### 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.

Original language | English |
---|---|

Article number | 046138 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 71 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1 2005 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

**Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1 + 1 dimensions.** / Ueno, K.; Sakaguchi, Hidetsugu; Okamura, Makoto.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1 + 1 dimensions

AU - Ueno, K.

AU - Sakaguchi, Hidetsugu

AU - Okamura, Makoto

PY - 2005/4/1

Y1 - 2005/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=41349103907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41349103907&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.046138

DO - 10.1103/PhysRevE.71.046138

M3 - Article

AN - SCOPUS:41349103907

VL - 71

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 046138

ER -