Lines on K3K3–Quartics Via Triangular Sets

We prove the sharp upper bound of at most 52 lines on a complex $K3$–surface of degree 4 with a non-empty singular locus. We also classify the configurations of more than 48 lines on smooth complex quartics

Synergistic ZIF-67(Co) anchoring NiAl-LDH nanosheets : morphology transformation for efficient electrocatalytic oxygen evolution reaction

Electrocatalytic water splitting is key for sustainable hydrogen production, requiring efficient catalysts. Morphological tailoring represents a promising strategy to optimize electrocatalytic performance by modifying material structures at the nanoscale. This study shows ZIF-67 transformation from nanocubes to rhombic dodecahedra when anchored to 3D NiAl-layered double hydroxide (LDH) nanosheets, enhancing its catalytic properties. The ZIF-67/NiAl-LDH/N composite showcases effective synergy, improving oxygen evolution reaction (OER) performance through better electron transfer. The rhombic dodecahedron’s greater surface area increases Co-based active sites, enhancing interaction with reactants. NiAl-LDH intrinsic catalytic properties from nickel further boost ZIF-67 performance. This composite demonstrates impressive durability and OER activity, with low overpotentials of 190 mV at $20 mA cm^{−2}$ and 260 mV at $50 mA cm^{−2}$, alongside a Tafel slope of $48 mV dec^{−1}$, indicating suitability for large-scale energy applications

Modeling diffusion of elongated particles through a narrowing channel

Simulations of the Brownian dynamics of diffusing particles in complex environments provide important information about the characteristics of the medium and the properties of biological processes. Notable examples include the diffusion of ions and macromolecular solutes through channels of varying cross-section, such as pores in biological membranes, living tissues, zeolites, carbon nanotubes, and synthetic porous materials. In these systems, the observed diffusion can exhibit anomalous behavior characterized by a nonlinear increase in the mean squared displacement. In this article, we present a toy model of the diffusion of rod-shaped particles through a narrowing, conical pore with a trapezoidal longitudinal cross-section. Particles of different sizes undergo a random walk due to interactions with the environment (modeled as noise). We study how the diffusion properties change with particle size as a function of pore width. The numerical analysis of diffusion-driven transport through narrowing conical channels reveals its effective subdiffusive, i.e., anomalous, character