论文标题
温度转变和脱落型在用宏观场的小簇控制中
Temperature transitions and degeneracy in the control of small clusters with a macroscopic field
论文作者
论文摘要
我们提出了对具有宏观场的几个粒子波动簇的控制的数值研究。我们的目标是达到给定的目标群集形状是最小时间。这个问题被称为集群配置空间中的第一个段落问题。我们发现使用动态编程将宏观场设置为观察到的形状的函数的最佳策略。我们的结果表明，最佳策略是非唯一的，其退化性主要与初始形状，力和目标形状共享的对称性有关。随着群集大小的增加，最佳选择最佳选择的形状总比例是非唯一的。此外，当温度变化时，最佳策略将表现出离散的过渡集。每个过渡都会导致与温度相对于目标到达目标的时间的不连续性。随着群集的大小增加，由于温度过渡而引起的策略的变化会增加，例如配置总数和连续限制。
We present a numerical investigation of the control of few-particle fluctuating clusters with a macroscopic field. Our goal is to reach a given target cluster shape is minimum time. This question is formulated as a first passage problem in the space of cluster configurations. We find the optimal policy to set the macroscopic field as a function of the observed shape using dynamic programming. Our results show that the optimal policy is non-unique, and its degeneracy is mainly related to symmetries shared by the initial shape, the force and the target shape. The total fraction of shapes for which optimal choice of the force is non-unique vanishes as the cluster size increases. Furthermore, the optimal policy exhibits a discrete set of transitions when the temperature is varied. Each transition leads to a discontinuity in the derivative of the time to reach with target with respect to temperature. As the size of the cluster increases, the change in the policy due to temperature transitions grows like the total number of configurations and a continuum limit emerges.
