论文标题
随机助行器中的延伸和动态阶段，沉积和随后的化学步道
Extension and dynamical phases in random walkers depositing and following chemical trails
论文作者
论文摘要
事实证明，活跃的步行者模型在理解蚂蚁小径形成和行人步道等生物学中的大量系统的演变非常有效。我们提出了一个随机助行器的简单模型，该模型修改其本地环境，进而影响助行器在{\ em后来}时间的运动。我们在离散的晶格中对Walker进行直接数值模拟，Walker积极地沉积了一种吸引助行器轨迹并及时蒸发的化学物质。我们提出了一种使用循环半径进行有限的时间步行的轨迹的结构过渡的方法。确定的时窗上的延伸显示出非单调的变化，其沉积速率特征是线圈全球转变的特征。在化学沉积和蒸发速率的参数空间的某些区域，沃克的延伸表现出重点行为。该动力学的特征是均方位移，显示出与中间时间尺度上扩散缩放的偏差，渐近地返回扩散行为。平均场理论捕获了渐近扩散率的变化。
Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its local environment that in turn influences the motion of the walker at a {\em later} time. We perform direct numerical simulations of the walker in a discrete lattice with the walker actively depositing a chemical which attracts the walker trajectory and also evaporates in time. We propose a method to look at the structural transitions of the trajectory using radius of gyration for finite time walks. The extension over a definite time-window shows a non-monotonic change with the deposition rate characteristic of a coil-globule transition. At certain regions of the parameter space of the chemical deposition and evaporation rates, the extensions of the walker shows a re-entrant behavior. The dynamics, characterised by the mean-squared displacement, shows deviation from diffusive scaling at intermediate time scales, returning to diffusive behavior asymptotically. A mean field theory captures the variation of the asymptotic diffusivity.
