Potapenko L. Mathematical modeling of the formation of relief in the thermoplastic medium

This thesis is devoted the process of formation of relief in display of hidden image by the numerical modeling. The paper summarizes and improved mathematical models of the fotmation of relief in thermoplastic medium. Based on these models patterns of formation the spatial relief on the surface of thermoplastic medium under external forces are investigated. The paper formulates mathematical model for the formation of relief in display of hidden image and conducted decomposition models into simpler models. An analytical solution of the linear system of Navier - Stokes equations, which describes the isothermal linearized model is obtained. The iterative algorithm of solution of nonlinear equations Navier - Stokes equations and thermal balance is developed. The convergence of the iterative process is investigated. The comparative analysis of the impact of normal and tangential components of surface forces on the development of surface relief of thermoplastic layer is obtained. A model display of hidden image in electrocapilary effect is investigated. A study of temperature field in the thermoplastic medium under pulse heating thermoplastic medium is made. The problem of optimal control pulse heating thermoplastic medium is solved.