A Numerical Study of KPZ Equation Based on Changing its Parameters

Abstract

In this article we investigate the behaviour of the scaling exponents<br />of KPZ equation through changing three parameters of the equation. In<br />other words we would like to know how the growth exponent β and the<br />roughness exponent α will change if the surface tension ν , the average<br />velocity λ and the noise strength γ<br />change. Using the discrete form of the<br />equation , first we come to the results α = 0.5 and β = 0.33 , then we<br />change the parameters in the range of 0 to 3 by small amounts , we observe<br />that the exponents change smoothly. In some limit states KPZ equation<br />transforms to RD and RDSR equations. Fortunately this is obvious in<br />the figures. As the parameters change and approach the limit states, the<br />KPZ universality class evolves to RD and RDSR regimes.