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Abstract Optical spectrometers are essential tools for analysing light‒matter interactions, but conventional spectrometers can be complicated and bulky. Recently, efforts have been made to develop miniaturized spectrometers. However, it is challenging to overcome the trade-off between miniaturizing size and retaining performance. Here, we present a complementary metal oxide semiconductor image sensor-based miniature computational spectrometer using a plasmonic nanoparticles-in-cavity microfilter array. Size-controlled silver nanoparticles are directly printed into cavity-length-varying Fabry‒Pérot microcavities, which leverage strong coupling between the localized surface plasmon resonance of the silver nanoparticles and the Fabry‒Pérot microcavity to regulate the transmission spectra and realize large-scale arrayed spectrum-disparate microfilters. Supported by a machine learning-based training process, the miniature computational spectrometer uses artificial intelligence and was demonstrated to measure visible-light spectra at subnanometre resolution. The high scalability of the technological approaches shown here may facilitate the development of high-performance miniature optical spectrometers for extensive applications. 

The capability of effectively moving on complex terrains such as sand and gravel can empower our robots to robustly operate in outdoor environments, and assist with critical tasks such as environment monitoring, search-and-rescue, and supply delivery. Inspired by the Mount Lyell salamander’s ability to curl its body into a loop and effectively roll across sand and gravel, in this study we develop a sand-rolling robot and investigate how its locomotion performance is governed by the shape of its body. We experimentally tested three different body shapes: Hexagon, Quadrilateral, and Triangle. We found that Hexagon and Triangle can achieve a faster rolling speed on sand, but also exhibited more frequent failures of getting stuck in sand. Analysis of the interaction between robot and sand revealed the failure mechanism: the deformation of the sand produced a local “sand incline” underneath robot contact segments, increasing the effective region of supporting polygon (ERSP) and preventing the robot from shifting its center of mass (CoM) outside the ERSP to produce sustainable rolling. Based on this mechanism, a highly-simplified model successfully captured the critical body pitch for each rolling shape to produce sustained rolling on sand, and informed design adaptations that mitigated the locomotion failures and improved robot speed by more than 200%. Our results provide insights into how locomotors can utilize different morphological features to achieve robust rolling motion across deformable substrates. 

Abstract We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight$${q \in [1,4)}$$ $q\in [1,4)$. Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values ofqthan the FK-Ising model ($$q=2$$ $q=2$). Given the convergence of interfaces, the conjectural formulas for other values ofqcould be verified similarly with relatively minor technical work. The limit interfaces are variants of$$\text {SLE}_\kappa $$ ${\text{SLE}}_{\kappa }$curves (with$$\kappa = 16/3$$ $\kappa =16/3$for$$q=2$$ $q=2$). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all$$q \in [1,4)$$ $q\in [1,4)$, thus providing further evidence of the expected CFT description of these models.