A crack on your new cell phone screen, a news announcement about a new material, drilling in a new territory, or tracking an endangered biological population are events that capture everyone’s attention. Mathematicians are especially interested in simulating the underlying phenomena or producing solutions that will change the outcome.
On April 18-19, 2015, the Department of Mathematics hosted the two-day conference “Recent Developments in Continuum Mechanics and PDEs,” following the Howard Rowlee Lecture, which was given by Professor Irene Fonseca, University Professor at Carnegie Mellon University.
Fonseca is an internationally recognized researcher and educator, former president of SIAM (the Society for International and Applied Mathematics), Fellow of the AMS, and was bestowed the knighthood of the Military Order of St. James (from Portugal) in 1997. Her research program is focused on variational techniques and is motivated by applications in material sciences (shape memory alloys, ferroelectric and magnetic materials, composites, liquid crystals, thin structures, phase transitions), and computer vision (image segmentation, staircasing and recolorization).
The conference, partially supported by a National Science Foundation Award, was organized by Petronela Radu and Mikil Foss, and brought together almost 50 participants from applied mathematics, computational science and engineering. Among them, there were prestigious experts such as Qiang Du (Columbia University), Stewart Silling and Michael Parks (both from Sandia Laboratories), Marta Lewicka (University of Pittsburgh), and Giovanni Leoni (Carnegie Mellon University), as well as graduate students and junior researchers who are just beginning their careers.
The interests of the speakers covered diverse areas, such as numerical analysis, variational problems, mathematical modeling, singular integrals, pseudo-differential operators, dispersive equations and nonlinear acoustics. The lectures addressed some of the major problems in the field, including modeling aspects and analytic and numerical results. The growing group of graduate students in PDEs and applied mathematics also benefited from the presentation of new techniques that have been recently developed, as well as open problems with possible venues for their investigation.
A particularly interesting topic of the conference was on nonlocal models, where many research efforts have been focused recently led by faculty in the Department of Mathematics, as well as by Florin Bobaru in the Department of Mechanical and Materials Engineering. One of the most promising nonlocal theories is peridynamics, which was introduced by Stewart Silling in 2000 to model dynamic fracture in solids. These phenomena are very difficult to track in mathematical models as cracks branch, coalesce and interact with each other. Systems formulated within peridynamics have successfully simulated dynamic cracks while capturing geometric features (such as angle between cracks) and physical aspects (such as speed of propagation).
Some of the participants are coming back to UNL to give additional lectures in Fall 2015 and Spring 2016. These talks and discussions are especially important for young researchers (including graduate students and recent Ph.D.s) as they can learn about recent developments in the field and also engage them in new collaborations. And this new generation may one day end the excitement behind dropping your iPhone by creating indestructible or self-healing materials.
– Petronela Radu