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1. On the effects of suitably designed space microstructures in the propagation of waves in time modulated composites

   https://doi.org/10.1063/5.0132899  

   Mattei, O.; Gulizzi, V. (February 2023, Applied Physics Letters)

   In the one-dimensional case, the amplitude of a pulse that propagates in a homogeneous material whose properties are instantaneously changed in time will undergo an exponential increase due to the interference between the reflected and transmitted pulses generated at each sudden switch. Here, we resolve the issue by designing suitable reciprocal PT-symmetric space-time microstructures so that the interference between the scattered waves is such that the overall amplitude of the wave will be constant in time in each constituent material. Remarkably, for the geometries proposed here, a pulse will propagate with constant amplitude regardless of the impedance between the constituent materials, and for some, regardless of the wave speed mismatch. We extend, then, these results to the two-dimensional case, by proposing suitable geometries that avoid the blow up of the wave amplitude at the source point due to the scattering associated with time modulation. Given that the energy associated with the wave will increase exponentially in time, this creates the possibility to exploit the stable propagation of the pulse to accumulate energy for harvesting. 

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2. An energy conserving mechanism for temporal metasurfaces

   https://doi.org/10.1063/5.0097591  

   Deshmukh, Kshiteej J.; Milton, Graeme W. (July 2022, Applied Physics Letters)

   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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3. General rogue waves in the three-wave resonant interaction systems

   https://doi.org/10.1093/imamat/hxab005  

   Yang, Bo; Yang, Jianke (March 2021, IMA Journal of Applied Mathematics)

   null (Ed.)

   Abstract General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a certain quartic equation arising from the dimension reduction, respectively. It is shown that while the first family of solutions associated with a simple root exists for all signs of the nonlinear coefficients in the three-wave interaction equations, the other two families of solutions associated with two simple roots and a double root can only exist in the so-called soliton-exchange case, where the nonlinear coefficients have certain signs. Many of these rogue wave solutions, such as those associated with two simple roots, the ones generated by a $$2\times 2$$ block determinant in the double-root case, and higher-order solutions associated with a simple root, are new solutions which have not been reported before. Technically, our bilinear derivation of rogue waves for the double-root case is achieved by a generalization to the previous dimension reduction procedure in the bilinear method, and this generalized procedure allows us to treat roots of arbitrary multiplicities. Dynamics of the derived rogue waves is also examined, and new rogue wave patterns are presented. Connection between these bilinear rogue waves and those derived earlier by Darboux transformation is also explained. 

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4. Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

   https://doi.org/10.1088/1367-2630/ab81b6  

   Rosa, Matheus I. N.; Ruzzene, Massimo (May 2020, New Journal of Physics)

   Abstract We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems. 

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5. Mechanical and Geophysical Monitoring of Slip Along Frictional Discontinuities

   El Fil, Hala; Bobet, Antonio; Pyrak-Nolte, Laura J. (June 2019, 53rd U.S. Rock Mechanics/Geomechanics Symposium)

   contain conspicuous acknowledgement of where and by whom the paper was presented. ABSTRACT: Shear strength along discontinuities plays a crucial role in the stability of rock structures. The development of geophysical methods to remotely monitor and assess changes in shear strength is essential to the identification of rock hazards that can lead to the loss of life and failure of civilian infrastructure. In this study, compressional and shear ultrasonic waves were used to monitor slip along discontinuities (with different surface profiles) during shearing. A series of laboratory direct shear experiments were performed on two gypsum blocks separated by a frictional discontinuity. The gypsum blocks had perfectly matched contact surfaces with a half-cycle sine wave profile that spanned the central third of the discontinuity, surrounded by planar surfaces. The amplitude of the half-cycle sine wave was varied and ranged between 2 to 10 times the height of the asperities. Compressional, P, and shear, S, ultrasonic waves were continuously transmitted and recorded throughout the shearing process, while Digital Image Correlation (DIC) was used to capture surface displacements. At low normal stresses, distinct maxima in the normalized P and S wave transmitted amplitudes occurred before shear failure in regions where dilation was observed. Where dilation was not detected, an increase in transmitted wave amplitude was observed, even after the peak shear stress was achieved. At high normal stresses, dilation was suppressed, which was associated with an increase in wave amplitude with shear stress until the peak, and then a decrease in amplitude. Monitoring changes in transmitted wave amplitude is a potential method for the detection of dilation along rock discontinuities. 

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