  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.
