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1. Metastability in the stochastic nearest-neighbour Kuramoto model of coupled phase oscillators

   https://doi.org/10.1088/1361-6544/ae05aa  

   Berglund, Nils; Medvedev, Georgi S; Simpson, Gideon (September 2025, Nonlinearity)

   Abstract The Kuramoto model (KM) ofncoupled phase-oscillators is analysed in this work. The KM on a Cayley graph possesses a family of steady state solutions called twisted states. Topologically distinct twisted states are distinguished by the winding number $q\in \mathbb{Z}$. It is known that for the KM on the nearest-neighbour graph, aq-twisted state is stable if $|q|<n/4$. In the presence of small noise, the KM exhibits metastable transitions betweenq–twisted states. Specifically, a typical trajectory remains in the basin of attraction of a givenq-twisted state for an exponentially long time, but eventually transitions to the vicinity of another such state. In the course of this transition, it passes in close proximity of a saddle of Morse index 1, called a relevant saddle. In this work, we provide an exhaustive analysis of metastable transitions in the stochastic KM with nearest-neighbour coupling. We start by analysing the equilibria and their stability. First, we identify all equilibria in this model. Using the discrete Fourier transform and eigenvalue estimates for rank–1 perturbations of symmetric matrices, we classify the equilibria by their Morse indices. In particular, we identify all stable equilibria and all relevant saddles involved in the metastable transitions. Further, we use Freidlin–Wentzell theory and the potential-theoretic approach to metastability to establish the metastable hierarchy and sharp estimates of Eyring–Kramers type for the transition times. The former determines the precise order, in which the metastable transitions occur, while the latter characterises the times between successive transitions. The theoretical estimates are complemented by numerical simulations and a careful numerical verification of the transition times. Finally, we discuss the implications of this work for the KM with other coupling types including non-local coupling and the continuum limit asntends to infinity. 

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2. Coordinated crawling via reinforcement learning

   https://doi.org/10.1098/rsif.2020.0198  

   Mishra, Shruti; van Rees, Wim M.; Mahadevan, L. (August 2020, Journal of The Royal Society Interface)

   Rectilinear crawling locomotion is a primitive and common mode of locomotion in slender soft-bodied animals. It requires coordinated contractions that propagate along a body that interacts frictionally with its environment. We propose a simple approach to understand how this coordination arises in a neuromechanical model of a segmented, soft-bodied crawler via an iterative process that might have both biological antecedents and technological relevance. Using a simple reinforcement learning algorithm, we show that an initial all-to-all neural coupling converges to a simple nearest-neighbour neural wiring that allows the crawler to move forward using a localized wave of contraction that is qualitatively similar to what is observed in Drosophila melanogaster larvae and used in many biomimetic solutions. The resulting solution is a function of how we weight gait regularization in the reward, with a trade-off between speed and robustness to proprioceptive noise. Overall, our results, which embed the brain–body–environment triad in a learning scheme, have relevance for soft robotics while shedding light on the evolution and development of locomotion. 

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3. Fitness consequences of marine larval dispersal: the role of neighbourhood density, arrangement, and genetic relatedness on survival, growth, reproduction, and paternity in a sessile invertebrate

   https://doi.org/10.1093/jeb/voae125  

   Barnes, Danielle K; Burgess, Scott C (September 2024, Journal of Evolutionary Biology)

   Hunt, John; Ravinet, Mark (Ed.)

   Abstract Dispersal can evolve as an adaptation to escape competition with conspecifics or kin. Locations with a low density of conspecifics, however, may also lead to reduced opportunities for mating, especially in sessile marine invertebrates with proximity-dependent mating success. Since there are few experimental investigations, we performed a series of field experiments using an experimentally tractable species (the bryozoan Bugula neritina) to test the hypothesis that the density, spatial arrangement, and genetic relatedness of neighbours differentially affect survival, growth, reproduction, paternity, and sperm dispersal. We manipulated the density and relatedness of neighbours and found that increased density reduced survival but not growth rate, and that there was no effect of relatedness on survival, growth, or fecundity, in contrast to previous studies. We also manipulated the distances to the nearest neighbour and used genetic markers to assign paternity within known mother–offspring groups to estimate how proximity affects mating success. Distance to the nearest neighbour did not affect the number of settlers produced, the paternity share, or the degree of multiple paternity. Overall, larger than expected sperm dispersal led to high multiple paternity, regardless of the distance to the nearest neighbour. Our results have important implications for understanding selection on dispersal distance: in this system, there are few disadvantages to the limited larval dispersal that does occur and limited advantages for larvae to disperse further than a few 10s of metres. 

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4. Tunable exciton-polaritons emerging from WS2 monolayer excitons in a photonic lattice at room temperature

   https://doi.org/10.1038/s41467-021-24925-9  

   Lackner, L.; Dusel, M.; Egorov, O. A.; Han, B.; Knopf, H.; Eilenberger, F.; Schröder, S.; Watanabe, K.; Taniguchi, T.; Tongay, S.; et al (December 2021, Nature Communications)

   Abstract Engineering non-linear hybrid light-matter states in tailored lattices is a central research strategy for the simulation of complex Hamiltonians. Excitons in atomically thin crystals are an ideal active medium for such purposes, since they couple strongly with light and bear the potential to harness giant non-linearities and interactions while presenting a simple sample-processing and room temperature operability. We demonstrate lattice polaritons, based on an open, high-quality optical cavity, with an imprinted photonic lattice strongly coupled to excitons in a WS 2 monolayer. We experimentally observe the emergence of the canonical band-structure of particles in a one-dimensional lattice at room temperature, and demonstrate frequency reconfigurability over a spectral window exceeding 85 meV, as well as the systematic variation of the nearest-neighbour coupling, reflected by a tunability in the bandwidth of the p-band polaritons by 7 meV. The technology presented in this work is a critical demonstration towards reconfigurable photonic emulators operated with non-linear photonic fluids, offering a simple experimental implementation and working at ambient conditions. 

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5. Strain-tuned incompatible magnetic exchange-interaction in La2NiO4

   https://doi.org/10.1038/s42005-024-01701-x  

   Biało, Izabela; Martinelli, Leonardo; De_Luca, Gabriele; Worm, Paul; Drewanowski, Annabella; Jöhr, Simon; Choi, Jaewon; Garcia-Fernandez, Mirian; Agrestini, Stefano; Zhou, Ke-Jin; et al (December 2024, Communications Physics)

   Abstract Magnetic frustration is a route for novel ground states, including spin liquids and spin ices. Such frustration can be introduced through either lattice geometry or incompatible exchange interactions. Here, we find that epitaxial strain is an effective tool for tuning antiferromagnetic exchange interactions in a square-lattice system. By studying the magnon excitations in La₂NiO₄films using resonant inelastic x-ray scattering, we show that the magnon displays substantial dispersion along the antiferromagnetic zone boundary, at energies that depend on the lattice of the film’s substrate. Using first principles simulations and an effective spin model, we demonstrate that the antiferromagnetic next-nearest neighbour coupling is a consequence of the two-orbital nature of La₂NiO₄. Altogether, we illustrate that compressive epitaxial strain enhances this coupling and, as a result, increases the level of incompatibility between exchange interactions within a model square-lattice system. 

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