Abstract
This chapter illustrates the influence produced by the material geometry in space-time on the wave propagation through the DM structures. For the wave equation with coefficients variable in 1D + time, there is suggested a special dynamic structure (spatial-temporal rectangular ”checkerboard”) that may support the energy accumulation in waves traveling through it. Energy is concentrated in progressively sharpening pulses carrying high (theoretically infinite) power. The structural parameters chosen within special ranges do not allow wave reflections, so the system becomes nonoscillatory and works on the principle that is different from parametric resonance. Instead its work is totally based on the ability of a checkerboard to support such a pattern of the wave routes that allows the energy to be pumped into the wave from outside but never permits its back into the environment. The material of this chapter is directly focused onto practical implementation, both in electromagnetic and mechanical setups.
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Notes
- 1.
Throughout the rest of this chapter, the symbols m 1 and n 1 in the figures will be identified with symbols m and n used in the main text.
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Lurie, K.A. (2017). Rectangular Material Structures in Space-Time. In: An Introduction to the Mathematical Theory of Dynamic Materials. Advances in Mechanics and Mathematics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-65346-4_5
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