We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is repeatedly diverted across the faces of the complex. For non-conservative initial configurations we show this process never terminates. For conservative initial flows we show the process terminates after a finite number of rerouting steps, but there are many possible final configurations reachable from a single initial state. Finally, for conservative initial flows around a topological hole we show the process terminates at a unique final configuration. In this case the process exhibits global confluence despite not satisfying local confluence.

我们考虑了一种离散的不确定流触发过程，用于在平面复合体的边缘重新路由流。该过程是高维芯片发射的一个实例。在射流过程中，复合物边缘上的流动反复转移到整个复合物的表面。对于非保守的初始配置，我们显示此过程永远不会终止。对于保守的初始流程，我们显示流程在有限数量的重新路由步骤后终止，但是从单个初始状态可以达到许多可能的最终配置。最后，对于拓扑孔周围的保守初始流，我们显示了过程终止于唯一的最终配置。在这种情况下，尽管不满足局部汇合，但是该方法仍表现出整体汇合。