Xu S-L-Y, Schwarz J M
National Institutes of Health, Bethesda, Maryland 20892, USA.
Physics Department, Syracuse University, Syracuse, New York 13244, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052130. doi: 10.1103/PhysRevE.88.052130. Epub 2013 Nov 21.
Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions (contacts) between particles in the steady state limit, while in the active phase collisions persist. To investigate this system at higher densities, we construct and study a conserved-particle-number contact process with three-body interactions, which are potentially more likely than two-body interactions at higher densities. For example, consider one active (diffusing) particle colliding with two inactive (nondiffusing) particles such that they become active and consider spontaneous inactivation. In mean field, this system exhibits a continuous dynamical phase transition. Simulations on square lattices also indicate a continuous transition with exponents similar to those measured for the conserved lattice gas (CLG) model. In contrast, the three-body interaction requiring two active particles to activate one inactive particle exhibits a discontinuous transition. Finally, inspired by kinetically constrained models of the glass transition, we investigate the "caging effect" at even higher particle densities to look for a second dynamical phase transition back to an inactive phase. Square lattice simulations suggest a continuous transition with a new set of exponents differing from both the CLG model and what is known as directed percolation, indicating a potentially new universality class for a contact process with a conserved particle number.
在低密度下周期性剪切的胶体，随着应变幅度的增加，会表现出从非活性相到活性相的动力学相变。非活性相在稳态极限下粒子之间不存在碰撞（接触），而在活性相中碰撞持续存在。为了在更高密度下研究这个系统，我们构建并研究了一个具有三体相互作用的守恒粒子数接触过程，在更高密度下三体相互作用可能比两体相互作用更有可能发生。例如，考虑一个活性（扩散）粒子与两个非活性（非扩散）粒子碰撞，使得它们变为活性，并考虑自发失活。在平均场中，这个系统表现出连续的动力学相变。在方形晶格上的模拟也表明存在连续相变，其指数与守恒晶格气体（CLG）模型测量的指数相似。相比之下，需要两个活性粒子激活一个非活性粒子的三体相互作用表现出不连续相变。最后，受玻璃化转变的动力学约束模型启发，我们在甚至更高的粒子密度下研究“笼效应”，以寻找回到非活性相的第二个动力学相变。方形晶格模拟表明存在连续相变，其具有一组不同于CLG模型和所谓定向渗流的新指数，这表明对于具有守恒粒子数的接触过程可能存在一个新的普适类。
