  Braids composed of two interwoven polymer chains exhibit a buckling
transition whose origin has been explained through the onset of plectonemic
structures. Here we study, by a combination of simulation and analytics, the
dynamics of plectoneme formation and their statistics in steady state. The
introduction of an order parameter, the plectonemic fraction, allows us to map
out the phase boundary between the straight braid phase and the plectonemic
one. We then monitor the formation and the growth of plectonemes, observing
events typical of phase separation kinetics for liquid-gas systems (fusion,
fission, 1D Ostwald ripening), but also of DNA supercoiling dynamics
(plectonemic hopping). Finally, we propose a stochastic field theory for the
coupled dynamics of twist and local writhe which explains the phenomenology
found with Brownian dynamics simulations as well the power laws underlying the
coarsening of plectonemes.
