标题： 复杂噪声环境中维斯克代理的涌现旋转序和再进入全局序 显示英文标题

标题： Emergent Rotational Order and Re-entrant Global Order of Vicsek Agents in a Complex Noise Environment

摘要： 在复杂环境中的噪声追逐推动了活性物质系统中涌现的集体行为。 研究环境线索影响的有力平台是由标准维斯克模型提供的，用于研究 flocking 和 swarming 现象。 在本研究中，我们探讨了维斯克代理人在复杂噪声环境中的集体动力学，该环境包含一个无噪声的圆形区域（$\eta_{\text{c}} = 0.0$），周围是一个可调节的噪声外部区域（$\eta_{\text{b}} = 1.0$），并且具有相互排斥的相互作用。 通过改变外部噪声强度，我们观察到一种涌现的旋转秩序（$\phi_r$），其在较高噪声水平（$\eta_{\text{b}}\sim 1$）时达到峰值，如相图和灵敏度图所示。 全局秩序遵循（$\phi$）呈现一个“U”形曲线，$\phi \sim 0.965$在$\eta_b=0$处下降至$\phi \sim 0.57$在$\eta_b=0.9$处，并在$\eta_b > 1$处重新进入，在$\phi \sim 0.960$处达到峰值$\eta_b=1.5$。 后者上升归因于$\phi_r$的增加。 较高的粒子速度增强了从圆形区域的逃逸率 ($\kappa$)，而移动较慢的代理表现出更大的虚拟限制。 我们通过时间平均和首次通过逃逸率来量化逃逸动力学，展示了速度依赖性的保留，使得在给定时间内找到双运动代理群集的概率产生分隔和捕获。 引入从圆心到外部区域的渐进噪声增加，降低了全局 ($\phi$) 和旋转 ($\phi_r$) 有序度，强调了环境异质性和突然退火相对于渐变变化的影响。 这些发现为预测和操控异质环境中的活性代理动力学提供了见解，适用于生物和合成群体系统。 显示英文摘要

摘要： Noisy pursuit in complex environments drives emergent collective behaviors in active matter systems. A compelling platform to study the impact of environment cues is provided by the standard Vicsek model for studying flocking and swarming phenomena. In this study, we explore the collective dynamics of Vicsek agents in a complex noise environment, featuring a noiseless circular region ($\eta_{\text{c}} = 0.0$) surrounded by a noisy outer region ($\eta_{\text{b}} = 1.0$, tunable), with a mutually repelling interactions. By varying the outer noise intensity, we observe an emergent rotational order ($\phi_r$) that peaks at higher noise levels ($\eta_{\text{b}}\sim 1$), as revealed by phase and susceptibility plots. Global order follows ($\phi$) follows a `U' shaped curve, $\phi \sim 0.965$ at $\eta_b=0$, dies down to $\phi \sim 0.57$ at $\eta_b=0.9$ and re-enters at $\eta_b > 1$ and peaks $\phi \sim 0.960$ at $\eta_b=1.5$. The latter rise attributing to $\phi_r$ increase. Higher particle velocities enhance escape rates ($\kappa$) from the circular region, with slower-moving agents exhibiting greater virtual confinement. We quantify escape dynamics through time-averaged and first-passage escape rates, demonstrating velocity-dependent retention on the probability of finding the bi-motility agent flocks at a give time resulting in segregation and trapping. Introducing a gradual noise increase from the circle's center to the outer region reduces both global ($\phi$) and rotational ($\phi_r$) order, underscoring the impact of environmental heterogeneity and sudden annealing over gradual change. These findings offer insights into predicting and manipulating active agent dynamics in heterogeneous environments, with applications in biological and synthetic swarming systems.