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Divide the self-similar object in strict sense into N small ones, whose forms and sizes are in full accord ,and the line-size of each one is 1/r times of the original figure, here ,the fractal dimension D of the self-similar object is : (2) Particle size distribution of aggregates As a kind of typical chondrule ,aggregate present scattered grain structure. the concept of its structure consists of particle composition and the arrangement relationship between particle and each other .The complexity of granular aggregate structure lies in three aspects, that is, particles’ stochastic arrangement in space, porous structure caused by it and irregularity of the contact relationship among particles where, particle size distribution (i.e. grading of aggregate) is the basic factor of determining the structure of asphalt mixture ,and it is also the important factor of causing mechanics properties of different granular asphalt mixture
Deduction of mass fractal characteristic function of aggregate.Certain a particle size r,assumed its distribution function is ,that is the cumulative percentage of particle size which is less than or equal to r is: (3) Where, is the total number of particles whose sizes are more than r (size r, unit is mm); is the total number of particles in the sample.
Obtained from formula (7): (8) Introduced density constant of aggregate, the relation between volume and mass is: (9) Where: is density constant of aggregate ; , are respectively volume and number of the particle whose size r is located at interval （r，r＋dr）.
Among them, number 1～3 are grading trend of AC-20,as Tab. 1 and Fig.1 shows, the meaning is that: 1 is upper limit of grading of AC-20, 2 is median of grading of AC-20, 3 is lower limit of grading of AC-20.
Number 4～6 are grading trend of SMA-20,as Tab. 2 and Fig.2 shows, 4 is upper limit of grading of SMA-20,5 is median of grading of SMA-20,6 is lower limit of grading of SMA-20.

Therefore, an important issue is the number of cycles to crack initiation, which need to be designated and considered.
Calculation of the effective length determining the fatigue zone can be dependent upon the radius of the notch [15], the grain size [16], the designated modelling zone [17, 18], or based on the stress gradient [1, 15].
The moment of crack initiation for which the number of cycles was determined was adopted, when the crack length was 0.1 mm.
After determining the number of cycles to crack initiation, the stress value corresponding to the level of loading was calculated.
Adaptation of this parameter allows for reference of the recognized approach to determine the material fatigue and the corresponding number of cycles to crack initiation.

Introduction Severe plastic deformation (SPD) has been studied extensively in the last few decades to obtain bulk material with ultrafine grained structures.
A number of SPD processes have been proposed, such as equal channel angular pressing (ECAP)[1,2], accumulative roll bonding (ARB)[3], multi directional forging and high pressure torsion (HPT)[1].
The shear strain applied by HPT is given by γ =2πrN/t (r: radius; N: number of HPT revolutions; t: thickness of the sample) and the von Mises equivalent strain εvM is given by εvM = γ/√3.
At 5 GPa ω phase is first detected after 1/8 turns and the volume fraction increases with the number of turns.
The hardness decreases with the increase in the number of HPT turns similar to that observed in pure Al.

Considering that the best fit correspond to the most probable disorientation between both lattices, the “O” lattice theory allows to obtain the relative orientation of the two considered grains.
Actually, it is necessary to limit the possible metal cells number (which is infinite), and so a maximum authorized value of the metal cell multiplicity Σ1 is chosen (which is considered as a numerical parameter and noted Σ1max).
Moreover, the number of local minima of the [VM2.det(I – A-1)] increases with Σ1max increases which means that the number of potential oxide orientations leading to a good metal/oxide “fit” increases.
Actually, as shown on Fig. 2, when the Σ1max value increases, the number of local minima increases which means that the number of potential oxide orientations leading to a good metal/oxide “fit” increases.

In recent years, extensive research has been conducted on manufacturing materials whose grain sizes are measured in nanometers (metal oxide nanoparticles (NPs)).
Reports on using nanofluids as heat transfer fluids in solar collectors are few in number up to date [17-21].
This means that the incorporation of a small amount of copper nanoparticles in alumina matrix significantly enhances the Nusselt number.
These results show that by increasing the Reynolds number the efficiency is increased.
Journal of Advanced Physics, Volume 4, Number 3, September 2015, pp. 169-173(5)

Patterns for garments made from high-stretch fabrics commonly eliminate the use of darts and reduce the number of contoured seams in favour of utilising a fabric’s stretch properties to contour the shape of the body[18, 19].
Langer’s lines can be said to represent the “grain of the skin”[24] and can denote in which direction the skin stretches and does not stretch on a mobile body.
LoNE and Langer’s Lines have be used as guides by which fabric grain and seam lines could be placed when cutting garments[24, 25].
A study with a larger number of participants would also strengthen the validity of these findings.
Lindqvist, "On the relationship between the shear forces in human skin and the grain direction of woven fabric," International Journal of Fashion Design, Technology and Education, vol. 9, no. 2, pp. 106-114, 2016, doi: 10.1080/17543266.2016.1173235

The number of specimens was four for each treatment.
The deformation process can cause a strain hardening mechanism, which leads the dislocations to be deformed and accumulate at the grain boundaries [41].
This phenomenon causes the strengthening of the material so that the gap between the grains gets smaller, slows down the corrosion process, and increases the material corrosion resistance.
The greater the deformation, the more the dislocations deformed and accumulation at the grain boundaries and the higher the corrosion resistance.
The number of Ti-6Al-4V ELI specimens from each thermomechanical treatment tested was 4.

The structure defects and grain size are also important for strength.
A great number of impurities leads to crack formation.
Porosity as a general index of density of thermal insulating material and thermal protection structure. 2) Number of pores – n, pcs/m3.
The number of pores for homogeneous structure in combination with porosity gives a general idea about pore distribution in the material.
It may also be represented as the multiplication of Grashof number by Prandtl number. 6) To determine the energy content of formed porous thermal insulating materials and structures of thermal protection elements used in industrial energy-generating plants, the energy of porous structure formation.

Because unambiguous evidences of gas hydrates from cores and drill holes are often lacking, the number of sites where gas hydrates are suggested to occur may be overestimated.
Deposition rate The formation of marine gas hydrates must have a large number of source supplying.
Sediment grain size is too small, and the gaps between the particles are too small, no conducive for hydrate storage.
Continental shelf in the northern Gulf of Mexico with dense gas hydrates, because of a large number of surface runoff inputting, changed the geology of the seabed near the shore [25].
Black Sea formed a unique water layer because of its special position, accepting a large number of terrestrial runoff, while the exports are narrow, leading the exchange with other ocean body blocked.

RUM, shown in Fig. 1, is recognized as a reliable and cost effective machining method that is being applied in a number of critical engineering applications [1-3].
The grain size of the diamond was 16.2 nanometers.
Taguchi orthogonal array were used to reduce the number of experimental combinations [12], which will result in cost savings due to the expensive diamond tools.
Taguchi L27 orthogonal array was used as the experimental layout of the milling process because it can accommodate up to a maximum number of five 3-level factors with 26 degrees of freedom.
In the present research, Smaller-the-Better (Eq. 1) type situation has been selected as objective function is needed to be minimized η=-10 log10{1n.i=1nyi2 (1) Where η is S/N ratio, n is the number of observations and y is the observed data, [15] Table 3: Experimental Results Exp. no.