CBE Doctoral Dissertation Defense: “A Fractal Landscape Dynamics Approach to Understanding Particle Motion in Soft Jammed Materials” (Clary Rodríguez-Cruz)

Soft jammed materials are disordered viscoelastic solids, composed of densely packed particles, that are commonly found both in the natural world and in a wide range of manufactured products. Their applications are widespread across various industries and technologies, including food, pharmaceuticals, agriculture and cosmetics. Understanding the fundamental physics and mathematics behind their highly complex particle motion and distinct response to external stress is essential for their improved design and stability, as well as the development of new materials with unique mechanical properties. Further, it is crucial for the development of theoretical models that better describe the complex interactions and dynamics of these materials. This thesis is centered around the observation that soft jammed materials exhibit fractal landscape dynamics, where the particles’ motion is not merely random but follows patterns influenced by the system’s underlying fractal energy landscape. Through experimental observations, theoretical models, and numerical simulations of ripening dense emulsions and foams, this work reveals two major findings. First, it demonstrates the numerical relationships between energy landscape geometry, microscopic particle dynamics, and macroscopic rheology through a novel high-dimensional approach. Second, it introduces a simplistic random walk model that generates fractal paths with specified dimensions, successfully reflecting the complex individual particle dynamics in a ripening foam after fitting to the data. This finding affirms the presence of fractal landscape dynamics as an explanation for behaviors such as non-Gaussian particle displacements, intermittent rearrangement events, and power-law rheology. Further exploration within this work extends the high-dimensional analysis framework to the dynamics of stock market prices, drawing an intriguing parallel between the motion of individual stocks and emulsion droplets. Lastly, the machine-learning metric of $\lq$softness’ is explored as a method to predict particle rearrangements in a ripening foam, showing that simply a particle’s number of neighbors achieves a surprisingly high prediction accuracy. This thesis not only enhances our understanding of soft jammed materials but also opens new avenues for applying fractal landscape dynamics across different materials and research fields.