Nguyen P The, Lee Sang-Hee, Ngo V Thanh
Department of Natural Science, Duytan University, K7/25 Quang Trung, Haichau, Danang, Vietnam.
Division of Fusion and Convergence of Mathematical Sciences, National Institute for Mathematical Sciences, Daejeon, Republic of Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Sep;92(3):032716. doi: 10.1103/PhysRevE.92.032716. Epub 2015 Sep 17.
The nature of the phase transition in a system of self-propelling particles has been extensively studied during the past few decades. A theoretical model was proposed by [T. Vicsek et al. Phys. Rev. Lett. 75, 1226 (1995)PRLTAO0031-900710.1103/PhysRevLett.75.1226] with a simple rule for updating the direction of motion of each particle. Based on the model of Vicsek et al., in this paper, we consider a group of animals as particles moving freely in a two-dimensional space. Due to the fact that the viewable area of animals depends on the species, we consider the motion of each individual within an angle φ=ϕ/2 (ϕ is called the angle of view) of a circle centered at its position of radius R. We obtained a phase diagram in the space (φ,η_{c}) with η_{c} being the critical noise. We show that the phase transition exists only in the case of a wide view's angle φ≥0.5π. The flocking of animals is a universal behavior of the species of prey but not the one of the predator. Our simulation results are in good agreement with experimental observation [C. Beccoa et al., Physica A 367, 487 (2006)PHYADX0378-437110.1016/j.physa.2005.11.041].
在过去几十年中，对自推进粒子系统中相变的本质进行了广泛研究。[T. 维克塞克等人，《物理评论快报》75, 1226 (1995年)PRLTAO0031 - 900710.1103/PhysRevLett.75.1226]提出了一个理论模型，该模型具有更新每个粒子运动方向的简单规则。基于维克塞克等人的模型，在本文中，我们将一群动物视为在二维空间中自由移动的粒子。由于动物的可视区域取决于物种，我们考虑每个个体在以其位置为圆心、半径为R的圆的角度φ = ϕ/2（ϕ称为视角）内的运动。我们在空间(φ,ηₑ)中获得了一个相图，其中ηₑ是临界噪声。我们表明，相变仅在宽视角φ≥0.5π的情况下存在。动物的群聚是猎物物种的普遍行为，而不是捕食者的行为。我们的模拟结果与实验观察结果[C. 贝科阿等人，《物理A》367, 487 (2006年)PHYADX0378 - 437110.1016/j.physa.2005.11.041]高度吻合。
