In this Focused Research Group project the investigators study the behavior of a class of soft materials characterized by strong coupling of electrical, optical, and mechanical properties. Such materials, which include some liquid crystals and elastomers, can be used to develop ultra-fast switches for video display -- based on electro-optical coupling -- and miniature sensors and actuators -- based on the electro-mechanical coupling. One goal is to determine the conditions that enhance the combined effects of the soft-elasticity modes of elastomers and their ferroelectric response by application of external electric fields. In these studies the investigators combine mathematical analysis, modeling, computer simulations, physical experiments, and application of the three-dimensional visualization techniques. These mathematical problems are analytically modeled by highly nonlinear elliptic, parabolic, mixed hyperbolic-parabolic and stochastic systems of partial differential equations, including the equations of nonlinear elasticity, viscoelastic flow, and Maxwell's equations of electrodynamics. Partial differential equation methods for phase transitions, modeling, and numerical tools such as spectral methods and adaptivity to simulate the solutions are among the techniques employed.
The project is a comprehensive effort towards modeling and development of soft matter actuator and sensor devices used in a vast array of applications, including ultra-fast optic and video switching, artificial muscles, biological membranes, and filaments. Increase of switching speeds and size reduction of the device are two relevant technological goals at the heart of the investigation. One type of materials to investigate, liquid crystal elastomers, can be thought of as rubber networks that require very little energy to be deformed along special directions. This property, coupled with the efficient response of the material to electric fields, may offer optimal ingredients for developing high speed devices able to provide very large mechanical deformations with the application of electric or magnetic fields of small magnitude. These are highly desirable properties, for instance, in the design of artificial muscles for robots. The investigators carry out the studies by combining mathematical analysis, computer simulations, and physical experiments. Use of three-dimensional visualization techniques is important in both conducting the work and disseminating the results. Many of the problems present modeling challenges that call for a synergistic effort of mathematicians and physicists. A central principle in this endeavor is close cross-disciplinary interaction among the applied and numerical analysts and the physicists of the group. A major component of the project is the interdisciplinary training of post-docs and graduate students, including the organization of a summer school, development of new courses, and summer research opportunities for undergraduate students. Interdisciplinary conferences, group workshops, and seminars devoted to the FRG project at each institution are also planned.
