11:30 am–1:30 pm
Zhaoning Liu's PhD Thesis Defense
Wednesday, November 4 at 11:30 AM CDT
CONTROLLING PATTERNS IN FLUIDS AND MEMORIES IN SPHERE PACKINGS
I will first discuss experiments in which the interface between a pair of fluids becomes unstable to viscous fingering when confined between the two flat plates of a radial Hele-Shaw cell. The goal is to understand how the shape of the interface in the perpendicular direction between the plates alters the formation of the planar patterns. Translational oscillatory shear between the plates smooths the shape of this interface in the direction parallel to the shear axis and offers a new way to suppress the instability. Because uniaxial shear breaks the radial symmetry, fingers evolve differently depending on their growth direction; shear elongates fingers in the direction parallel to the shear axis, whereas it widens fingers in the perpendicular direction and smears the concentration profile. When the shear amplitude exceeds a threshold, which is roughly five times the excess finger width at onset, neighboring perpendicular fingers reconnect near their bases and become shorter. These experiments show how controlling the azimuthal interface shape influences the radial finger growth.
I will then turn to jammed particle packings. Mechanically stable particle packings lie at the minima of a high-dimensional potential energy landscape. By repeatedly generating random initial configurations and minimizing their energies, we find many of those stable configurations. All initial conditions that end at the same minimum belong to the same catchment basin. We find that the distribution of catchment basin volumes follows a nearly power-law form with some basins being at least eight orders of magnitude larger than others. From this statistical distribution, I am able to study the correlations between neighboring basin volumes and the basin shapes. This has implications for how memory under cyclic perturbation can be encoded.
Committee members:
Sidney R. Nagel (Chair)
Heinrich M. Jaeger
Robert Rosner
David Schmitz