Dr. Emil Prodan was just awarded a three-year grant from the National Science Foundation (NSF). The $277,958 will cover the costs of collaborative research on “Topological Dynamics of Hyperbolic and Fractal Lattices” being done with Dr. Massimo Ruzzene (University of Colorado) and Dr. Camelia Prodan (New Jersey Institute of Technology). The money will also support undergraduate and postdoctoral students, travel, materials and publications. From Dr. Prodan:

The collaborative grant was awarded by the NSF Division Of Civil, Mechanical and Manufacturing Innovation, through its program Dynamics, Control and System Diagnostics. One of the main interests of this division is in materials, mechanisms and engineering solutions that perform functions or have dynamical properties that are fundamentally different from everything known to date.

In our winning proposal, we focused on the dynamics of lattices of resonators, mechanical or acoustical, coupled with each other and arranged in space according specific algorithms. If one kicks one of the resonators, oscillations  will start propagating throughout the lattice, very much like the water ripples when throwing a stone in a lake. In our context, however, we can shape how these ripples propagate by adjusting the resonator-to-resonator couplings or the geometry of the lattice.

Using pure mathematics borrowed from operator algebras, K-theory and Noncommutative Geometry, we explained in the winning proposal that we have a rigorous way to enumerate all possible dynamical features that can be achieved with such lattices and argued that there is a infinite tower of opportunities that can be efficiently and methodically explored with the mathematics I mentioned.

The collaboration involves Dr. Massimo Ruzzene of the College of Engineering and Applied Science at University of Colorado Boulder and Dr. Camelia Prodan of the Physics Department at New Jersey Institute of Technology, two world-leading researchers in meta-material science. The concrete plan of the collaboration is to bring the abstract predictions to life and incorporate them in practical applications, such as sensing devices, new paradigms for energy and information transfer and storage, or perfectly sound absorbing or reflecting surfaces.

At Yeshiva University, the award will support one postdoctoral and two undergraduate students who will assist Dr. Emil Prodan in generating specialized algorithms to arrange and couple the resonators. The award will also supply funds for the purchasing of a performant 3D printer such that small prototypes can be fabricated and characterized at YU before the designs are sent to the collaborators for full scale fabrication. The 3D printer will be located in and shared with Dr. Ran Drori’s lab, who will share with us their expertise and equipment for image analysis.