Supplementary material for Turuban et al., 2018, submitted to JFM

This page contains supplementary animations for « Chaotic Mixing in Crystalline Granular Media » by Turuban et al., submitted to JFM (2018). Animations are displayed in the order in which they appear along the paper’s and supp. mat.’s text.

LineFoldingAndStretching :

Stretching and folding of a line of fluid particles (black line) which is a circle at initial time. The line is shown successively for increasing travel distance of the fluid inside the porous medium (in bead diameter unit).The initial circle is shown in red on top of the black line to indicate the scale.
The flow orientation is $({\mathrm{\theta \_}}_{\text{f}},{\mathrm{\varphi \_}}_{\text{f}})=(\pi /40,7\pi /90)$.

ManifoldsAroundSphere :

Strongly hyperbolic 2D stable (non-transparent blue) and unstable (non-transparent red) manifolds emanating from a (non-transparent) sphere in the BCC packing, and the same manifolds emanating from adjacent (transparent) spheres.
The flow orientation is $({\mathrm{\theta \_}}_{\text{f}},{\mathrm{\varphi \_}}_{\text{f}})=(\pi /8,\pi /40)$.

ManifoldAroundSphere :

Strongly hyperbolic 2D stable (non-transparent blue) and unstable (non-transparent red) manifolds emanating from a (non-transparent) sphere in the BCC packing, and the same manifolds emanating from adjacent (transparent) spheres.
The flow orientation is $({\mathrm{\theta \_}}_{\text{f}},{\mathrm{\varphi \_}}_{\text{f}})=(\pi /8,\pi /40)$.

TransverseConnection :

Heteroclinic transverse connection of a 2D unstable manifold (in red) and a 2D stable manifold (in blue) in the BCC geometry. The flow orientation is $({\mathrm{\theta \_}}_{\text{f}},{\mathrm{\varphi \_}}_{\text{f}})=(\pi /20,0)$.

SmoothConnection :

Heteroclinic smooth connection of a 2D unstable manifold (in red) and a 2D stable manifold (in blue) in the SC geometry.
The flow orientation is $({\mathrm{\theta \_}}_{\text{f}},{\mathrm{\varphi \_}}_{\text{f}})=(3\pi /20,0)$.