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The input layer has two nodes, respectively, deformation temperature and strain rate, the output layer also has two nodes, representing the recrystallized grain size and flow stress.
Literature[2] indicates that, the geometric mean can be used to select the processing unit the number of rules to the intermediate layer.
For the three networks, where the number of nerve cells between the hidden layer is selected by the following formula: （2） （3） In the formula, is the number of units in the hidden layer, is the number of units of the input layer, is the output layer unit, is the learning capacity of the sample, is a constant.
After the increase in the number of cells in the middle layer, network with fewer steps training can converge to a certain error range.
Figure 2 is the recrystallized grain size and the prediction error image training error.

At the same times, the 0.125mm grain diameter raindrop speed was about at 0.6-1.4m/s, the 0.25mm grain diameter raindrop speed was about at 1-1.4m/s, the 0.375mm grain diameter raindrop speed was about at 1-1.4m/s, the 0. 5mm grain diameter raindrop speed was about at 1-3.4m/s, the 0.75mm grain diameter raindrop speed was about at 3.4m/s, the 1mm grain diameter raindrop speed was about at 4.2m/s, the 1.25mm grain diameter raindrop speed was about at4.2-5m/s, the 1.5mm grain diameter raindrop speed was about at5m/s.
Researchers carried out a large number of research about soil erosion on the Loess Plateau (Tang Keli, 2004; Chen Lei, 2002), both prototype test model test a large collection of information, and achieved fruitful results.
At abroad, soil erosion observation experimental had start early on 1915 in Utah, United States, observed the amount runoff and soil loss; 1917, Head of soil department University of Missouri, M.F.Miller imitation of the early German research built a number of experimental plots to study the factor quantitative work firstly.
At the same times, the 0.125mm grain diameter raindrop speed was about at 0.6-1.4m/s, the 0.25mm grain diameter raindrop speed was about at 1-1.4m/s, the 0.375mm grain diameter raindrop speed was about at 1-1.4m/s, the 0. 5mm grain diameter raindrop speed was about at 1-3.4m/s, the 0.75mm grain diameter raindrop speed was about at 3.4m/s, the 1mm grain diameter raindrop speed was about at 4.2m/s, the 1.25mm grain diameter raindrop speed was about at4.2-5m/s, the 1.5mm grain diameter raindrop speed was about at5m/s.
At the same times, the 0.125mm grain diameter raindrop speed was about at 0.6-1.4m/s, the 0.25mm grain diameter raindrop speed was about at 1-1.4m/s, the 0.375mm grain diameter raindrop speed was about at 1-1.4m/s, the 0. 5mm grain diameter raindrop speed was about at 1-3.4m/s, the 0.75mm grain diameter raindrop speed was about at 3.4m/s, the 1mm grain diameter raindrop speed was about at 4.2m/s, the 1.25mm grain diameter raindrop speed was about at4.2-5m/s, the 1.5mm grain diameter raindrop speed was about at5m/s.

High-Cycle Fatigue in Polycrystalline Materials: The Grain-Boundary Formulation Voronoi grain-boundary representation.
The above expression can also be expressed in discrete terms, considering the accumulation of damage over a finite number of cycles DN.
Fig.2 shows the average damage for the two tested specimens versus the number of load cycles as function of the amplitude of the applied cyclic stress (average damage is defined as surface average of the local damage over all the grains interfaces).
a b c Fig.2: Average damage versus number of cycles at different amplitudes of the applied cyclic stress. a) Convex specimen; b) Non-convex specimen; c) s-N curves for the tested specimens.
Since only meshing of the grain boundaries is required, simplification in data preparation and reduction in the number of DoFs are attained, with consequential computational benefits, appealing in the context of micro/multiscale simulations.

Effect of Electroplastic Deformation on Martensitic Transformation in Coarse Grained and Ultrafine Grained Ni-Ti Shape Memory Alloy A.E.
The coarse grained state was obtained by quenching after annealing at 800°C for 1 hour and it formed microstructure with grain size of 80 µm.
As a result total number of the structure defects is decreasing, recovering martensitic transformation.
In this case there is no difference in steps number - both samples have 2-step transformation and no current influence (After cold rolling during cooling we can see only one peak - the second one will appear at lower temperature).
It can be explained by high dislocation density and grain refinement after ECAP

In the presence of lutecium (a), the diametrical growth of the silicon nitride grain is faster than when lanthanum (b) is present, resulting in low aspect ratio grains.
Combined with the greater preference of La for residing at the silicon nitride grain surfaces, these can be taken as mechanisms for limiting diametrical grain growth resulting in high aspect ratio grains when La is one of the components of the sintering additives.
With increase in creep strain, one observes an increasing number of these elongated grains that either contain cracks or are fractured.
As a result diametrical grain growth is impeded and elongated grains, which are desired to toughen the ceramic, are formed.
Rühle, "Grain Boundary Films in Rare-Earth-Based Silicon Nitride," J.

