Trans-disciplinary team investigates topological defects

Researchers from the College of Engineering and Mellon College of Sciences have received a National Science Foundation (NSF) Growing Convergence Research (GCR) grant to investigate a ubiquitous phenomenon impacting an array of disciplines ranging from mechanics and materials science, to seismology, to even string theory.

Led by Amit Acharya, a professor of civil and environmental engineering (CEE), the project will create a mathematical and conceptual framework to describe the phenomenon that occurs when two uniform patterns in organized matter (a jet turbine blade, the earth’s crust, a galaxy, etc.) are offset from one another, rotated differently, or otherwise have some form of deformation in the surface at which they meet. The string or curve created where the joining surface ends is called a topological line defect, and depending on the situation and material, its effects can range from useful, to interesting, to even catastrophic.  

Acharya’s team is as diverse as the disciplines it spans and includes fellow CEE faculty Jerry Wang and Jacobo Bielak, Mathematical Sciences’ Irene Fonseca and Franziska Weber, Physics’ Ira Rothstein and Bob Suter, and researchers from the University of Arizona.

“I think Amit had a wonderful vision for this work and this team that has come together is very much because of the connections and relationships he’s created with a lot of folks in a lot of disciplines who all have very different expertise, who all can shed some light on this very mathematically, physically, ‘engineering-ly` challenging problem,” says Wang.

Wang’s research uses computational analysis to study complex molecular dynamics, while Bielak is an expert on earthquake engineering and engineering seismology. Acharya’s expertise is in continuum mechanics, mathematical materials science, and applied mathematics.

“Understanding the dynamics of solids is one of the most fundamental problems in science,” said Rothstein, professor of physics, who will be contributing his knowledge of quantum field theory and string theory to the collaboration. “What could be more simple than asking how a piece of material deforms under stress?”

“The advancement of research in this area requires an interdisciplinary confluence and dialogue of different expertise, including civil engineering, astronomy, mechanics, materials, seismology, physics, and science at large,” says Fonseca, the Kavčić-Moura University Professor of Mathematics and director of Carnegie Mellon’s Center for Nonlinear Analysis. “In recent years, modern mathematical techniques in the calculus of variations and partial differential equations have led to remarkable discoveries in the field of materials defects and having worked on these problems was at the core of my interest in joining this collaboration.”

Fonseca’s contributions to the effort will be focused on “rigorous mathematical validation” of the data obtained by the engineers and physicists on the team, she says. One physicist on the team is Suter, an emeritus professor of physics who calls himself “something of an outlier in the group.”

“I bring the ability to collect and probe large experimental data sets that study defect development inside of bulk polycrystalline materials as they undergo plastic deformation,” Suter says. “We will develop computational tools to search these data sets for specific types of defects for which we have only preliminary and anecdotal evidence at this point in time.”

“One of the reasons the project is of interest to me is that it gives us an opportunity to mine existing data sets for new phenomena whereas previous analysis has revealed in new detail the most expected responses to imposed deformation,” Suter adds.

The authors write in their proposal, “Our team envisions a future where new knowledge from our research can be leveraged to seed advances in technology relevant for grand challenges in seismic forecasting, infrastructure renewal, and energy-efficient transportation.” 

Through mathematically defining how topological defects agree and differ within these different materials, scientists and engineers in civil and mechanical engineering, advanced manufacturing, astronomy, seismology, and countless more fundamental fields will have a universal tool for defining one of the most ubiquitous phenomena in our physical world.

Our emphasis is not only on topological defects, but also their energetic and dynamic consequences across different cases.

Amit Acharya, Professor, Civil and Environmental Engineering

“The similarities in this phenomenon across cases are what allows for this type of interdisciplinary convergence research, but it’s important to recognize that these are also different materials with different properties,” says Acharya, “Our emphasis is not only on topological defects, but also their energetic and dynamic consequences across different cases.”

“The hope is that with new theoretical developments we will be able to accurately model materials behaviors that are critically important in many technological applications,” Suter says.

Assembling faculty from such disparate fields also means bringing their labs together, and the team’s plans include trans-disciplinary training for the many student researchers who will contribute as well. Externally, a multi-spectrum educational outreach effort will prioritize building connections between the four pillars of STEM for a diverse audience.