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

Scanning Probe Microscopy 2017

Kulikov, D.A.^1 ; Potapov, A.A.^2,3 ; Rassadin, A.E.^4 ; Stepanov, A.V.^5

P.G. Demidov Yaroslavl State University, Yaroslavl

150003, Russia^1

Kotel'Nikov Institute of Radio Engineering and Electronics of RAS, Moscow

125009, Russia^2

Joint-Lab. of JNU-IREE RAS, JiNan University, China^3

Nizhny Novgorod Mathematical Society, Nizhny Novgorod, 603950, Russia^4

Chuvash State Agricultural Academy, Cheboksary

428003, Russia^5

关键词: Kardar-Parisi-Zhang equations;    Method of characteristics;    Methods of verifications;    Non-differentiability;    Solid-state surface;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/256/1/012026/pdf
DOI  :  10.1088/1757-899X/256/1/012026

来源: IOP

【 摘 要 】

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.