A control-theoretic perspective on optimal high-order optimization

Mathematical Programming - We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function...     

Surface Reconstruction Engineering with Synergistic Effect of Mixed-Salt Passivation Treatment toward Efficient and Stable Perovskite Solar Cells

Surface passivation treatment is a widely used strategy to resolve trap-mediated nonradiative recombination toward high-efficiency metal-halide perovskite photovoltaics. However, a lack of passivation with mixture treatment has been investigated, as well as an in-depth understanding of its passivation mechanism. Here, a systematic study on a mixed-salt passivation strategy of formamidinium bromide (FABr) coupled with different F-substituted alkyl lengths of ammonium iodide is demonstrated. It is obtained better device performance with decreasing chain length of the F-substituted alkyl ammonium iodide in the presence of FABr. Moreover, they unraveled a synergistic passivation mechanism of the mixed-salt treatment through surface reconstruction engineering, where FABr dominates the reformation of the perovskite surface via reacting with the excess PbI₂. Meanwhile, ammonium iodide passivates the perovskite grain boundaries both on the surface and top perovskite bulk through penetration. This synergistic passivation engineer results in a high-quality perovskite surface with fewer defects and suppressed ion migration, leading to a champion efficiency of 23.5% with mixed-salt treatment. In addition, the introduction of the moisture resisted F-substituted groups presents a more hydrophobic perovskite surface, thus enabling the decorated devices with excellent long-term stability under a high humid atmosphere as well as operational conditions.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.