An Analytical and Numerical Study of Dynamic Materials

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This project focuses on the development and study of dynamic materials, i.e., material composites assembled on a microscale in space and time. Both analytic and computational means will be used to analyze the effective properties of such materials in many spatial dimensions and time. Analytically, by applying homogenization to the relevant hyperbolic systems with spatio-temporally varying senior coefficients, attainable bounds will be specified for the effective parameters of the binary mixtures of isotropic dielectrics in the framework of Maxwell's theory. Computationally, a direct numerical simulation of the original equations will be used to better understand the physics of wave propagation through heterogeneous media with complex microstructure. Together, both approaches will lead to a correct formulation and analysis of optimal material design in space time in response to a dynamic environment.By allowing spatio-temporal variability in the material properties, it is possible to create effects that are unachievable through purely spatial design. For example, by appropriately controlling the design factors of an elastic construction, i.e., its mass and stiffness, it is possible to selectively screen major parts of it from the invasion of destructive dynamic disturbances caused by impactsor other dynamic factors. Disturbances can be purposefully guided into regions where their effect is less pernicious. Another example is related to electromagnetic or acoustic waveguides. To function properly, a conventional waveguide must have a certain minimum diameter relative to the wavelength of the signal. If the waveguide is too narrow or the frequency of the waves is too low, then propagation will not be possible. However, by allowing the material properties of the filling of the waveguide to vary both in space and in time, it will become possible to transmit waves of all frequencies.