活性物质系统是指自驱动单元组成的系统。与经典的平衡系统不同，活性物质系统中 的个体(单元) 能够不断地通过消耗自身能量推动自身运动，因而该系统是远离平衡态的。 生物种群、细胞团、合成材料和工程中的微观领域都是活性物系统组成的，并且这些系统 广泛存在于自然界以及人工合成材料中。研究活性物质系统的意义，就在于理解系统的集 体行为(自组织、模式形成)、动力学过程以及由活性物相互作用呈现出来的其他性质。此外，研究活性物系统对跨学科领域，尤其对材料科学、机器人技术和自驱动微纳机械设计， 都具有重要的理论指导意义。目前为止，活性物质系统的研究，是通过发展理论模型、数学框架和计算方法，去探究活性物质系统的基本原理、描述和预测系统的行为。活性物质 系统研究，预期会为新材料、新技术的发展做出重要贡献。

自然界中的生物在面临碰撞时，会基于本能转换方向以避免或者减轻碰撞所带来的伤 害。受这种生物本能行为的启发，结合我们的合作者关于活性粒子的实验，我们建立了一个具有主动重新定向能力的活性物模型。该模型具有丰富的相动力学特性，包括全局集体一致性运动和瞬态聚集(相分离)。我们对这些相进行了详细的刻画与探究，证明了主动重 新定向对自推进颗粒系统的涌现行为的重要性。这个致密的活性系统表现出受多体相互作用调控下的相动力学，而这些相行为之间的关系不能用分子混沌假设理论来解释。因此，为了探究不同相行为之间关系的基本原理，我们提出了一个合理的动力学解释，并修正了 分子混沌假设。通过对粒子对碰撞行为进行分类，我们处理了多体效应，发现了系统的集体一致性运动生长最快所对应的群体的最佳密度，这为理解密集活性系统提供了新的视角。

此外，我们研究了由具有主动重新定向能力的自驱动粒子组成的活性系统中的初始条 件对于集体一致性运动和聚集(相分离) 的演化过程和稳态的影响。我们观察到受初始状 态的有序程度的影响，系统稳态参数相空间中出现了不稳定的区域。我们发现双稳态的存 在是由不同的初始状态产生的动态路径造成的，表现为通过增加(降低) 系统初始状态的有 序程度，双稳态可以转移到更有序的集体一致性运动或是无序聚集(相分离) 状态。这些结 果对于我们如何调控主动系统涌现出的集体运动具有指导作用。其次，我们通过改变混合比例研究了由具有和不具有主动重新定向能力的活性粒子组成的混合物的相行为。我们得到了在不同混合比例下关于集体一致性行为的相图，并观察到随着混合比例增加，有序相对应的区域缩小。这是因为不具有主动重新定向能力的粒子会破坏具有主动重新定向能力的粒子之间的对齐，这相当于减少了活性转动的贡献。上述研究结果为活性物质合成或者实现更高程度的控制等方面提供思路。

Active matter is a physical system composed of self-propelled units. Unlike classical equilibrium system, the individual (unit) in the active system can constantly drive its own movement by consuming energy, so they are far from equilibrium. These systems are widespread in natural and artificial environments, such as biological populations, cell clusters, synthetic materials and engineering micro-systems and so on. The significance of studying active systems lies in the understanding of the collective behavior (self-organization, pattern formation), dynamical processes, and other properties of the system as revealed by the interactions of the active units. The research of active system has a wide range of applications in various interdisciplinary fields, especially in the fields of materials science, robotics and the design of self-driving micro-nano machines. So far, the research of active matter system is to explore the basic principle, describe and predict the behaviors of system by developing theoretical models, mathematical frames and calculating methods, which is expected to contribute to the development of new materials and new technologies.

Animals in nature will instinctively switch directions to avoid or reduce the damage caused by collisions when facing collisions. Inspired by this biological instinct and combined with experiment, we develop a simple numerical model with active reorientation, which exhibits rich phase dynamics including a robust global flocking state and a transient clustering state and reveals the unexpected link between different collective behaviors. Our study illustrates the importance of active reorientation on the emergent behaviors of self-propelled particles relevant to many natural and engineered active systems. This dense active system shows unusual phase dynamics strongly regulated by many-body interactions, which cannot be explained by theories assuming molecular chaos. To rationalize the interplay between different emergent phases, a simple kinetic model is proposed with a revised molecular chaos hypothesis, which treats the many- body effect implicitly via categorizing different types of particle pair collisions. Our model predicts an optimal growth rate of flocking and illustrates a generic approach for understanding dense active systems.

Besides, We study the influence of initial conditions on the two phenomena (flocking and clustering) in this active system. First of all we numerically investigate the initial state induced evolution of flocking and clustering in a system consisting of self-propelled particles with active reorientation. We consider the interplay between flocking and clustering phases under different initial states, and observe an instable domain in order parameter phase diagrams due to initial states even in the absence of an explicit attraction. In particular, we find that the existence of bi-stable states is due to the diversity of dynamic paths arising from different initial states. By increasing (decreasing) the initial degree of ordering, the bi-stable state can be shifted to a more ordered flocking (disordered clustering) state. These results enlighten us to manipulate emergent behaviors and collective motions of active system. Next we study phase behaviors of mixtures comprising active particles with and without active reorientation. We observe that under different mixing ratios, the system exhibits different phases in the steady state. We also calculate and obtain phase diagrams of flocking under different mixing ratios. The domain corresponding to flocking experiences a contraction with the increase of mixing ratio. This is because particles without active reorientation can disrupt the alignment between particles with active reorientation, which is equivalent to reducing the contribution of active reorientation. The above results can provide insights into the synthesis of active matter or higher levels of control.