Self-similar inhomogeneous stationary states under constrained dynamics

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 renders 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.

Automated summary

This paper discusses the dynamics of rigid objects and proposes a coarse-grained modeling approach by treating it as a Markov process, effectively reducing the dimensionality of the configuration space.