Speed Limits on Pattern Formation in Dynamic Materials

This grant will fund research that enables future engineering of materials that form functional patterns in response to external triggers such as light or heat, with application to chemical and optical sensors and microelectronics, thereby promoting the progress of science and advancing the national prosperity. Cellular materials in living systems can quickly adapt to their surroundings, organizing their structural patterns accordingly.

Engineering the next generation of human-made materials to exhibit such behavior requires new theoretical methods to clarify the relationship between design decisions and the dynamics of functional pattern formation. This project will address this need by creating new methods for the analysis of the rates of pattern formation, with particular emphasis on upper bounds on such rates that would inform the future creation of materials that form patterns on predetermined time schedules.

Such smart materials will benefit applications across the energy, biomedical, chemical, and healthcare industries. Online, open-science computational notebooks will help make the science of pattern formation widely accessible to students and other researchers. Outreach to a local McNair Scholars Program will help broaden participation in STEM of students from currently underrepresented groups.

This research aims to make fundamental contributions to the characterization of speed limits associated with the transient dynamics of nonequilibrium pattern formation. It will accomplish this outcome by focusing on pattern formation in reaction-diffusion systems, a dynamical mechanism that has previously been leveraged to fabricate microstructures, enable new sensor modalities, and generate work.

The theoretical framework will rely on a new density matrix formulation, inspired by classical statistical mechanics and quantum-mechanical analogies. Analytical results will be validated using numerical simulations that permit a broad exploration of the design space associated with transient pattern formation. The target theory will enable a systematic separation between the contributions of deterministic and stochastic dynamics, and will inform the possible use of control to regulate the dynamic response to transient fluctuations.

The project will lay the groundwork for in-silico design of the behaviors of complex dynamic systems, produce computationally tractable links between the geometries of phase space and information, and place bounds on the response of systems to external stimuli that can serve as a design principle for the actuation of material functionality.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.