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The complex propagation wave number has been determined as an eigen value using the formulation.
The variational functional is used here determine the complex propagation wave number
Due to homogeneous grain structure, the reluctance of the circuit reduces and a more uniform magnetization profile also decreases the low-field loss.

And, the numbers of internode are random, so the interval of branches growth is also a random quantity, introduce as a random number and variance
Fine-grained simulation of the plant stem growth process.

The resistance provided by a number of measures.
The number of stabilizers must be increased with increase carbon content to bind all the carbon and should exceed the carbon content about 5 times [1].
The main purpose of the modeling was to predict the percentage this element of the stabilizer (titanium) alloy, which ensures the formation titanium carbides, not chromium carbides are in solution with the matrix alloy during heating and doesn’t fall in the secondary phase, depleting the area of grain boundary chromium [5].

Introduction Development of building materials based on modeling the processes of formation the structure and properties is virtually reduced to the solution of a number of interrelated tasks: -construction of a hierarchical structure of the system (material) with estimates its elements (base long-term planning and development of the whole complex of individual systems); -definition of methodological principles of synthesis of building materials (the use of classical control theory and methods of system analysis in combination with the experimental, heuristic methods of materials); -identification of kinetic processes of formation the structure and basic physical and mechanical characteristics of the material for assessment of the accuracy of mathematical modeling; -creation of a generalized model of kinetic processes; -definition of the connection between the structure parameters and kinetic processes; -formation of functional quality; -analysis of the possibilities and the choice
According to Pareto principle, "80% of losses due to deficiency or rework arise as a result of 20% of the causes" (a large part of the results is caused by a relatively small number of reasons).
Applying of Pareto principle greatly facilitates the determination of the parameters: the content of the ingredients, grain size, etc.; it allows selecting elements of the material, which are mainly determined properties of the composite (example, for strength and density - the degree of filling and a view of the modifier).

The structural changes at the initials stages of sintering, characterised by the number of contact per particle and an increase of the areas of interparticle contact have been modelled and examined.
Despite the huge number of published studies, there remain big uncertainties about the materials properties.
As a result, strong grain coarsening occurs, so that the effort of synthesizing nanosized particles is lost during the sintering process.
Of course the local field extrema cause local extrema of the current density and Joule losses, which leads to the softening and partial melting and hence to an increase in the number and the size of the contact area.

PVA grains were fully dissolved in water by stirring at 95℃.
A small number of bead-like irregularities appear in the nanofibers spun from solutions with 10 wt% MWNTs concentration.
It was observed that the absorption peak at about 3406 cm-1 concerned with –OH stretching vibrations shifted to a higher wave number with the increase of MWNT content in the blends.

Among them, a number of studies demonstrated the fabrication of scaffolds with a gradient of mineral content for mimicking the composition and mechanical function of the interface between soft tissue to hard tissue (i.e., tendon-to-bone, ligament-to-bone, and cartilage-to-bone) [3,4].
Our more recent study demonstrated the presence of dopamine in mineralizd solution can tailor the grain size and morphology of minerals deposited to the electrospun fibers [7].
Acknowledgements This work was supported in part by grant number UL1RR033173 from the National Center for Research Resources (NCRR), funded by the office of the Director, National Institutes of Health (NIH) and supported by the NIH roadmap for Medical Research and start-up funds from Marshall Institute for Interdisciplinary Research and Center for Diagnostic Nanosystems at Marshall University.

The number of yellow silicon carbide particles attached to the susceptor surface decreased after exposure at 250 oC, as shown in Figs. 3 (a) and (b).
By the additional etching at 270 oC, most of the silicon carbide particles were detached, but a small number of particles remained, as shown in Fig. 3 (c).
The susceptor surface had ambiguous-shaped shallow hills, which might be related to the grains of the silicon carbide coating film.

The length of the FEM mesh was 2mm in this article, and the thickness of the shell was 7mm.The total number of Nodes were 133631,and the Elements were 647224.
(see Table 2) Table 2 The data Number Pouring temperature(℃) Pouring speed(m/s) Initial temperature of shell (℃) Maximum effective stress (MPa) a 750 0.6 500 131 b 750 0.8 500 131 c 750 0.6 400 130 d 800 0.6 400 108.7 (a) 0.6m/s (b) 0.8m/s (c)700℃ (d) 800℃ Fig.7 The effective stress on different pouring speeds and temperatures From table2 and fig.7 can be seen, the largest effective stress of the casting appeared in the root of connection castings, which belonged to sprue runner, took no influence on the casting.
Shrinkage of castings will be increased if the temperature is too high, and the grain will become larger

Results and discussion Measurement of recovery stress Recovery stress of Ni47Ti44Nb9 alloy in forging state After different pre-strain in low temperature range (-60℃ ±5℃) for Ni47Ti44Nb9 alloy, the evolution of recovery stress in heating process (increase to 473K) was measured and the result of the samples which were named number 1, 2 and 3 respectively, was shown in Fig1.
As shown in Fig1, when the temperature increase to 423K, the recovery stress of the three samples reached the peak values, which is 212MPa, 215MPa and 210MPa for number 1, 2 and 3 samples respectively.
ARB and other new techniques to produce bulk ultrafine grained materials[J], Advanced Engineering Materials, 2003, 5(5): p.338