Studies in Nonequilibrium Behaviors of Tagged Particles

该项目的目的是研究在简单排斥和零射程粒子系统的某些模型中，一个特殊的或标记的粒子与其他粒子相互作用的渐近涨落。物理感觉是，标记粒子在某种尺度上是一种均匀化的随机行走或布朗运动，其参数反映了系统的相互作用。根据平均律，这幅一阶图已经建立。此外，在某种程度上，在平衡条件下，二阶特征，如“波动”已被理解。但在“非均衡”情况下，人们所知甚少。在这种情况下，具体的拟议工作是在某些“平均零”简单的排斥和零范围的系统，其中一些计算是可能的非平衡波动的特点。这些问题的解决也将有一定的影响非平衡波动的“流体动力学限制”，这也是一个开放的problem.Informally，拟议的项目是调查一些渐近行为的一个区别，或标记组件与其他人在某些模型的交通，排队和流体。更具体地说，拟议的工作是研究“非平衡”波动的标记组件。 该提案的更广泛影响在于其与统计物理学的联系，其中确定标记组件行为对于理解“传输”和“多尺度”现象很重要。

The proposed project is to study some asymptotic fluctuations of a distinguished, or tagged particle interacting with others in certain models of simple exclusion and zero-range particle systems. The physical feeling is that the tagged particle is in some scale a type of homogenized random walk or Brownian motion with parameters reflecting system interactions. This picture to first order in terms of the law of averages has been established. Also, to some extent, under equilibrium conditions, second order features such as "fluctuations" have been understood. But less is known in "non-equilibrium" situations. In this context, the specific proposed work is to characterize the non-equilibrium fluctuations in certain "mean-zero" simple exclusion and zero-range systems where some calculation is possible. Resolution of these issues will also have some bearing on non-equilibrium fluctuations of "hydrodynamic limits" which is as well an open problem.Informally, the proposed project is to investigate some asymptotic behaviors of a distinguished, or tagged component interacting with others in certain models of traffic, queuing and fluids. More specifically, the proposed work is to study "non-equilibrium" fluctuations of such tagged components. The broader impacts of the proposal are in its connections with statistical physics where determining tagged component behavior is important to understanding "transport," and "multi-scale" phenomena.