Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics withA+B→0
| Autor: | Mustansir Barma, Robin Stinchcombe, Mahendra D. Khandkar |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Physical Review E. 95 |
| ISSN: | 2470-0053 2470-0045 |
| DOI: | 10.1103/physreve.95.012147 |
| Popis: | We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads $lg$ on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, $gl$ ($A$) and $lg$ ($B$). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the $A$ domain walls diffuse, while the $B$ walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation $A+B\ensuremath{\rightarrow}0$, quite different from the $A+A\ensuremath{\rightarrow}0$ kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for $A+A\ensuremath{\rightarrow}0$. In the thermodynamic limit with a finite density of walls, coarsening as a function of time $t$ is studied by simulation. While the number of walls falls as ${t}^{\ensuremath{-}\frac{1}{2}}$, the fraction of persistent arrowheads decays as ${t}^{\ensuremath{-}\ensuremath{\theta}}$ where $\ensuremath{\theta}$ is close to $\frac{1}{4}$, quite different from the Ising value. The global persistence too has $\ensuremath{\theta}=\frac{1}{4}$, as follows from a heuristic argument. In a generalization where the $B$ walls diffuse slowly, $\ensuremath{\theta}$ varies continuously, increasing with increasing diffusion constant. |
| Databáze: | OpenAIRE |
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