Dynamic scaling of the growing rough surfaces

We have numerically investigated the self-affinity of the bacterial colony model. In order to examine the growth exponent β, we find a new approach to the dynamic scaling hypothesis for the growing rough surface. We have first investigated the self-affinity of the well-known Eden model to check the validity of the new approach. The obtained results of the exponents α ≅ 0.50 and β ≅ 0.33 coincide with the well-known values of the exponents of the Eden model. We have then applied it successfully to growing interfaces produced by the bacterial colony model. We have found that the self-affinity of the bacterial colony model is characterized as α ≅ 0.80 and β ≅ 0.65.