A Numerical Study of KPZ Equation Based on Changing its Parameters

In this article we investigate the behaviour of the scaling exponentsof KPZ equation through changing three parameters of the equation. Inother words we would like to know how the growth exponent β and theroughness exponent α will change if the surface tension ν , the averagevelocity λ and the noise strength γchange. Using the discrete form of theequation , first we come to the results α = 0.5 and β = 0.33 , then wechange the parameters in the range of 0 to 3 by small amounts , we observethat the exponents change smoothly. In some limit states KPZ equationtransforms to RD and RDSR equations. Fortunately this is obvious inthe figures. As the parameters change and approach the limit states, theKPZ universality class evolves to RD and RDSR regimes.

Keywords:

KPZ equation , scaling exponents , nonequilibrium surface growth