Buckling transition of a semiflexible filament in extensional flow

An analytical expression for the fluctuation-rounded stretch-coil transition of semiflexible polymers in extensional flows is derived. The competition between elasticity and tension is known to cause a buckling instability in filaments placed near hyperbolic stagnation points and the effect of thermal fluctuations on this transition has yet to receive full quantitative treatment. Motivated by the findings of recent experiments as well as our simulations, we solve for the amplitude of the first buckled mode near the onset of the instability. This reveals a stochastic supercritical bifurcation, which is in excellent agreement with full numerical simulations.