论文标题
在受限动态下，自相似的不均匀固定状态
Self-similar inhomogeneous stationary states under constrained dynamics
论文作者
论文摘要
$ n $刚性对象的动力学，每个对象具有$ d $自由度，在尺寸$ nd $的配置空间中播放。由于严格，工作中还有其他限制，使得配置空间的一部分无法访问。在本文中，我们断言将总体动力学视为马尔可夫过程，其状态是由刚性物体之间建立的接触数量定义的，这提供了有效的粗粒子表征，对原本复杂的现象。这种粗糙的谷物将空间的维度从$ nd $降低到一个。我们测试了该断言的曲线正方形的一个维数阵列，每个曲线正处于其角方向的偏置扩散。
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.
