主动局部搜索器绕其共同起始位置的对准分析
Analysis of aligning active local searchers orbiting around their common home position
摘要：
我们讨论了成对对齐相互作用的影响，在一个合奏的中心位置觅食或搜索连接到一个共同的家。从更广泛的意义上说，我们也考虑被吸引到一个中心位置的自我移动实体，例如，浮游动物水蚤被吸引到一束光。单个觅食者由于某种推进机制而以恒定的速度移动。他们随意探索周围的空间，然后押韵地回到自己的家。在系综中，一个粒子的速度方向与其相邻粒子的运动方向一致。首先，我们进行模拟，这个合奏，并找到一个合作的行为的实体。超过一个过临界的相互作用强度，搜索者的轨迹发生了质的变化，搜索者开始沿着原点周围的圆圈移动。因此，所有的搜索者都围绕中心位置顺时针或逆时针旋转，就像浮游动物水蚤一样。第二，计算结果进行了分析解释的非线性平均场Fokker-Planck方程所考虑的情况下的输运方程的制定。在渐近稳定极限下，我们找到了临界相互作用强度、搜索者的平均径向和轨道速度及其速度方差的表达式。我们还获得了边缘的空间和角密度在下临界政权的觅食行为像个人，以及在过临界政权，他们集体旋转周围考虑的家。此外，我们阐述了过阻尼Smoluchowski限制合奏。
英文摘要：
We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self moving entities that are attracted to a central place such as, for instance, the zooplankton Daphnia being attracted to a beam of light. Single foragers move with constant speed due to some propulsive mechanism. They explore at random loops the space around and return rhytmically to their home. In the ensemble, the direction of the velocity of a searcher is aligned to the motion of its neighbors. At first, we perform simulations of this ensemble and find a cooperative behavior of the entities. Above an over-critical interaction strength the trajectories of the searcher qualitatively changes and searchers start to move along circles around the home position. Thereby, all searchers rotate either clockwise or anticlockwise around the central home position as it was reported for the zooplankton Daphnia. At second, the computational findings are analytically explained by the formulation of transport equations outgoing from the nonlinear mean field Fokker-Planck equation of the considered situation. In the asymptotic stationary limit, we find expressions for the critical interaction strength, the mean radial and orbital velocities of the searchers and their velocity variances. We also obtain the marginal spatial and angular densities in the under-critical regime where the foragers behave like individuals as well as in the over-critical regime where they rotate collectively around the considered home. We additionally elaborate the overdamped Smoluchowski-limit for the ensemble.
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