# Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems

Source: [Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems](<https://www.sota2.com/research/paper/68fa24162c2a37601939f4e5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T07:57:45.414Z

Authors: A.D. Rutenberg, A.J. Bray

Published: 1994-04-15T17:18:46.000Z

## Abstract

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\\sigma)}$) interactions with $\\sigma\>0$, \`\`Energy-Scaling'' arguments predict a growth-law of the average domain size $L \\sim t^{1/(1+\\sigma)}$ for all $\\sigma \>0$. Numerical results for $\\sigma=0.5$, $1.0$, and $1.5$ demonstrate both scaling and the predicted growth laws. For purely short-range interactions, an approach of Nagai and Kawasaki is asymptotically exact. For this case, the equal-time correlations scale, but the time-derivative correlations break scaling. The short-range solution also applies to systems with long-range interactions when $\\sigma \\rightarrow \\infty$, and in that limit the amplitude of the growth law is exactly calculated.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9404046>)

[PDF](<https://arxiv.org/pdf/cond-mat/9404046.pdf>)