Mathias Casiulis
Center for Soft Matter Research, Department of Physics ; Simons Center for Computational Physical Chemistry, Department of Chemistry; New York University
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Understanding and harnessing complexity, from point patterns to materials
Paradigmatic examples of useful materials are crystals, that display a variety of interesting properties, e.g. optical. It is not by chance: by virtue of their periodicity, these structures possess long-range order ranging from the scale of the atom to that of a block of material.Yet, from bird feathers to weevil scales, many biological systems instead rely on aperiodic structures, that look disordered at short range but display correlations at long range, to achieve functions such as structural color.
The study of such correlated disordered structures is challenging. Experimentally, few synthesis pathways are known so that these materials are often numerically engineered then 3d printed. Theoretically, a new toolbox is necessary to study systems that are neither periodic nor at thermodynamic equilibrium. Numerically, producing arbitrary correlations in disorder is a daunting task that has greatly limited the scale and number of available systems for experiments.
In this talk, I present an algorithm, the Fast Reciprocal-Space Correlator (FReSCo), that enables me to embed arbitrary correlations into point patterns at lightning speed.
I first showcase the power of the algorithm using the example of hyperuniformity, a suppression of density fluctuations at long range, that has attracted considerable attention in both physics and mathematics. I show that FReSCo has produced the largest, unquestionably hyperuniform point patterns, and show that the algorithm can be extended to accommodate geometric constraints like excluded volume. More practically, I discuss how FReSCo can be used to functionalize disorder. Using the example of bandgap materials, I show how a simple heuristic on the structure-function relationship can be used to produce new classes of disordered materials that outperform previously known structures.
I finally discuss how the optimization approach in FReSCo can be paired to recent progress in the study of the structure of loss and energy landscapes to quantify the number of solutions that an inverse-design problem has, thus giving precious insight on both geometric and physical constraints in correlated disordered materials.
I highlight perspectives for this line of work, ranging from cost-efficient 3d rendering to fundamental questions on allowed sphere packings and materials design.
