to 50% softening as a function of strain for a number of different steels and deformation conditions.
Figure 4: Variation of average recrystallized grain size for IF grade with strain at s/1=ε& and 900°C Dynamic Strain Induced Transformation A number of groups have shown the potential for dynamic strain induced transformation to refine the grain size to around 1µm.

Based on Cellular Automata method, combining the laboratory triaxial tests of coarse-grained soil developed the HHC-CA model which generated the coarse-grained soil samples of different initial fabric of grain to characterize the heterogeneous and random distribution of coarse-grained soil grain group.
When the cellular state was zero, the total neighbor cellular numbers with similar state will be calculated.
Num_1 is representative of the total number of neighbor cellular whose state is 1, Num_2 is representative of the total number of neighbor cellular whose state is 2.
To compare Num_1 with Num_2, the central center has the evolution trend to the cellular of big number, its probability of evolution is Max (Num_1, Num_2) × 0.125.
For obtaining the gravel contents of shear band, the article generated the total cell N (the HHC-CA model unit numbers) and displayed the ID number of grid to use the FLAC3D in the triaxial simulation test, and then inducing the producing grid image into Autocad and setting the shear band.

During evolution, a grain boundary or a grain may shrink and disappear.
Our objective is to discuss the histogram of the grain boundary character distribution, which we define here as the relative arc length corresponding to a given α, Journal Title and Volume Number (to be inserted by the publisher) 3 versus α.
We form a histogram of the arc-length corresponding to the collection of numbers α = θ − ω, θ - ω*, where the orientations ω, ω* are assigned randomly at the beginning of the simulation.
Journal Title and Volume Number (to be inserted by the publisher) 5 1.001 1.005 1.009 1.013 -0.80.80.80.8 -0.40.40.40.4 0000 0.40.40.40.4 0.80.80.80.8 αααα, radians Energy, ϕϕϕϕ(αααα) (a) 0.5 0.6 0.7 0.8 0.9 -0.8 -0.4 0 0.4 0.8 αααα, radians f(αααα) (b) Figure 3.
In three dimensional systems, there are five independent parameters and the average number of neighbors each grain has increases by more than a factor of two.

In the present 3D simulations the number of MCUs are 200200200 ×× .
Figure 3: Temporal development of: a - the standard deviation; b - the relative number of grains.
Therefore, the number of grains (cf.
To demonstrate this we have considered the number of neighboring grains s as a function of the relative grain size x of the enclosed grain (cf.
Within this scaling state the average number of faces s of a given grain of size x can be described by a self-similar time-invariant function of the relative grain size (Fig. 4b).