“

“We use direct numerical simulations to solve for a filament (with bending modulus B, length

L), suspended in the fluid (with dynamic viscosity ), obeying Stokesian dynamics in a linear shear flow whose strain rate,  , is a periodic function of time(t),  = S sin(t). The dynamical behaviour is determined by the elasto-viscous number, and . For a fixed , for small enough , the filament remains straight; as  increases we observe respectively buckling, breakdown of time-periodicity and appearance of two-period and eventually complex spatiotemporal solutions. To analyze the dynamics of this non-autonomous system, we consider the map obtained by integrating the dynamical equations over exactly one period. We find that this map has multiple fixed points and periodic orbits for large enough . For  and  within a certain range we find qualitative evidence of mixing of passive tracers.”

We use direct numerical simulations to solve for a filament (with bending modulus B, length

L), suspended in the fluid (with dynamic viscosity ), obeying Stokesian dynamics in a linear shear flow whose strain rate,  , is a periodic function of time(t),  = S sin(t). The dynamical behaviour is determined by the elasto-viscous number, and . For a fixed , for small enough , the filament remains straight; as  increases we observe respectively buckling, breakdown of time-periodicity and appearance of two-period and eventually complex spatiotemporal solutions. To analyze the dynamics of this non-autonomous system, we consider the map obtained by integrating the dynamical equations over exactly one period. We find that this map has multiple fixed points and periodic orbits for large enough . For  and  within a certain range we find qualitative evidence of mixing of passive tracers.”