fractal dimension

Effects of Brownian Motions and Fractal Structure of Nanoparticles on Natural Convection

The study simulated heat transfer in alumina-water nanofluid in a natural convection flow and Rayleigh-Benard configuration considering the Brownian motions and fractal structure of the nanofluids. The simulations were based on a two-dimensional, Eulerian-Eulerian method. Many simulations have been performed to examine the effect of aspect ratio, heat flux, and para-meters related to the structure of the nanoclusters including size, fractal dimension, and volume fraction on the natural convective heat transfer coefficient.

Localization of steel fractures based on the fractal model of their metallographic images

There are a number of tasks that require assessment of the condition of the material and its mechanical characteristics. Such tasks may arise at the production stage, when there’s a need to control the content of various components of the material, strength, hardness, etc. Also similar tasks arise during exploitation of materials, which is especially relevant today, when most of the responsible products and structures in the field of nuclear energy, chemical industry, machine-building industry are on the verge of wearing down.

Hurst exponent evaluated via calculated by box-counting method on short time series example fractal dimension

The three versions of box counting algorithm for determining the fractal dimension of a spreadsheet Ms Excel is implemented. Values of Hearst exponent have been obtained for ten short individual time series, by the designed algorithm, based on the equation D = 2-H. The values of Hearst exponent received by means of general methods are given. The research results prove that the exact value of the fractal dimension and Hearst exponent can be obtained using the third version of the algorithm.

Development and research of technology for automation of the calibration and account of digital SEM images having geometric distortion obtained with JCM 5000 (Neoscope) (Jeol, Japan)

Purpose. Solids microsurface digital images obtained with scanning electron microscopes (SEM) are characterized by significant geometric distortions, which must be defined and taken into account when determining the quantitative parameters of microsurface solids with high accuracy. Therefore, this problem is so important and urgent, especially during the high-tech quality control of production processes using nanotechnology, particularly in mechanical engineering, aircraft construction, and for creating space and military equipment.