Finally taken the coarse-grained community as a starting point, we use the strategy of LPA to propagate labels through the network further.
Proposed Algorithm In this paper, for a given network, and represent the node set and edge set respectively, we calculate the similarity between two nodes and as the ratio of the number of their shared neighbors to the total number of both of them, that is: is a set contains all the neighbors of the node .
However, if the number of classified neighbors with the most same label is less than those of unclassified neighbors, that node can be regarded as a kernel, temporarily.
At the end of the Algorithm 1, all the nodes with the same label are grouped as a community implicitly, and all the communities constitute the coarse-grained community structure.
We use both modularity and accuracy as validate metrics; modularity is computed using the method in the literature[6, 7], and accuracy is defined as the ratio of the number of nodes classified correctly to the total number of nodes in the network.

Effects of grain sizes and density on removal rate and roughness.
Effect of grain sizes on removal rate and roughness showed as Fig.4.
The change of removal rate drops firstly then rises up with increasing of grain sizes, and the values are greater of the W3.5﹠W14 grain sides.
The explanation of this phenomenon follows as: the numbers of smaller grains participating in lapping are so multiple in unit time that the removal rate improves quickly because of sufficient cutting, and the scratches of smaller grains are shallow that forms the smooth surface.
The experimental results of optimization parameters as shown in Fig. 6: in the number of group two, the removal rate reaching 109.2nm/min with large size (W10) abrasive is higher than that of small size, so its parameters can be used for coarse lapping process of sapphire; in the number of group one, the surface roughness reaching 1nm with small size (W3.5) abrasive is obviously better than that of large size, so its parameters can be used for fine lapping process of sapphire.

The flat grain boundary (Fig. 2 a) included, for example, the grain boundaries in which {100}<011> grain was adjacent to {111}<112> grain.
Grain boundaries with fine grains (Fig. 2 c) comprised the various combinations of differently oriented neighboring grains as shown in Table 1; expressly, grains of {111}<011> and {111}<112>.
With a focus on the fine grains in the grain boundary (type 3), an attempt was made to statistically examine the relationship between the characteristics of the grain boundary and the formation of fine grains.
It was found that in the examination of the 84 grain boundaries, 22 grain boundaries formed fine grains.
The number of grain boundaries with fine grains, in particular having ND//<111>, is counted. g1, g2, a1, and a2 stand for orientation of {111}<112>, {111}<011>, {100}<011> , and {211}<011>, respectively [11].

For such nanometre scale grain sizes, the volume fraction of grain boundaries (GBs) becomes significant and the mechanical properties of nc materials exhibit unique properties when compared to their coarser grained counterparts.
With decreasing grain sizes, a transition from dislocation mediated plasticity within the grains, towards a plasticity that is primarily accommodated by the GB structure is to be expected.
Simulating nanocrystalline microstructures There exist a number of techniques to construct computer generated nc systems [6,7].
Fig. 1 displays the two-theta spectrum for two computer generated nc samples, one containing 15 grains with a computed average grain size of 12 nm and another containing 125 grains with a computed average grain size of 5 nm [14].
More recently, collective processes such as cooperative grain boundary sliding via the formation of shear planes spanning several grains have been observed [17,18].

The grain size in Fig. 5 (a) is smaller as compared to that in Fig. 5 (b) and (c) which shows that an increase in pressure resulted in grain growth.
Grain growth manifested in the form of large grains in Fig. 5 (b) and (c) as compared to small grains in Fig. 5 (a) is an evidence of reduced hardness with an increase in applied pressure.
This will cause more surface diffusion and hence more grain growth [6, 7].
Such complex phenomena can cause unexpected grain growth [9].
Acknowledgments The authors would like to acknowledge financial support from King Abdul Aziz City for Science and Technology (KACST) through project number ARP-28-122.