论文标题
平均场限制中的孤立状态
Solitary states in the mean-field limit
论文作者
论文摘要
我们研究了主动物质系统，其中基础自propelled颗粒遵守二阶方程的方向动力学。通过主要集中于用于颗粒分布的空间均匀设置，我们的分析结合了主动物质和振荡网络的理论。对于此类系统，我们通过同型分叉分析孤立状态的外观，作为频率聚类的机制。通过引入噪声，我们建立了一个随机版本的孤立状态，并得出了一个由偏微分方程描述的单粒子概率密度函数所描述的平均场限制，人们可以将其称为惯性和噪声的连续体kuramoto模型。通过研究此限制，我们建立了极性和无序之间的二阶相变。在我们的研究中，分析方法和数值方法的结合表明，平均场和有限尺寸模型之间存在出色的定性一致性。
We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite size models.
