具有两个非排斥选项的排序动态：语言竞争中的双语现象
Ordering dynamics with two non-excluding options: Bilingualism in language competition
摘要：
我们考虑修改的选民模型，其中一组相互作用的元素（代理）可以在两个等价的状态（A或B）或在第三个额外的混合AB状态。该模型的动机是语言竞争动力学的研究，其中AB状态与双语。我们研究了规则晶格和小世界网络中的有序化过程以及相关的界面和粗化动力学。处于AB状态的代理定义接口，将投票者模型的接口噪声驱动的粗化改变为曲率驱动的粗化。我们认为，这种变化的粗化机制是通用的扰动的选民模型的动态。当互动是通过一个小世界网络的AB代理恢复粗化，消除选民模型的亚稳态。达到吸收状态的时间与系统大小成比例，为$τ\sim \ln N$，以与小世界网络中投票者模型的结果$τ\sim N$进行比较。
英文摘要：
We consider a modification of the voter model in which a set of interacting elements (agents) can be in either of two equivalent states (A or B) or in a third additional mixed AB state. The model is motivated by studies of language competition dynamics, where the AB state is associated with bilingualism. We study the ordering process and associated interface and coarsening dynamics in regular lattices and small world networks. Agents in the AB state define the interfaces, changing the interfacial noise driven coarsening of the voter model to curvature driven coarsening. We argue that this change in the coarsening mechanism is generic for perturbations of the voter model dynamics. When interaction is through a small world network the AB agents restore coarsening, eliminating the metastable states of the voter model. The time to reach the absorbing state scales with system size as $τ\sim \ln N$ to be compared with the result $τ\sim N$ for the voter model in a small world network.
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