Dynamic Looping of a Free-Draining Polymer

摘要: We revisit the celebrated Wilemski--Fixman (WF) treatment for looping time of a free-draining polymer. The WF theory introduces sink term into Fokker--Planck equation $3(N+1)$-dimensional Ornstein--Uhlenbeck process polymer dynamics, which accounts appropriate boundary condition due to formation loop. assumption is considerably relaxed. A perturbation method approach developed that justifies and generalizes previous results using either delta or Heaviside sink. For both types sinks, we show under small dimensionless $\epsilon$, ratio capture radius Kuhn length, are able systematically produce all known analytical asymptotic obtained by other methods. This includes most notably transition regime between $N^2$ scaling Doi, $N\sqrt{N}/\epsilon$ Szabo, Schulten, Schulten. mathematical issue at play nonuniform convergence $\epsilon\to 0$ ...