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Model for growth of fractal solid state surface and possibility of its verification by means of atomic force microscopy

IOP Conference Series: Materials Science and Engineering (MSE). 2017. Vol. 256. P. 012026–012026.
Куликов Д. А., Потапов А. А., Рассадин А. Э., Степанов А. В.

In the paper, methods of verification of models for growth of solid state surface by means of atomic force microscopy are suggested. Simulation of growth of fractals with cylindrical generatrix on the solid state surface is presented. Our mathematical model of this process is based on generalization of the Kardar-Parisi-Zhang equation. Corner stones of this generalization are both conjecture of anisotropy of growth of the surface and approximation of small angles. The method of characteristics has been applied to solve the Kardar-Parisi-Zhang equation. Its solution should be considered up to the gradient catastrophe. The difficulty of nondifferentiability of fractal initial generatrix has been overcome by transition from a mathematical fractal to a physical one.

Research target: Physics
Language: English
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Keywords: atomic force microscopyфрактал fractalатомная силовая микроскопия
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