Collections of many electrons or atoms display phenomena derived from their interactions across multiple scales in space and time. In the biological regime such systems include viruses, cells, and aggregates of myeloid proteins that cause degenerative nerve diseases. Quantum nanosystems that support emergent phenomena include quantum dots, graphene nanoribbons, molecular wires, and magnetic or superconducting nanoparticles. These systems present mathematical and computational challenges when attempting to understand them from the principles of Newtonian or quantum physics.
In the Ortoleva group these challenges are being addressed via the development of novel computational and mathematical techniques. These techniques are implemented as software which is being used to gain a fundamental understanding of these systems and to address grand challenges in materials science, nanomedicine, and vaccine discovery. Through their advances made over the past 35 years, the Ortoleva group has pioneered the theory of self-organization, leading to a fundamental understanding of how matter and energy spontaneously evolve into structure spanning many scales in space and time. These self-organization phenomena range from the self-assembly of viruses to the generation of kilometer-scale distribution of petroleum and minerals in the Earth's subsurface. Techniques used to understand these emergent phenomena include bifurcation theory, finite element computer simulation, homogenization theory, matched asymptotic analysis, molecular dynamics, multiscale analysis, and quantum coarse-graining. Our advances and the phenomena we address have been summarized in over 220 peer-reviewed papers, 3 monographs, and 3 edited volumes.