两种绳系运动模型的比较
Comparison of two models of tethered motion
摘要：
我们考虑一个随机的步行者，其运动被束缚在一个焦点周围。我们使用两个模型，表现出相同的空间依赖性在稳态，但广泛不同的动态。在一种情况下，助行器受到朝向焦点的确定性偏置，而在另一种情况下，其在随机时间将其位置重置到焦点。与重置型步行者返回的随机性相比，偏向型步行者的确定性倾向使得远离焦点的突袭更不可能。这种差异对中间时间的时空动态有影响。为了显示这两种模型的差异，我们分析了它们的概率分布和它们的动力学存在和不存在的部分或完全吸收陷阱。我们推导出解析各种数量：（一）平均首次通过时间到一个目标，我们恢复先前获得的结果通过不同的技术，（二）分裂概率的两个目标以及生存概率时，一个或两个目标是部分吸收。限制，扩散和吸收陷阱之间的相互作用产生有趣的非单调效应，在各种数量，所有潜在的实验中访问。这里开发的形式主义可能有各种各样的应用，从研究动物在家庭范围内漫游和电子激发在有机晶体中移动，以开发有效的搜索算法在拥挤的环境中定位目标。
英文摘要：
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic bias towards the focal point, while in the other case, it resets its position to the focal point at random times. The deterministic tendency of the biased walker makes the forays away from the focal point more unlikely when compared to the random nature of the returns of the resetting walker. This difference has consequences on the spatio-temporal dynamics at intermediate times. To show the differences in the two models, we analyze their probability distribution and their dynamics in presence and absence of partially or fully absorbing traps. We derive analytically various quantities: (i) mean first-passage times to one target, where we recover results obtained earlier by a different technique, (ii) splitting probabilities to either of two targets as well as survival probabilities when one or either target is partially absorbing. The interplay between confinement, diffusion and absorbing traps produces interesting non-monotonic effects in various quantities, all potentially accessible in experiments. The formalism developed here may have a diverse range of applications, from study of animals roaming within home ranges and of electronic excitations moving in organic crystals to developing efficient search algorithms for locating targets in a crowded environment.
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