APPLIED PROBABILITY AND STATISTICS SEMINAR

Fall 2006 / Spring 2007
Upcoming Talks / Past talks


Time:Wed April 4, 1.30pm-2.30pm

Place: PHYS 129

Speaker: Mashid Atapour

Title: Asymptotic Behavior of the Entanglement Complexity of Polymer Systems in Tube

Abstract: Polymers are modeled mathematically by self-avoiding walks (SAW) in the simple cubic lattice. A SAW is a walks in the lattice which does not intersect itself. In this presentation I will present some rigorous results on a mathematical model of polymers in dense systems. This model is motivated by a mainly numerical work (Orlandini et al 2004). We imagine cutting an infinite rectangular tube out of a polymer system. This tube will capture several polymers running through its interior, and starting and ending on the boundary. These sub-chains will be mutually entangled. Associating a 2-component link to each pair of polymers, we use the linking number to measure the entanglement complexity of polymer systems. We model these polymer systems mathematically by Systems of Self-avoiding Walks (SSAWs), then we rigorously prove that there exists a positive number a such that the probability that a polymer system of size n has entanglement complexity greater than and approaches 1 as n goes to infinity. Furthermore, for a special sub-class of SSAWs we prove that the entanglement complexity grows exactly linearly in n.