Directed Control for the Thermal Diffusion Fractal Growth of Thin Plate

Abstract

A new theoretical model for the directed thermal diffusion fractalgrowth of thin plate with environmental disturbance is considered to control thediffusion direction. Using the norm theory, a quantitative relationship of such anoptimal control problem is obtained, and the following simulations show that therelationship controls the diffusion direction effectively. In addition, the comparisonof the dimensions between the diffusion with round controlled region and thegrowth with piecewise region illustrates that the controlled regions play differentroles in the real complex fractal growth.