Table 1 Numerical estimation of the exponents for the QEW on top of the FBM correlated lattice. The data for each set of scaling functions have been separated by a triple line, see Eqs. (26), (29), (34), and (36), which has been already shown in Figs. 3, 4, 5, and 6 respectively.
From: Edwards–Wilkinson depinning transition in fractional Brownian motion background
\(H=0.3\) | \(H=0.4\) | \(H=0.5\) | \(H=0.6\) | \(H=0.7\) | \(H=0.8\) | |
---|---|---|---|---|---|---|
\(F_{c}\) | \(1.5\pm 0.04\) | \(1.4\pm 0.03\) | \(1.4\pm 0.02\) | \(1.3\pm 0.02\) | \(1.2\pm 0.01\) | \(1.1\pm 0.01\) |
\(\gamma _{F}^{-1}\) | \(0.55\pm 0.05\) | \(0.45\pm 0.04\) | \(0.25\pm 0.025\) | \(0.24\pm 0.015\) | \(0.22\pm 0.02\) | \(0.21\pm 0.02\) |
\(\theta\) | \(0.58\pm 0.0918\) | \(0.62\pm 0.05\) | \(0.64\pm 0.03\) | \(0.91\pm 0.03\) | \(1.25\pm 0.04\) | \(1.38\pm 0.066\) |
b | \(1.116\pm 0.08\) | \(1.146\pm 0.077\) | \(1.223\pm 0.0575\) | \(1.252\pm 0.0565\) | \(1.232\pm 0.065\) | \(1.276\pm 0.049\) |
\(\tau _{t}\) | \(1.446\pm 0.05\) | \(1.427\pm 0.048\) | \(1.463\pm 0.042\) | \(1.457\pm 0.042\) | \(1.424\pm 0.04\) | \(1.448\pm 0.04\) |
q | \(1.735\pm 0.5\) | \(1.794\pm 0.3\) | \(2.558\pm 0.7\) | \(2.45\pm 0.5\) | \(2.538\pm 0.4\) | \(2.487\pm 0.1\) |
A | \(4.2\pm 0.01\) | \(3.31\pm 0.02\) | \(3.29\pm 0.02\) | \(3.23\pm 0.02\) | \(3.09\pm 0.03\) | \(2.99\pm 0.04\) |
\(\alpha _w\) | \(2.59\pm 0.2\) | \(2.73\pm 0.13\) | \(2.92\pm 0.26\) | \(2.94\pm 0.2\) | \(3.1\pm 0.2\) | \(3.247\pm 0.24\) |
\(\beta _w\) | \(0.8\pm 0.01\) | \(0.815\pm 0.01\) | \(0.827\pm 0.012\) | \(0.832\pm 0.013\) | \(0.839 \pm 0.014\) | \(0.847\pm 0.016\) |
z | \(1.855\pm 0.42\) | \(1.905\pm 0.25\) | \(2.05\pm 0.32\) | \(1.839 \pm 0.3\) | \(1.929\pm 0.31\) | \(1.982\pm 0.4\) |
\(\gamma _w\) | \(0.8\pm 0.02\) | \(0.88\pm 0.01\) | \(0.95\pm 0.026\) | \(0.99\pm 0.0575\) | \(1\pm 0.1\) | \(1.01\pm 0.12\) |