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arXiv 1306.0570cond-mat.stat-mech
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自推进粒子的密度无关模型

Density-Independent Model of Self-Propelled Particles

Daniel Schubring, Paul R. Ohmann

摘要:

我们研究了密度无关的修改Vicsek模型中,一个粒子与Delaunay三角定义的邻居相互作用。为了可行地模拟该模型,开发了一种随时间修复三角剖分的算法。该算法也适用于任意时变二维Delaunay三角剖分。该模型表现出一个连续的相变与噪声,和一组不同的临界指数测量满足超标度关系。临界指数被发现之间的低和高的速度制度,但他们是强大的排斥相互作用的列入下。我们提出的证据表明,相关长度近似尺度与系统的大小,即使在有序相。

英文摘要:

We examine a density-independent modification of the Vicsek model in which a particle interacts with neighbors defined by Delaunay triangulation. To feasibly simulate the model, an algorithm for repairing the triangulation over time was developed. This algorithm may also be applied to any time-varying two-dimensional Delaunay triangulation. This model exhibits a continuous phase transition with noise, and a distinct set of critical exponents were measured which satisfy a hyperscaling relationship. The critical exponents are found to vary between a low and high velocity regime, but they are robust under the inclusion of a repulsive interaction. We present evidence that the correlation length approximately scales with the size of the system even in the ordered phase.

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