Two-particle Statistics Research Articles

Influence of the sampling time on the kinematics of turbulent diffusion from a continuous source

A kinematic description is presented of how turbulent diffusion from a continuous source varies with the sampling time in stationary, homogeneous turbulence. Unlike most previous theories, the sampling is assumed to take place at fixed downstream distances from the source. It is shown that the sampling-time effects depend on two-particle velocity statistics. Thus, time-average diffusion at fixed downstream distances is more akin to relative diffusion than to absolute diffusion. Two simple diffusion models are developed from the kinematic equations. These models are in fairly good agreement with diffusion data obtained both in a wind tunnel and in the field. Moreover, these models have significant practical implications. For example, the models indicate that care must be taken when using band-pass spectral filtering as a paradigm for turbulent diffusion. Also, the models show that the mean flow speed U has an important influence on the sampling-time effects. To account for U properly, diffusion measurements with differing sampling times Λ should be compared using the product UΛ, and not just Λ.

STATISTICS ON NETWORKS

One-dimensional networks are excellent examples of topological spaces which are not manifolds and which admit interesting quantum physics. They are of importance in the free electron model for molecules and crystals. They also occur as fabricated mesoscopic networks. We review single-particle quantum physics on networks from topological and operator theoretic points of view and then initiate study of identical particles on networks. It is established that the available statistics on networks in its range and complexity rival the richness of statistical options in two dimensions. We treat two-particle statistics on simple networks with detail, taking care to cover operator theoretic issues pertaining to multiple connectivity and also those due to basic topological differences between a generic network and a manifold.