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Many soft and biological materials display so-called ‘soft glassy’ dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening foam, suggested that the random motions of its bubbles are due to the system configuration moving over a fractal energy landscape in high-dimensional space. Here we show that the salient geometrical features of such high-dimensional fractal landscapes can be explored and reliably quantified, using empirical trajectory data from many degrees of freedom, in a model-free manner. For a mayonnaise-like dense emulsion, analysis of the observed trajectories of oil droplets quantitatively reproduces the high-dimensional fractal geometry of the configuration path and its associated local energy minima generated using a computational model. That geometry in turn drives the droplets’ complex random motion observed in real space. Our results indicate that experimental studies can elucidate whether the similar dynamics in different soft and biological materials may also be due to fractal landscape dynamics.more » « less
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Thirumalaiswamy, Amruthesh ; Riggleman, Robert A. ; Crocker, John C. ( , Proceedings of the National Academy of Sciences)The complex physics of glass-forming systems is controlled by the structure of the low-energy portions of their potential energy landscapes. Here we report that a modified metadynamics algorithm efficiently explores and samples low-energy regions of such high-dimensional landscapes. In the energy landscape for a model foam, our algorithm finds and descends meandering canyons in the landscape, which contain dense clusters of energy minima along their floors. Similar canyon structures in the energy landscapes of two model glass formers—hard sphere fluids and the Kob–Andersen glass—allow us to reach high densities and low energies, respectively. In the hard sphere system, fluid configurations are found to form continuous regions that cover the canyon floors up to densities well above the jamming transition. For the Kob–Andersen glass former, our technique samples low-energy states with modest computational effort, with the lowest energies found approaching the predicted Kauzmann limit.more » « less