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We demonstrate the large scale effects of the interplay between shape andhard core interactions in a system with left- and right-pointing arrowheads~$\textless ~~ \textgreater$~ on a line, with reorientation dynamics. Thisinterplay leads to the formation of two types of domain wall, diffusive ($A$)and static ($B$). The correlation length in the equilibrium state divergesexponentially with increasing arrowhead density, with an ordered state of likeorientations arising in the limit. In time, the approach to the ordered stateis described by a coarsening process governed by the kinetics of domain wallannihilation $A+B\rightarrow 0$, quite different from $A+A \rightarrow 0$kinetics pertinent to the Glauber-Ising model. The survival probability of afinite set of walls is shown to decay exponentially in time, in contrast to thepower law decay known for $A+A \rightarrow 0$. In the thermodynamic limit witha finite density of walls, coarsening as a function of time $t$ is studied bysimulation. While the number of walls falls as $t^{-\frac{1}{2}}$, the fractionof persistent arrowheads decays as $t^{-\theta}$ where $\theta$ is close to$\frac{1}{4}$, quite different from the Ising value. The global persistence toohas $\theta=\frac{1}{4}$, as follows from a heuristic argument. In ageneralization where the $B$ walls diffuse slowly, $\theta$ variescontinuously, increasing with increasing diffusion constant.

Coarsening in a 1-D system of Orienting Arrowheads: Persistence with $A+B \rightarrow$ 0