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The results indicated that irrigated 60 mm each at jointing and heading stages during the winter wheat growing seasons, grain yield was the highest, which could be attributed to significantly (LSD, P<0.05) increase the spike numbers.
Spike number per m2, kernel numbers per spike, and thousand kernel weights were determined.
T3 resulted in the highest grain yield, which contributed to the spike numbers were significantly increased.
Kernel numbers were not significantly different among any treatments.
The result showed that irrigated 60 mm each at jointing and heading stages of winter wheat significantly increase spike number, hence, the grain yield significantly enhanced.

Grain growth will take place if the grain boundary curvature of the matrix, H, is larger than HL.
The grain growth anneals were carried out in the temperature range of 500 oC to 620 oC in 20 oC Journal Title and Volume Number (to be inserted by the publisher) 3 steps.
TA, the number of points of tangency between a sweeping test line and a curved grain boundary trace on a section per unit test area was measured.
Below 540 oC, the measured grain boundary area is lower than the limiting grain boundary area and grain growth, that is, a decrease in grain boundary area, cannot take place.
Journal Title and Volume Number (to be inserted by the publisher) 5 Figure 4 - Grain boundary curvature, H, as a function of annealing temperature in an Al1mass%Mn alloy.

Even, grain growth of <100>//ND textured grains is occurred as abnormal grain growth when <100>//ND textured grains are surrounded by <111>//ND fiber textured grains.
If we assume isotropic GB energies and mobilities, the phase field equation for the grain growth of the poly-crystalline microstructure is [1] (1) where the order parameter q(q=1,2,3, …, Q) represents the orientation state of a point in a polycrystalline system containing of Q grains, an integer q can be regarded as a number indicating a specific orientation of the grain, and the sum of all q values in a spatial point is conserved as 1 ( , , ) 1 Q q q i j k .
Then the number of phase coexisting in a given point is S.
The initial number of grains was 10054 with different crystallographic orientations (Euler angles).
Figure 2 Microstructures and pole figures of a polycrystalline structure composed of minor <100>//ND fiber (0.3% of total grain number) and major <111>//ND fiber texture.

The condition for the microstructural instability of a single grain of given size and grain boundary properties reads where and are the grain boundary mobility and energy of the isolated grain,and are the grain boundary mobility and energy of the surrounding matrix and and are the radius of the selected grain and the average grain radius of the matrix [7] (figure 1).
Figure 3 shows the ratios of a set of 9 selected grains versus the total number of remaining grains in the studied structure, which reflects the time evolution.
(a) (b) (c) Figure 3: Radius of potentially abnormal grains divided by average grain radius plotted against the remaining total number of grains for different relative grain boundary energies (a)-(c).
Grains with 14 faces only showed abnormal grain growth, when the grain received an adequate energy and mobility advantage.
The evolving grain morphology of an abnormally growing grain is shown in figure 4.

In 2-dimensional case, the Betti numbers are consisting of two numbers.
The other is b1= H1(X), which is the number of holes.
Because the Betti numbers are invariant, the shape of the grain has nothing to do with the Betti numbers.
The number of b1 in the substrate area and HAZ area also has not changed except for the fine grains, but WMZ is decreasing.
The number of grains of more than 6µm2 seems to be the same of WMZ and HAZ.

The evolved substructures with nodes of the Fe precipitates gradually changed to new grains surrounded by low- and high-angle boundaries with increasing number of the repeated processes.
Introduction Numerous numbers of thermo-mechanical processes (TMPs) have been applied for grain refinement of bulky metallic materials.
Because RX normally involves grain coarsening due to grain boundary migration, lower limit of the minimum grain size seems to exist.
It is evident that fine grains were gradually evolved with increasing number of cycles.
Such slight grain coarsening took pace more significantly where fine grains were evolved in groups.

It can be attributed to fact that grain growth phenomena are more likely for smaller grain (i.e. 3 nm grain size) as compared to larger grain (i.e. 6 nm grain size).
Discussion on vacancy formation during creep Plots of number of vacancy formed during creep deformation versus time for nanocrystalline nickel specimens having 3 nm and 6 nm grains are shown in Fig. 10.
On the other hand, number of vacancy curves is observed to be shifted towards downward with decreasing grain size of specimens at 1400 K and 1500 K operative temperatures (refer Figs. 10(c) and 10(d) respectively).
It is observed that formed vacancy number versus time plots also supports the nature of creep curves (as evident from Fig. 2, Fig. 3 and Fig. 10).
Fig. 10 The plots of evaluated number of vacancy vs. creep time for 3 nm and 6 nm grain size NC Ni at (a) 1100 K, (b) 1200 K, (c) 1400 K and (d) 1500 K 3.7.

For example, every town has its own grain purchasing station before mergence, but after mergence, because of simplifying structure, it is no double that the former grain purchasing locations will be decreased.
The research on grain purchasing is limited.
The cost in the process of food transportation is related to the transport distance, expenses, and the total public grain which is handed in by every village and the quantity of grain purchasing locations.
Therefore, the objective function can be expressed: (1) (1)N=｛1, 2, …, n｝represents sequence number set; Mij is the assembling place whose distance is less than d between the village and the grain purchasing location; kij represents the distance between villages (i) to gain purchasing (j); Hj represents the operation cost of gain purchasing location (j); Sj represents variable from 0 to 1.
Major Parameters The names of parameter Value Statement populationsize 13 population size memorycapacity 8 memory capacity iterativetimes 20 iteration number crossoverprobability 0.5 crossover probability mutationprobability 0.4 mutation probability evaluationparameter 0.95 evaluation parameter Grainnumber 2-13 purchasing location number punishnumber 3000 threshold carryprice 4 transportation price （kg/km） managerprice 20000 Acquisition cost/every place In order to meet the minimum cost during the process of grain transportation in objective function F (i, j), solution is produced by adopting immune algorithm.

Anisotropic behaviour of grain boundaries V.
The number of papers containing data on different grain boundaries is very limited.
A large number of good quality bicrystals is needed for such measurements and their preparation is a substantial obstacle to be overcome.
Grain Boundary Segregation Diagrams.
The enthalpy of segregation derived from such measurements on sufficiently large number of samples is a better characteristic of segregation than the enrichment factor that depends on the thermal history of the sample.

For interface controlled abnormal grain growth there may be a number of processes associated with atomic attachment at the interface that can be the controlling mechanism.
In the past decade, a number of researchers have invoked the idea of a non-linear relationship between driving force and grain boundary velocity to explain abnormal grain growth during nucleation limited interface controlled grain growth.[8-10,19-20] A schematic of this is shown in Fig. 4.
The nucleation limited interface controlled abnormal grain growth mechanism has been invoked to describe abnormal grain growth in single phase and pseudo-single phase systems.[16,21] Systems where only a small number of the grain boundaries contain a nanoscale intergranular film may be considered to be pseudo-single phase.
If the grain with the defect can not grow any faster than the normal grains then this grain can not grow abnormally.
Arrhenius behavior has been observed in alumina in a number of studies, where the driving force varied with temperature.[4,26,29-31] It then remains to explain how abnormal grain growth occurs by a diffusion controlled mechanism in pseudo-single phase alumina.