We are concerned with how the implementation of growth determines the expected number of state-changes in a growing self-organizing process. With this problem in mind, we examine two versions of the voter model on a one-dimensional growing lattice. Our main result asserts that the expected number of state-changes before an absorbing state is found can be controlled by balancing the conservative and disruptive forces of growth. This is because conservative growth preserves the self-organization of the voter model as it searches for an absorbing state, whereas disruptive growth undermines this self-organization. In particular, we focus on controlling the expected number of state-changes as the rate of growth tends to zero or infinity in the limit. These results illustrate how growth can affect the costs of self-organization and so are pertinent to the physics of growing active matter.

我们关注的是增长的实施方式如何决定不断增长的自组织过程中预期的状态变化数量。考虑到这个问题，我们在一个一维增长的格子上研究了选民模型的两个版本。我们的主要结果断言，可以通过平衡增长的保守力和破坏力来控制发现吸收状态之前状态变化的预期数量。这是因为保守增长会在投票者模型寻求吸收状态时保留选民模型的自组织，而破坏性增长则会破坏这种自组织。特别是，我们专注于控制状态变化的预期数量，因为增长率趋于零或无穷大。