含有广义守恒律的生长方程标度奇异性的直接标度分析

利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性，得到强弱耦合区域的奇异标度指数.作为其特殊情况，这个方程包含Kardar-Parisi-Zhang（KPZ）方程、 Sun-Guo-Grant（SGG）方程以及分子束外延（MBE）生长方程，并能对其进行统一的研究.研究发现, KPZ方程和SGG方程，无论在弱耦合还是在强耦合区域内都遵从自仿射Family -Vicsek正常标度规律；而MBE 方程在弱耦合区域内服从正常标度，在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好. 关键词： 标度奇异性 强耦合 弱耦合

Scaling approach to the conservation-law growth equations in anomalous surface roughening

We employ an analytical approach introduced by López to determine the anomalous scaling exponent of the growth equation with a generalized conservation law in both the weak-and strong-coupling regimes, which included the Kardar-Parisi-Zhang（KPZ）, Sun-Guo-Grant（SGG）, and molecular beam epitaxy （MBE）equations as special cases and allows for a unified treatment of growth equations. Analysis shows that KPZ equation and SGG equation exhibit normal Family-Vicsek scaling behavior, whether in the weak-coupling or strong-coupling regime. Differently, MBE equation exists intrinsic anomalous scaling in the strong-coupling regime and normal Family-Vicsek scaling behavior in weak coupling regime. All the conclusions obtain here are well consistent with the corresponding results derived by the dynamic renormalization group theory, numerical simulation and experiment.