Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-06-03
Phys. Rev. E, 77, 031134 (2008)
Physics
Condensed Matter
Statistical Mechanics
17 pages, 6 figures, 1 table
Scientific paper
10.1103/PhysRevE.77.031134
We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in 1+1 and 2+1 dimensions using an Euler discretization scheme and the replacement of ${(\nabla h)}^2$ by exponentially decreasing functions of that quantity to suppress instabilities. When applied to the equation in 1+1 dimensions, the method of instability control provides values of scaling amplitudes consistent with exactly known results, in contrast to the deviations generated by the original scheme. In 2+1 dimensions, we spanned a range of the model parameters where transients with Edwards-Wilkinson or random growth are not bserved, in box sizes $8\leq L\leq 128$. We obtain roughness exponent $0.37\leq \alpha\leq 0.40$ and steady state height distributions with skewness $S= 0.25\pm 0.01$ and kurtosis $Q= 0.15\pm 0.1$. These estimates are obtained after extrapolations to the large $L$ limit, which is necessary due to significant finite-size effects in the estimates of effective exponents and height distributions. On the other hand, the steady state roughness distributions show weak scaling corrections and evidence of stretched exponentials tails. These results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.
Aarao Reis Fabio D. A.
Miranda Vladimir G.
No associations
LandOfFree
Numerical study of the Kardar-Parisi-Zhang equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Numerical study of the Kardar-Parisi-Zhang equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical study of the Kardar-Parisi-Zhang equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-195953