Giuggioli L, Potts J R, Harris S
Bristol Centre for Complexity Sciences, University of Bristol, Bristol, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061138. doi: 10.1103/PhysRevE.83.061138. Epub 2011 Jun 23.
Inspired by the collective phenomenon of territorial emergence, whereby animals move and interact through the scent marks they deposit, we study the dynamics of a 1D Brownian walker in a random environment consisting of confining boundaries that are themselves diffusing anomalously. We show how to reduce, in certain parameter regimes, the non-Markovian, many-body problem of territoriality to the analytically tractable one-body problem studied here. The mean square displacement (MSD) of the 1D Brownian walker within subdiffusing boundaries is calculated exactly and generalizes well known results when the boundaries are immobile. Furthermore, under certain conditions, if the boundary dynamics are strongly subdiffusive, we show the appearance of an interesting nonmonotonicity in the time dependence of the MSD, giving rise to transient negative diffusion.
受领地出现这一集体现象的启发，即动物通过它们留下的气味标记来移动和互动，我们研究了一维布朗粒子在由自身反常扩散的限制边界组成的随机环境中的动力学。我们展示了如何在某些参数范围内，将领地性的非马尔可夫多体问题简化为这里所研究的可解析处理的单体问题。精确计算了亚扩散边界内一维布朗粒子的均方位移（MSD），并推广了边界固定时的著名结果。此外，在某些条件下，如果边界动力学是强亚扩散的，我们展示了MSD时间依赖性中有趣的非单调性的出现，从而产生瞬态负扩散。
