Microscopic definition of entanglement

We propose to define polymer entanglements as long-lived contacts between the mean paths. The mean path is defined as a path connecting average positions of every monomer over characteristic time of entanglement $\tau_e$. We performed molecular dynamics simulations on variety of bead-spring models in equilibrium and under shear and investigated properties of entanglements defined in such way. A new algorithm for identification of entanglements allows tracing evolution of individual entanglements and quantifying such mechanisms as constraint release and convective constraint release.