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Asymmetric tadpole-shaped Janus particles with micrometer-sized flexible SiO₂tails can distort the surrounding LC field into butterfly-shaped defects and create metastable cavities by balancing capillary, elastic, and viscous forces. 

Abstract The stable reduction theorem says that a family of curves of genus$$g\ge 2$$ $g\ge 2$over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new this result for curves defined over$${\mathbb {C}}$$ $C$, using the Kähler–Einstein metrics on the fibers to obtain the limiting stable curves at the punctures. 

Abstract The blue phase of liquid crystals (BPLCs) with a cubic lattice of disclination lines and 3D nanostructure enables the modulation of photonic bandgap thus casting them in the category of photonic crystals. Its unique nature promises applications in display technologies, electro‐optics, and sensors. To integrate these ordered materials into wearable devices a fundamental understanding of curvature, and spatial confinement is necessary. Although continuous confinement in flat geometries have been studied, confining curvature has shown to induce strong destabilization effects on the cubic structure and formation of topological defects, thereby deteriorating their optical performance. Moreover, limitations in controlling the curvature of droplets further hinder studies of nucleation and growth of BPLCs. To address these challenges, micro‐scale patterned surfaces of concentric cylinders are exploited to systematically control curvatures. The impact of curvature on the confined BPLCs is revealed in terms of phase transition temperature, nucleation and growth, morphology, as well as phase transformation. This research offers valuable insights into the stability, and structural characteristics of BPLCs in adaptive photonic devices, paving the way for future advancements in flexible displays, sensors, and other technologies leveraging liquid crystal (LC) materials. 

We prove two new results on the K K -polystability of Q \mathbb {Q} -Fano varieties based on purely algebro-geometric arguments. The first one says that any K K -semistable log Fano cone has a special degeneration to a uniquely determined K K -polystable log Fano cone. As a corollary, we combine it with the differential-geometric results to complete the proof of Donaldson-Sun’s conjecture which says that the metric tangent cone of any point appearing on a Gromov-Hausdorff limit of Kähler-Einstein Fano manifolds depends only on the algebraic structure of the singularity. The second result says that for any log Fano variety with the torus action, K K -polystability is equivalent to equivariant K K -polystability, that is, to check K K -polystability, it is sufficient to check special test configurations which are equivariant under the torus action. 

Living organisms have evolved, over billions of years, to develop specialized biostructures with switchable adhesion for various purposes including climbing, perching, preying, sensing, and protecting. According to adhesion mechanisms, switchable adhesives can be divided into four categories: mechanically-based adhesion, liquid-mediated adhesion, physically-actuated adhesion and chemically-enhanced adhesion. Mimicking these biostructures could create smart materials with switchable adhesion, appealing for many engineering applications in robotics, sensors, advanced drug-delivery, protein separation, etc. Progress has been made in developing bioinspired materials with switchable adhesion modulated by external stimuli such as electrical signal, magnetic field, light, temperature, pH value, etc. This review will be focused on new advance in biomimetic design and synthesis of the materials and devices with switchable adhesion. The underlying mechanisms, design principles, and future directions are discussed for the development of high-performance smart surfaces with switchable adhesion.