To reduce overall latency for each directional sweep, all the particles moving to either the left or right neighbor are packed
together in a buffer and sent at the same time. It is important to note that a processor may not have any particles to send to
or receive from either of its directional neighbors. To eliminate the need for the expensive queries for such information we
introduce the concept of a ‘‘fake’’ particle. In all the exchanges, whenever no real particles need to move, a fake particle is
sent. Thus every processor can assume that it will receive something from, and send something to, both its neighbors in
the given dimension. The result is a regular nearest neighbor communication pattern with greater efficiency.