### Abstract

One-dimensional interfaces with curvature-driven growth kinetics are investigated. We calculate the steady-state distribution P(w2) of the square of the width of the interface w2 and show that, as in the case for random-walk interfaces, the result can be written in a scaling form w2P(w2)=(w2/w2), where w2 is the average of w2. The scaling function (x) is found to be distinct from that of random-walk interfaces, but, as our Monte Carlo simulations indicate, this function is universal for curvature-driven growth. It is argued that comparison of scaling functions can be a useful method for distinguishing between universality classes of growth processes.

Original language | English |
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Pages (from-to) | 3589-3593 |

Number of pages | 5 |

Journal | Physical Review E |

Volume | 50 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jan 1 1994 |

### ASJC Scopus subject areas

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

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## Cite this

Plischke, M., Rcz, Z., & Zia, R. K. P. (1994). Width distribution of curvature-driven interfaces: A study of universality.

*Physical Review E*,*50*(5), 3589-3593. https://doi.org/10.1103/PhysRevE.50.3589