Ueno K, Sakaguchi H, Okamura M
Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Apr;71(4 Pt 2):046138. doi: 10.1103/PhysRevE.71.046138. Epub 2005 Apr 27.
The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation in 1 + 1 dimensions are investigated by use of the dynamic renormalization group (RG) and direct numerical simulations. It is shown that the noisy KS equation is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in the sense that they have scale invariant solutions with the same scaling exponents in the long-wavelength limit. The RG analysis reveals that the RG flow for the parameters of the noisy KS equation rapidly approach the KPZ fixed point with increasing strength of the noise. This is supplemented by numerical simulations of the KS equation with a stochastic noise, in which scaling behavior close to the KPZ scaling can be observed even in a moderate system size and time.
利用动态重整化群（RG）和直接数值模拟研究了一维加一维含噪声的Kuramoto-Sivashinsky（KS）方程的长波特性。结果表明，含噪声的KS方程与Kardar-Parisi-Zhang（KPZ）方程属于同一普适类，即在长波极限下它们具有相同标度指数的标度不变解。RG分析表明，随着噪声强度的增加，含噪声KS方程参数的RG流迅速趋近于KPZ不动点。对带有随机噪声的KS方程进行数值模拟进一步证实了这一点，在该模拟中，即使在中等系统规模和时间内也能观察到接近KPZ标度的标度行为。
