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Diatom Cribellum-Inspired Hierarchical Metamaterials The cribellum layer of diatom skeleton, termed frustule, features a hierarchical porous structure on the nanoscale. In article number 2403304 by Xin Zhang and co-workers, diatom cribellum inspired hierarchical metamaterials are presented to integrate the perfect absorption and subwavelength color printing. These diatom cribellum-inspired metamaterials offer a fresh perspective on multifunctional metamaterial design, promising scalability production by utilizing the frustule as a template for nanopatterning or bio-template synthesis. 

A survey of 23 commercially available cation exchange membranes was performed for the downselection of membranes for use in a polysulfide-permanganate redox flow battery (pS-Mn RFB). The survey measured the flux of permanganate ions across a 0.1 mol L⁻¹concentration gradient as well as the membrane resistance in a 0.5 mol L⁻¹sodium chloride solution. The membranes exhibited the characteristic flux/resistance trade-off observed in most classes of membranes. To connect the individual membrane testing to how the membranes will perform in a device, cell performance data in a pS-Mn RFB was collected for three membranes from the survey. The coulombic, voltaic, and energy efficiency at low cycle counts aligned with the predictions from the membrane flux and resistance survey results. The study also identified three membranes—Fumapem F-930-RFS, Fumapem FS-715-RFS, and Aquivion E98-09S—that outperformed most other membranes regarding their position on the flux-resistance trade-off curve, indicating them to be good candidates for further testing.

 

We establish both the uniqueness and the existence of the solutions to a hidden-memory variable-order fractional stochastic partial differential equation, which models, e.g., the stochastic motion of a Brownian particle within a viscous liquid medium varied with fractal dimensions. We also investigate the inverse problem concerning the observations of the solutions, which eliminates the analytic assumptions on the variable orders in the literature of this topic and theoretically guarantees the reliability of the determination and experimental inference.

 

Diatom exoskeletons, known as frustules, exhibit a unique multilayer structure that has attracted considerable attention across interdisciplinary research fields as a source of biomorphic inspiration. These frustules possess a hierarchical porous structure, ranging from millimeter‐scale foramen pores to nanometer‐scale cribellum pores. In this study, this natural template for nanopattern design is leveraged to showcase metamaterials that integrates perfect absorption and subwavelength color printing. The cribellum‐inspired hierarchical nanopatterns, organized in a hexagonal unit cell with a periodicity of 300 nm, are realized through a single‐step electron beam lithography process. By employing numerical models, it is uncovered that an additional induced collective dipole mode is the key mechanism responsible for achieving outstanding performance in absorption, reaching up to 99%. Analysis of the hierarchical organization reveals that variations in nanoparticle diameter and inter‐unit‐cell distance lead to shifts and broadening of the resonance peaks. It is also demonstrated that the hierarchical nanopatterns are capable of color reproduction with high uniformity and fidelity, serving as hexagonal pixels for high‐resolution color printing. These cribellum‐inspired metamaterials offer a novel approach to multifunctional metamaterial design, presenting aesthetic potential applications in the development of robotics and wearable electronic devices, such as smart skin or surface coatings integrated with energy harvesting functionalities.

 

We prove the well‐posedness and smoothing properties of a distributed‐order time‐fractional diffusion equation with a singular density function in multiple space dimensions, which could model the ultraslow subdiffusion processes. We accordingly derive a finite element approximation to the problem and prove its optimal‐order error estimate. Numerical results are presented to support the mathematical and numerical analysis.