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In recent years, non-reciprocally coupled systems have received growing attention. Previous work has shown that the interplay of non-reciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction--diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a non-zero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common ``normal form'' that can be seen as a spatially extended generalization of the FitzHugh--Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal non-reciprocal Cahn--Hilliard (NRCH) equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the local dispersion relation at interfaces far away from the homogeneous steady state. The traveling waves are therefore a consequence of spatially localized coalescence of hydrodynamic modes arising from mass conservation and translational invariance of displacement fields. Our work thus generalizes previously studied non-reciprocal phase transitions and identifies generic mechanisms for the emergence of dynamical patterns of conserved fields.
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An energy conserving mechanism for temporal metasurfaces
Changing the microstructure properties of a space–time metamaterial while a wave is propagating through it, in general, requires addition or removal of energy, which can be of an exponential form depending on the type of modulation. This limits the realization and application of space–time metamaterials. We resolve this issue by introducing a mechanism of conserving energy at temporal metasurfaces in a non-linear setting. The idea is first demonstrated by considering a wave-packet propagating in a discrete medium of a one-dimensional (1D) chain of springs and masses, where using our energy conserving mechanism, we show that the spring stiffness can be incremented at several time interfaces and the energy will still be conserved. We then consider an interesting application of time-reversed imaging in 1D and two-dimensional (2D) spring–mass systems with a wave packet traveling in the homogenized regime. Our numerical simulations show that, in 1D, when the wave packet hits the time-interface, two sets of waves are generated, one traveling forward in time and the other traveling backward. The time-reversed waves re-converge at the location of the source, and we observe its regeneration. In 2D, we use more complicated initial shapes and, even then, we observe regeneration of the original image or source. Thus, we achieve time-reversed imaging with conservation of energy in a non-linear system. The energy conserving mechanism can be easily extended to continuum media. Some possible ideas and concerns in experimental realization of space–time media are highlighted in conclusion and in the supplementary material.
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- Award ID(s):
- 2107926
- PAR ID:
- 10405888
- Date Published:
- Journal Name:
- Applied Physics Letters
- Volume:
- 121
- Issue:
- 4
- ISSN:
- 0003-6951
- Page Range / eLocation ID:
- 041702
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0097591
