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1. Order to disorder in quasiperiodic composites

   https://doi.org/10.1038/s42005-022-00898-z  

   Morison, David; Murphy, N. Benjamin; Cherkaev, Elena; Golden, Kenneth M. (December 2022, Communications Physics)

   Abstract From quasicrystalline alloys to twisted bilayer graphene, the study of material properties arising from quasiperiodic structure has driven advances in theory and applied science. Here we introduce a class of two-phase composites, structured by deterministic Moiré patterns, and we find that these composites display exotic behavior in their bulk electrical, magnetic, diffusive, thermal, and optical properties. With a slight change in the twist angle, the microstructure goes from periodic to quasiperiodic, and the transport properties switch from those of ordered to randomly disordered materials. This transition is apparent when we distill the relationship between classical transport coefficients and microgeometry into the spectral properties of an operator analogous to the Hamiltonian in quantum physics. We observe this order to disorder transition in terms of band gaps, field localization, and mobility edges analogous to Anderson transitions — even though there are no wave scattering or interference effects at play here. 

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2. Fracture tolerance induced by dynamic bonds in hydrogels

   https://doi.org/10.1016/j.jmps.2022.105083  

   Yang, Hang; Chen, Xi; Sun, Bonan; Tang, Jingda; Vlassak, Joost J. (December 2022, Journal of the Mechanics and Physics of Solids)

   Among soft materials, hydrogels with dynamic bonds that can be activated by a range of stimuli including temperature, pH, and infrared or ultraviolet light, constitute a special class of materials with unusual properties such as self-healing, actuation, and controlled degradation. Here, we take a hydrogel with reconfigurable disulfide crosslinks as an example and investigate its mechanical behavior. We demonstrate that this material has excellent fracture and fatigue resistance when the disulfide crosslinks are activated by ultraviolet illumination. We propose a simple constitutive model that describes the mechanical behavior of the material under a broad range of conditions. 

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3. Universality and quantum criticality in quasiperiodic spin chains

   https://doi.org/10.1038/s41467-020-15760-5  

   Agrawal, Utkarsh; Gopalakrishnan, Sarang; Vasseur, Romain (May 2020, Nature Communications)

   Abstract Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition. 

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4. On Gaps in the Spectra of Quasiperiodic Schrödinger Operators with Discontinuous Monotone Potentials

   https://doi.org/10.1093/imrn/rnaf085  

   Kachkovskiy, Ilya; Parnovski, Leonid; Shterenberg, Roman (April 2025, International Mathematics Research Notices)

   We show that, for one-dimensional discrete Schrödinger operators, stability of Anderson localization under a class of rank one perturbations implies absence of intervals in spectra. The argument is based on well-known results of Gordon and del Rio–Makarov–Simon, combined with a way to consider perturbations whose ranges are not necessarily cyclic. The main application of the results is showing that a class of quasiperiodic operators with sawtooth-like potentials, for which such a version of stable localization is known, has Cantor spectra. We also obtain several results on gap filling under rank one perturbations for some general (not necessarily monotone) classes of quasiperiodic operators with discontinuous potentials. 

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5. Effect of electromechanical coupling on locally resonant quasiperiodic metamaterials

   https://doi.org/10.1063/5.0119914  

   LeGrande, Joshua; Bukhari, Mohammad; Barry, Oumar (January 2023, AIP Advances)

   Electromechanical metamaterials have been the focus of many recent studies for use in simultaneous energy harvesting and vibration control. Metamaterials with quasiperiodic patterns possess many useful topological properties that make them a good candidate for study. However, it is currently unknown what effect electromechanical coupling may have on the topological bandgaps and localized edge modes of a quasiperiodic metamaterial. In this paper, we study a quasiperiodic metamaterial with electromechanical resonators to investigate the effect on its bandgaps and localized vibration modes. We derive here the analytical dispersion surfaces of the proposed metamaterial. A semi-infinite system is also simulated numerically to validate the analytical results and show the band structure for different quasiperiodic patterns, load resistors, and electromechanical coupling coefficients. The topological nature of the bandgaps is detailed through an estimation of the integrated density of states. Furthermore, the presence of topological edge modes is determined through numerical simulation of the energy harvested from the system. The results indicate that quasiperiodic metamaterials with electromechanical resonators can be used for effective energy harvesting without changes in the bandgap topology for weak electromechanical coupling. 

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