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Two nodes numbered 1857 and 23950 located on the fringe of protruding column and bottom of casting, where the heat dissipates quickly.
Fig.5 Temperature field distribution of casting system 1800s after pouring Simulation of Grain Structure Mathematical Model of Grain Structural Feature Values.
Rappaz firstly suggested that nuclei of crystal arise at different positions during heterogeneous nucleation which accord with statistic laws, and that a number of nucleation position should be activated under each supercooling degree ∆T.
The grain feature values of measured and simulated are listed in Table 1.
Fig.6 The factual grain structure and simulation result around node 1857 Fig.7 The factual grain structure and simulation results around node 23950

Comparison between the growth behaviour of the small Goss grains and that of the large matrix grains in silicon steels.
The growth of a given grain depends on the evolution of its surrounding grain boundaries and not the average evolution of the whole matrix, the mean parameters of the matrix can hide the effect of the real neighbourhood for a grain located in a textured cluster.
-a- -b- -c- Fig.4: Spatial distribution of grains with orientation A (-a-), orientation (-b-) and other orientations (-c-) Figure 4 shows the spatial distribution of grains A, grains B and random grains corresponding to {200} pole figures of the figure 3.
It can be confirmed that the grains A form clusters, whereas the distribution of the other grains is more homogeneous.
A site is not characterized by an orientation number, but by a triplet (φ1, φ, φ2) in the Euler orientation space, the grain orientations are not random.

The average value of the total misorientation over one sample was increased with the number of cycles.
Number of cycles 0 200 400 700 Average of β (deg.) 0.53 0.58 0.59 0.62 Table 3.
The fatigue tests were interrupted and DCT imaging was conducted after certain numbers of cycles.　
In either table, the number of cycles indicated in the last column is just before the fracture of specimen.
It is obvious that the values are increased with the number of cycles, suggesting that the dislocation density increased with number of cycles.

Experimental Procedures Workpiece materials and grain structures.
The milling tool used in this study was carbide cutter which diameter of the end mill was 12 mm and number of tungsten carbide inserts in the cutter was 4.
In experiment, we found that the length of chip became shorter as the grain size of specimen increases, which may be attributed to heterogeneous deformation in specimen with coarse grains.
The grain shapes in specimens with large grains such as specimen 1# and 2# are branch-like or dendrite, whereas the grain shapes in specimens with fine grains such as 5# and 6# are globular, which can be seen in figure 3.
The increase of strength of materials will increase cutting force, but the key point of questions is that what extent of grain refining can bring rising to cutting force, which is needed deeper research works. 1 2 3 4 5 6 0 200 400 600 800 1000 1200(a) Milling force,* Specimen number Main milling force Radial milling force 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 200 400 600 800 1000 1200 1400(b) Main milling force Radial milling force Milling force,* Average grain size,mm Fig. 2 The relationship between milling force with grain size of specimen (a) The testing results of main milling force and radial force (b) The variation of main milling force and radial milling force with grain size of specimen Fig. 3 Microstructure in as-cast workpieces of Inconel 718C (a) lengthened dendrite in specimen 1# (b) uniform equiaxed grains in specimen 5# In order to understand the relationship between the grain size and cutting force,

ρ can be determined from the number of effective grains Nt divided by the evaluation area Ae.
When t is determined, Nt can be calculate from the distribution Ng(h) as the number of grains existing within the range from the most periphery to the depth of t (h=0～-t).
The highest points of the grains exist within the width of the average grain diameter d0 centered with the measuring line.
On the other hand, since the number of peaks is same as that of grains, the overall frequency is also same for both distributions.
(3) Since the estimated grain-height distribution agreed well to the distribution determined from the 3D-topography, the validity of the method has been confirmed. 0.3 0.2 0.1 0.48 0.24 0 -40 -30 -20 -10 0 10 20 30 Height μｍ Direction of wheel axis mm Direction of wheel circumference mm width -120 -100 -80 -60 -40 -20 0 20 0 100 200 300 400 500 600 Height μｍ Frequency Peak height distribution Grain height distribution Peak-height distribution Grain-height distribution Depth μm Frequency 0 1 2 3 4 5 6 7 8 9 10 11 12 0 5 10 15 20 25 Actual cutting-edge density Cutting-edge density Effective thicknee μm Density number/mm2 ρ　1/ｍｍ2 ｔ μm Acknowledgment A part of this study has been supported by a Grant in Aid for Scientific Research (Year: 2008, Science Research (C), Subject number: 20560112) from the Japan Society for the Promotion of Science.

Grain growth is the coarsening process in which curvature-driven motion of grain boundaries leads to elimination of grains and increasing average grain size.
The anecdotal nature of the demonstration in Fig. 2 needs to be extended to statistically significant numbers of occurrences of each of the phenomena mentioned as well as to other materials.
These numbers translate to 1.2 x 106 voxels in the current data to as many as 3 x 107 voxels.
While optimized meshes can reduce these numbers by using larger voxels in regions of uniform orientation, the numbers are still daunting for finite element and other modeling efforts.
This work was supported in part by the Metals and Nano-Structures program of the National Science Foundation under award number DMR-0805100 and in part by the MRSEC program of the National Science Foundation under Award Number DMR-0520425.

It was found through experiment that, the grain was very coarse in the cast ingot of 5N5 high pure aluminum, and the average grain size is about 50~60mm.
The grains are very coarse, and the average grain size is about 50~60mm.
We can see the presence of a large number of dislocations and the dislocation has occurred tangles, and has formed cellular sub-structures.
The dislocation inside the sub-grains significantly reduced.
(3) The large number of dislocations can be observed in the sample applied 1 pass extrusion.

The transition probability from one orientation number to another is given by: T (8) where is the energy change.
To test the model, the problem has been simplified by considering Goss grains (G) (gray grains) in an isotropic matrix of (M) grains.
Conclusion The onset of abnormal grain growth of Goss grains can be linked to the preferential interaction between particles and grain boundaries.
AGG occurs only when normal grain growth is pinned for Goss neighboring grains.
The large size grains resist AGG and the Goss grain shape becomes anisotropic.

The built tool can operate real-time and fine-grained monitoring.
In other words, they offer coarse-grained network monitoring.
Then reading kernel data in Proc Interface module, Kernel module can get all open port numbers and the corresponding inode numbers.
At this point, from the correspondence of specified process inode numbers with system-open port inode numbers, we can get the correspondence of specified process with port numbers.
It verifies that the software achieves real-time online as well as fine-grained network monitoring.

The mechanism of the MgAlON grains to generate Joule heat was the same as Al grains.
So each grain would form 12 necks.
So, (4) According to geometrical rules, the relationship of r2 and r1 could be expressed by: (5) Based on formula (3) to formula (5), the relationship of h and r1 was: (6) (a) (b) Fig. 2 Schematic diagram of the necks formed between grains: (a) Diagram of 12 coordination number of CPH; (b) Diagram of the necks formed between grains Computing results and analysis Influence of Joule heat on the temperature distribution in Al grains.
In view of process control, if I and B remained unchanged, the contact point number and the heating rate of samples would increase with the particle size decreasing.
The heating and melting process in Al grains would further promote the contact point number increasing and samples heating rapidly, so the materials’ structure and property would be regulated and controlled.