Khandkar, Mahendra D. ; Stinchcombe, Robin ; Barma, Mustansir (2017) Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics withA+B→0 Physical Review E: covering statistical, nonlinear, biological, and soft matter physics, 95 (1). ISSN 2470-0045
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Official URL: http://doi.org/10.1103/PhysRevE.95.012147
Related URL: http://dx.doi.org/10.1103/PhysRevE.95.012147
Abstract
We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A) and <>(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→0, quite different from the A+A→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→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^{-1/2}, the fraction of persistent arrowheads decays as t^{-θ} where θ is close to 1/4, quite different from the Ising value. The global persistence too has θ=1/4, as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |
ID Code: | 129694 |
Deposited On: | 06 Dec 2022 10:37 |
Last Modified: | 06 Dec 2022 10:37 |
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