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Numbers of grains in all Ac area are enough to evaluate the structures.
This feature is not affected by the number of grains or quenching times.
Table 3 Ratio of the Betti number b1 to number of grains.
This means the b1 represents number of grains.
It was concluded that the Betti numbers were strongly correlated to number of grains.

The selector of block and spiral were tested to determine the grain size and the number of grains.
The initial number of nucleation was about 38,000.
However, through competitive growth of 4mm, the total number of grains was reduced by an order of magnitude to 3,440, and the grain density has been reduced to 34 /mm2.
Entering the pig tail of the selector, the grain number was in order of 102, and the mean size of grain was in order of 10-1.
The results showed that the number of grains decreased roughly linearly as the distance to the water-cooling chill increased.

.% Ni Alloy in the Ultrafine-Grained State after Multiple Martensitic Transformations with a Large Number of Cycles Anna Churakova1,2,a*, Dmitry Gunderov1,2,b 1Institute of Molecule and Crystal Physics, Ufa Federal Research Center of the Russian Academy of Sciences, 151 pr.
The microstructure и mechanical properties of the ultrafine-grained Ti–50.8 at.% Ni alloy after thermal cycling treatment with the number of cycles up to 250 was investigated.
The number of thermal cycles ranged from 0 to 250.
With increasing number of TCT cycles grains with non-equilibrium boundaries are observed, indicating a highly defective structure (Figure 2).
The average size of microdimples decreases with increasing number of thermal cycles.

We grouped and correlated the data to Mendeleev number.
The idea is that the periodic table of elements can be ordered in two ways, either as the usual ordering by ascending atomic number Z equal to the number of all electrons, or in the vertical ordering using MN [10], which takes into account the fact that the chemical bonding mainly depends on the number of outer electrons.
Figure 1 Strength of embrittlement on x-axis versus the Mendeleev number MN for segregation of foreign atoms at (a) Ni, (b) Fe grain boundaries.
Figure 2 Segregation energies on x-axis versus the Mendeleev number MN for segregation of foreign atoms at (a) Ni, (b) Fe grain boundaries.
Figure 3 Logarithm of solubility at 800K of foreign atoms in Ni versus (a) the Mendeleev number MN, and (b) versus the segregation energy at grain boundaries E_GB.

The number of active grains was determined by counting the high frequency impulses in the measured temperature signals.
So the number of grains per unit length of wheel surface is 1 mm66.1N − = .
The number of polished grains could be calculated (about 3.31 2 mm− ) by counting out the number of light reflecting areas from microscope photos.
So the number of active grains was always less than the theoretic grains [7].
The ratio of active grain to theoretic number was thg n/n=η .

Although the number of triple junctions is of the same order of magnitude as the number of grain boundaries, the kinetic behavior during grain growth is usually only attributed to grain boundary kinetics.
This increase was due to a change of the number of triple junctions of the grain.
First the grain had n = 4 triple junctions but after some time the number decreased to n = 3, and the velocity of the triple junction increased.
At 300 C the angle decreased towards the end of the measurement owing to the change in the number of sides of this grain as mentioned above.
The rate of the grain area change dS dt was measured in the current experiment for a number of grains with a different number of sides n (topological class of the grain) from n=3 up to n=10 (Fig. 4).

Based on the observation that the ratio of the perimeter, P, to the square root of the area, A 0.5, of the grains for a given material is nearly constant, it is suggested that the grain shape may be treated as a regular polygon with a non-integral side number.
It was found that, for a given material, the ratio of the perimeter, P, to the square root of the area, A 0.5, of the real grains is nearly constant, implying that the grain shape may be treated as a regular polygon with a non-integral side number.
Since the P/A 0.5-ratio keeps constant for a given sample despite of the large variations in the area and the perimeter of the grains, we may reasonably treat the grain shape in a given material as a regular polygon with a non-integral side number of n.
Note that the P/A 0.5-ratio is a decreasing function of the side number, n.
This seems to indicate an imaginary regular polygon with the side number of n = 4.46 is the most stable grain configuration for the system we examined.

Figure 1 (a)-(c) show the influence of several Mach number ,,,, and respectively for (a) screened potential, (b) wake potential, and (c) total interaction potential between two dust grains as a function of with and .
From Fig. 1 (a), we can see that screened potential will increase with the Mach number, while the oscillation frequency of wake potential will decrease with the increasing of Mach number from Fig. 1.
The influence of different Mach numbers on (a) screened potential, (b) wake potential, and (c) total interaction potential between two dust grains as a function of with and .
Fig.2. 3D profiles of wake potential Effects of wake potential between two dust grains for diferent Mach numbers (a) , (b) , and (c) with Conclusion Using the linearized hydrodynamic model in conjunction with the Poisson equation to describe the characteristics of the interaction potential between two dust grains embedded in a flowing plasma.
Numerical results show that the Mach number is a very important factor in describing the interaction among the grains, in such a manner that the wavelength of the oscillating potential increases, while its amplitude decreases, along with the increasing of Mach number.

When the surveyed intercept numbers of WC grain exceeded 200, the statistic data for the mean grain size of WC were reproduced.
The well-defined second electron (SE) images for the microstructure of WC-10Co alloys were obtained by high resolution Philips XL30 S-FEG field emission scanning election microscope (FESEM) when magnification was equal or higher than 100,000: Fig. 1 Typical SE image of nano-grained WC-10Co alloy by FESEM According to the counted number of WC grains, 3 to 10 mages were taken at different positions on the samples.
Values [nm] 108 105 93 109 Counted numbers 438 247 270 207 It is easy to measure and count the intercept of WC grain on the polished surface of WC-Co cemented carbides, but in the case of WC with a multifaceted crystal in 3D space, the reproduction of evaluated data is related to the counted number of WC grains.
Table 1 also illustrates that the data have desirable representation if the evaluated number of WC grains is over 200.
When the surveyed intercept numbers of WC grain on randomly settled testing line exceeds 200, the statistic datum for the mean grain size of WC can be easily reproduced. 3.

A number q of orientations was randomly located for each grain where 1≤ q ≤ qmax.
Grain area was computed by the number of cells inside this grain.
The average grain size was calculated by dividing the sum of all grains areas by the number of the grains in each CA step.
Average grain size (number of cells) as a function of CA steps.
Number of grains in simulation region via CA steps.