Overdamped stress relaxation in buckled rods.
We present a comprehensive theoretical analysis of the stress relaxation in a multiply but weakly buckled incompressible rod in a viscous solvent. For the bulk, two interesting parameter regimes of generic self-similar intermediate asymptotics are distinguished, which give rise to approximate and exact power-law solutions, respectively. For the case of open boundary conditions the corresponding nontrivial boundary-layer scenarios are derived by a multiple-scale perturbation ("adiabatic") method. Our results compare well with--and provide the theoretical explanation for--previous results from numerical simulations, and they suggest directions for further fruitful numerical and experimental investigations.
Hallatschek
Oskar
O
Hahn-Meitner Institut, Glienicker Strasse 100, D-14109 Berlin, Germany.
Frey
Erwin
E
Kroy
Klaus
K