Exploring energy landscapes experimentally via hyper-dimensional tracking in a ripening emulsion

Many different soft materials, such as soap foams, mayonnaise, toothpaste and living cells, are known to exhibit similar viscoelastic properties. Their behavior has been recently related to the geometrical properties of their energy landscapes, which evolve due to Ostwald ripening and provide an abstract description of the systems’ total energy function spanning a high-dimensional configuration space. Simulations show that these energy landscapes resemble those around river canyons, having a fractal and highly tortuous structure. Here we experimentally demonstrate the ability to explore the geometry of these high-dimensional energy landscapes, using mayonnaise-like dense emulsion droplets amenable to confocal microscopy. We observe super-diffusive particle motion and large cooperative particle rearrangements, or avalanches, as well as a power-law rheology exponent that corresponds to the fractal dimension of the path taken by the system. Closer examination of avalanche behavior reveals that the canyons that the system follows are distributed uniformly in angle over roughly 30-dimensional subspaces. These findings suggest that such hyper-dimensional exploration may find application in the study of other systems with similar dynamics, such as cytoskeleton networks or stock indices.