双稳态基因开关模型中的确定性级联粗化
Deterministic cascade coarsening in a Bistable Gene Toggle model
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中文总结 AI 辅助
研究具有扩散耦合的双稳态基因开关模型的确定性粗化动力学，发现其与经典曲率驱动粗化机制不同，畴壁有独特行为，粗化有对数周期振荡且\(\delta<0.5\)，还表明对数周期振荡由消失的畴控制，符合离散尺度不变性。
中文摘要 AI 辅助
我们研究了具有扩散耦合的空间扩展双稳态基因开关模型中的确定性粗化动力学。与经典曲率驱动粗化不同，在经典模型中畴壁连续移动并逐渐湮灭，而本系统表现出质的不同机制。畴壁长时间固定，通过集体级联事件突然消失。畴壁密度按\(\rho(t)\sim t^{-\delta}\)衰减，但粗化在幂律行为上叠加有明显的对数周期振荡。对于所考虑的所有启动子强度\(\alpha\)值，测量指数满足\(\delta<0.5\)，表明与曲率驱动粗化的经典艾伦 - 卡恩预测\(\delta = 1/2\)有系统偏差。我们表明对数周期振荡不由畴壁密度控制，而是由每个级联中消失的畴控制。消失畴的平均大小随级联指数大致线性增长，产生级联时间的恒定几何间距，符合离散尺度不变性。
英文摘要
We investigate deterministic coarsening dynamics in a spatially extended bistable gene toggle model with diffusive coupling. Unlike classical curvature-driven coarsening, where domain walls move continuously and annihilate gradually, the present system exhibits a qualitatively different mechanism. The domain walls remain pinned for long intervals and disappear abruptly through collective cascade events. The density of domain walls decays approximately as $ρ(t)\sim t^{-δ}$, but the coarsening exhibits clear log-periodic oscillations superimposed on the power-law behavior. For all values of the promoter strength $α$ considered, the measured exponent satisfies $δ<0.5$, indicating a systematic deviation from the classical Allen--Cahn prediction $δ=1/2$ for curvature-driven coarsening. We show that log-periodic oscillations are not controlled by the density of domain walls, but by the \emph{domains that disappear} in each cascade. The average size of disappearing domains grows roughly linearly with cascade index, producing a constant geometric spacing of cascade times, consistent with discrete scale invariance.
