S. Torquato
Dept.
of Chemistry, PRISM, and Program in Applied
& Computational Mathematics
Many tasks in computational materials science can be posed as optimization problems. I discuss three examples. The first concerns particle packing problems. Optimal packing problems, such as how densely hard particles can fill a volume, have fascinated people since the dawn of civilization. The determination of the maximally random jammed state using packing generation algorithms is discussed. The second example describes how the topology optimization method can be used to determine material microstructures with optimized or targeted properties. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The last example is concerned with the generation of realizations of random heterogeneous materials with specified but limited microstructural information: an intriguing inverse problem of both fundamental and practical importance. This problem is solved using stochastic optimization techniques.