Boltzmann approach to collective motion via nonlocal visual interaction.

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Susumu Ito, Nariya Uchida
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引用次数: 0

Abstract

Visual cues play crucial roles in the collective motion of animals, birds, fish, and insects. The interaction mediated by visual information is essentially nonlocal and has many-body nature due to occlusion, which poses a challenging problem in modeling the emergent collective behavior. In this paper, we introduce a Boltzmann-equation approach incorporating nonlocal visual interaction. Occlusion is treated in a self-consistent manner via a coarse-grained density field, which renders the interaction effectively pairwise. Our model also incorporates the recent finding that each organism stochastically selects a neighbor to interact at each instant. We analytically derive the order-disorder transition point, and show that the visual screening effect raises the transition threshold, which does not vanish when the density of the agents or the range of the intrinsic interaction is taken to infinity. Our analysis suggests that the model exhibits a discontinuous transition as in the local interaction models, and but the discontinuity is weakened by the nonlocality. Our study clarifies the essential role of nonlocality in the visual interactions among moving organisms.

通过非局部视觉相互作用研究集体运动的玻尔兹曼方法。
视觉线索在动物、鸟类、鱼类和昆虫的集体运动中起着至关重要的作用。视觉信息介导的相互作用本质上是非局部的,并且由于遮挡而具有多体性,这给紧急集体行为的建模带来了挑战。本文引入了一种包含非局部视觉相互作用的玻尔兹曼方程方法。通过粗粒度密度场以自一致的方式处理遮挡,从而有效地两两呈现相互作用。我们的模型还结合了最近的发现,即每个生物体在每个瞬间随机选择一个邻居进行互动。我们解析导出了有序-无序过渡点,并表明视觉筛选效应提高了过渡阈值,当主体密度或内在相互作用范围趋近无穷大时,过渡阈值不会消失。我们的分析表明,在局部相互作用模型中,模型表现出不连续的过渡,但非局域性削弱了这种不连续。我们的研究阐明了非定域性在运动生物之间的视觉相互作用中的重要作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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