约束动力学下的自相似非齐次stationary states
Self-similar inhomogeneous stationary states under constrained dynamics
摘要：
$n$刚性物体的动力学，每个都有$d$自由度，在尺寸为$nd$的配置空间中进行。由于是刚性的，因此存在使配置空间的一部分不可访问的附加约束。在本文中，我们作出的断言，治疗的整体动态作为一个马尔可夫过程，其状态是由刚性物体之间的接触数量定义的，提供了一个有效的粗粒度表征，否则复杂的现象。这种粗粒化将空间的维数从$nd$减少到1。我们测试这一论断的一个一维阵列的弯曲的正方形，其中每一个正在经历一个有偏见的扩散在其角度方向。
英文摘要：
The dynamics of $n$ rigid objects, each having $d$ degrees of freedom, is played out in the configuration space of dimension $nd$. Being rigid, there are additional constraints at work that render a portion of the configuration space inaccessible. In this paper, we make the assertion that treating the overall dynamics as a Markov process whose states are defined by the number of contacts made between the rigid objects provides an effective coarse grained characterization of the otherwise complex phenomenon. This coarse graining reduces the dimensionality of the space from $nd$ to one. We test this assertion for a one dimensional array of curved squares each of which is undergoing a biased diffusion in its angular orientation.
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