Related Experiment Video
Updated: Aug 18, 2026

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
Published on: April 25, 2019
Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1 + 1 dimensions
K Ueno1, H Sakaguchi, M Okamura
1Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan. ueno@fcs.coe.nagoya-u.ac.jp
Abstract:
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.
Related Concept Videos
Dimensionless Groups in Fluid Mechanics
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Partial Differential Equations
Separable Differential Equations
Differential Equations: Problem Solving
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.