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For that purpose let us also expand into Tailor series the objective function (Eq. 10): Using (Eq. 16) we obtain: (17) In this manner the optimal descent direction must minimize the expression (18) among all possible descent directions The total number of possible descent directions is defined by an expression where – is the number of unknowns.
However from of the obvious inequality and the expression (Eq. 17) we derive the following necessary condition which determines the number of possible descent directions, not exceeding the value Up to now we assumed that upon checking feasibility of solution only one in equality of the type (Eq. 11) was violated.
Conclusion The results of this study were used in the development of information system in a large-scale company, "Tcesna-Astyk", specializing in storage, processing and marketing of grain.
The production units of this company are characterized by an extensive network of tiered and parallel processing structures, where each production step involves multiple parallel units processing grain.
Šćekić: Information system for modelling the grain size distribution, Journal of theoretical and applied information technology Vol. 23, No.1 (2011), p.1-6

In this simulation, a wheel model set with a plural number of abrasive grits (14 pieces on the wheel width x 10 pieces on the circumferential direction + 1 piece = 141 pieces) was manufactured.
The grain size of the wheel prepared was SD170 (or SD80) and its concentration was 100.
Fearing that the random number value might vary or overlap every time, the simulation was conducted using the 5-wheel models manufactured under the same conditions.
Fig.14 Change of feed rate (SD170,Vs=1000 m/min) Fig.15 Prediction of the roughness in the case of using SD80 wheel (SD80 and SD170, Vs=1000 m/min) In addition, the prediction of the ground surface when the grain size was changed to SD80 from SD170 was conducted.
By helical scan grinding using a coarse grain SD80, it was predicted that the roughness obtainable was nearly 2/3 of the value obtained by conventional grinding using SD170.

The MQ-HPDC process requires the use of a number of metallic containers.
The number required is determined by the specified melt dose, cycle time and container thermal mass.
The high cooling rate achieved by pouring superheated alloy melt into a relatively cold metallic container results in a large thermal undercooling, which allows an increased number of existing solid particles in the melt to nucleate.
The simultaneous growth of an increased number of primary grains results in a relatively small growth of each primary grain and therefore large dendrites are eliminated.
In this process, melt quenching by a purpose designed metallic container is used to enhance heterogeneous nucleation; and the latent heat released by the growth of the increased number of nuclei in the shot sleeve is used to achieve a relatively uniform melt temperature.

Round co- penetrating grains are visible, with a size between 5 and 20 mm.
In this way, rupture was achieved when the number of deleted elements was sufficient to macroscopically separate the sample.
Two different parametric studies were run: we varied the surface energy for microcrack to occur (g), and we varied the number of elements of the whole sample.
More realistically, a distribution of values is present, if the microstructure contains defects, grains, impurities, small intergranular phases (mostly Si).
It has been found that by changing the sample size (i.e. the number of elements, for a fixed element volume), the FEM predictions of the non-linear stress-strain behavior come much closer to the experimental data.

This module illustrates the 4 main routes to strengthen the Aluminium alloys by solid solution strengthening, age hardening (precipitation), strain and grain size hardening.
The new "softening mechanisms" module is divided in the seven sub-topics : 1) Cold Work and Stored Energy, 2) Recovery, 3) Recrystallisation , 4) Grain Growth , 5) Solution Treatment 6) Overaging and 7) Annealing.
Co-ordinated by the European Aluminium Association (EAA), the AluMATTER project is supported by the major European aluminium producers, by some national aluminium associations, by a number of important technical and training centres and by some renowned university departments in Europe.

Fig. 1 displays diffraction reflections broadening caused by grains refinement of Fe3O4 nanoparticles.
A large number of generated surface defects with high specific surface area and particles distortions caused by high interfacial tension of smaller grains contribute to diffraction reflection broadening.

Model and Method The phase-field model was proposed to deal with grain growth in polycrystals [8].
The detail of the new local free energy functional can be written as (3) Where W is the well depth parameter of local free energy, is a whole number, Tc and Cc are critical temperature and critical composition of the spinodal region of Al-Ag phase diagram, respectively.
The new free energy functional can also be applied to a dilute solute composition field of spinodal decomposition interacting with many precipitates or grain boundary.

Al/TiCp (particle) composites have been studied by a number of researchers [4-6] but the workability studies are still lacking.
In the specimens tested at the 400°C and 0.01/s, at the 500°C and 0.1/s, and at the 500°C and 0.001/s corresponding to the high-efficiency domain, the grain shape and high fraction of high-angle boundaries indicated that the matrix was dynamically recrystallized with breaking-up the cast structure.
The grain structure of the specimens tested at the 200°C and 0.001/s of which the efficiency was 0.15 represented the deformed structure wherein dynamic recovery may occur. 400°C, 0.01/s 500°C, 0.1/s 500°C, 0.001/s 200°C, 0.001/s Fig. 2 EBSD maps of the tested specimens of composite Fig. 3 shows the fraction of high-angle boundaries analyzed by EBSD as a function of the efficiency of power dissipation of several representative specimens.

With increasing specific surface area of powders, the number of contact between reactants increases, which may in some cases lead to much faster reaction rates.
The formation of nitride ceramics by direct nitridation of elemental powders in a combustion regime is accompanied by a significant grain growth of product powders.
The densified samples exhibited sub-micron structure with grain sizes in the range of 100-200 nm.
Unfortunately, a significant grain growth was observed during in situ densification of combustion synthesized products (see Fig. 13).
SEM image of nanosized grains NiAlAl2O3 nanocomposite reinforced with SWNT's.

Being in solid solution, the latter is especially effective in retarding the transformation, since it restricts the diffusion of iron and carbon along grain boundaries.
Thereby, austenite grain coarsening as well as recrystallization processes are effectively influenced, resulting in a fine-grained microstructure.
The equally distributed and fine Nb carbonitrides of typically less than 20 nm diameter control successfully the austenite grain size and thus the microstructure after transformation.
In this context one usually defines a suitable cooling time t8/5, since this characteristic value combines various welding parameters including the heat input into one number.
In particular, it refines the grain size and thus improves the toughness of the material guaranteeing a high resistance against brittle fracture.