论文标题
部分可观测时空混沌系统的无模型预测
Local resetting with geometric confinement
论文作者
论文摘要
最近引入了“局部重置”，以描述相互作用的系统中的随机重置，其中粒子独立地试图重置为常见的“原点”。我们对重置过程本身受到交互作用本身的这种系统的理解仍然非常有限。通常对相互作用粒子的动力学施加的无处不在的约束是几何限制，例如将刚性球形颗粒限制在如此狭窄的通道上，以至于超车变得困难。我们在这里探讨了由两种扩散粒子组成的系统中局部重置与几何限制之间的相互作用：“浴”粒子和“示踪剂”，这些粒子经历了局部重置。平均场分析和数值模拟表明，重置示踪剂的固定密度曲线表现出典型的“帐篷状”形状，并将这种形状烙印到浴缸密度曲线上。在改变几何限制程度与颗粒扩散率的比率之比后，该系统被发现在两个状态之间过渡。在一个示踪剂中，将浴粒子从原点驱逐出境，而在另一个示踪剂中，它们却陷入了困境。在这两种状态之间，我们找到了一种特殊情况，即平均场近似变得精确。
"Local resetting" was recently introduced to describe stochastic resetting in interacting systems where particles independently try to reset to a common "origin". Our understanding of such systems, where the resetting process is itself affected by interactions, is still very limited. One ubiquitous constraint that is often imposed on the dynamics of interacting particles is geometric confinement, e.g. restricting rigid spherical particles to a channel so narrow that overtaking becomes difficult. We here explore the interplay between local resetting and geometric confinement in a system consisting of two species of diffusive particles: "bath" particles, and "tracers" which undergo local resetting. Mean-field analysis and numerical simulations show that the resetting tracers, whose stationary density profile exhibits a typical "tent-like" shape, imprint this shape onto the bath density profile. Upon varying the ratio of the degree of geometric confinement over particle diffusivity, the system is found to transition between two states. In one tracers expel bath particles away from the origin, while in the other they ensnare them instead. Between these two states, we find a special case where the mean field approximation becomes exact.
