Dynamic Materials as Spatial-Temporal Entities: Physical Effects and Mathematical Specifics

Monday, March 13, 2017 - 9:00am - 9:50am
Keller 3-180
Konstantin Lurie (Worcester Polytechnic Institute)
1. The concept of dynamic materials (DM) as thermodynamically open formations in space-time. Cross-disciplinary implementations: properly material (mechanical or electromagnetic), biological (living tissue), environmental (traffic), etc.

2. Mathematical description: Minkowskian space-time. Tensor formulation of electrodynamics of moving bodies. Lorentz group, electrodynamic material tensor. Classification of DM into activated and kinetic.

3. Unusual effects: screening, light trapping, energy and power accumulation.

4. Activated materials: wave propagation across property interfaces in space-time. Regular and irregular reflection/transmission. Smooth and rugged property interfaces.

5. Homogenization of regular DM laminates. Coordinated wave propagation and screening.

6. A regular doubly periodic checkerboard DM in 1D-space + time. Energy and power accumulation along limit cycles. Limited energy supply.

7. Material geometry optimization in space-time. Relaxation through scaling and homogenization in a regular case, and through addition of special collision scenarios in irregular case.

8. Conclusions