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1. Nonreciprocal Pattern Formation of Conserved Fields

   https://doi.org/10.1103/PhysRevX.14.021014  

   Brauns, Fridtjof; Marchetti, M Cristina (April 2024, Physical Review X)

   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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2. On the Whitham system for the (2+1)‐dimensional nonlinear Schrödinger equation

   https://doi.org/10.1111/sapm.12543  

   Ablowitz, Mark J.; Cole, Justin T.; Rumanov, Igor (December 2022, Studies in Applied Mathematics)

   Abstract Whitham modulation equations are derived for the nonlinear Schrödinger equation in the plane ((2+1)‐dimensional nonlinear Schrödinger [2d NLS]) with small dispersion. The modulation equations are obtained in terms of both physical and Riemann‐type variables; the latter yields equations of hydrodynamic type. The complete 2d NLS Whitham system consists of six dynamical equations in evolutionary form and two constraints. As an application, we determine the linear stability of one‐dimensional traveling waves. In both the elliptic and hyperbolic cases, the traveling waves are found to be unstable. This result is consistent with previous investigations of stability by other methods and is supported by direct numerical calculations. 

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3. What computations can be done with traveling waves in visual cortex?

   https://doi.org/10.21203/rs.3.rs-1903144/v1  

   Benigno, Gabriel; Budzinski, Roberto; Davis, Zachary; Reynolds, John; Muller, Lyle (August 2022, Research Square)

   Abstract Recent analyses have found waves of neural activity traveling across entire visual cortical areas in awake animals. These traveling waves modulate excitability of local networks and perceptual sensitivity. The general computational role for these spatiotemporal patterns in the visual system, however, remains unclear. Here, we hypothesize that traveling waves endow the brain with the capacity to predict complex and naturalistic visual inputs. We present a new network model whose connections can be rapidly and efficiently trained to predict natural movies. After training, a few input frames from a movie trigger complex wave patterns that drive accurate predictions many frames into the future, solely from the network’s connections. When the recurrent connections that drive waves are randomly shuffled, both traveling waves and the ability to predict are eliminated. These results show traveling waves could play an essential computational role in the visual system by embedding continuous spatiotemporal structures over spatial maps. 

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4. Understanding and Tuning Magnetism in Layered Ising‐Type Antiferromagnet FePSe ₃ for Potential 2D Magnet

   https://doi.org/10.1002/aelm.202300738  

   Basnet, Rabindra; Patel, Taksh; Wang, Jian; Upreti, Dinesh; Chhetri, Santosh_Karki; Acharya, Gokul; Nabi, Md_Rafique_Un; Sakon, Josh; Hu, Jin (January 2024, Advanced Electronic Materials)

   Abstract Recent developments in 2D magnetic materials have motivated the search for new van der Waals magnetic materials, especially Ising‐type magnets with strong magnetic anisotropy. Fe‐basedMPX₃(M= transition metal,X= chalcogen) compounds such as FePS₃and FePSe₃both exhibit an Ising‐type magnetic order, but FePSe₃receives much less attention compared to FePS₃. This work focuses on establishing the strategy to engineer magnetic anisotropy and exchange interactions in this less‐explored compound. Through chalcogen and metal substitutions, the magnetic anisotropy is found to be immune against S substitution for Se whereas tunable only with heavy Mn substitution for Fe. In particular, Mn substitution leads to a continuous rotation of magnetic moments from the out‐of‐plane direction toward the in‐plane. Furthermore, the magnetic ordering temperature displays non‐monotonic doping dependence for both chalcogen and metal substitutions but due to different mechanisms. These findings provide deeper insight into the Ising‐type magnetism in this important van der Waals material, shedding light on the study of other Ising‐type magnetic systems as well as discovering novel 2D magnets for potential applications in spintronics. 

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5. Connecting Complex Electronic Pattern Formation to Critical Exponents

   https://doi.org/10.3390/condmat6040039  

   Liu, Shuo; Carlson, Erica W.; Dahmen, Karin A. (December 2021, Condensed Matter)

   Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin–Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems. 

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