Reactivity of a N-Coordinated Germylene-Borane Complex: From Ge→B to Ge→Ga Coordination

Reactivity studies of the Ge^II→B complex L(Cl)Ge⋅BH₃ ( 1 ; L=2-Et₂NCH₂-4,6-tBu₂-C₆H₂) were performed to determine the effect on the Ge^II→B donation. N-coordinated compounds L(OtBu)Ge⋅BH₃ ( 2 ) and [LGe⋅BH₃]₂ ( 3 ) were prepared. The possible tuning of the Ge^II→B interaction was proved experimentally, yielding compounds 1-PPh₂-8-(LGe)-C₁₀H₆ ( 4 ) and L(Cl)Ge⋅GaCl₃ ( 5 ) without a Ge^II→B interaction. In 5 , an unprecedented Ge^II→Ga coordination was revealed. The experimental results were complemented by a theoretical study focusing on the bonding in 1 − 5 . The different strength of the Ge^II→E (E=B, Ga) donation was evaluated by using energy decomposition analysis. The basicity of different L(X)Ge groups through proton affinity is also assessed.     

Superradiant Emission from Coherent Excitons in van Der Waals Heterostructures

Recent advancements in isolation and stacking of layered van der Waals materials have created an unprecedented paradigm for demonstrating varieties of 2D quantum materials. Rationally designed van der Waals heterostructures composed of monolayer transition-metal dichalcogenides (TMDs) and few-layer hBN show several unique optoelectronic features driven by correlations. However, entangled superradiant excitonic species in such systems have not been observed before. In this report, it is demonstrated that strong suppression of phonon population at low temperature results in a formation of a coherent excitonic-dipoles ensemble in the heterostructure, and the collective oscillation of those dipoles stimulates a robust phase synchronized ultra-narrow band superradiant emission even at extremely low pumping intensity. Such emitters are in high demand for a multitude of applications, including fundamental research on many-body correlations and other state-of-the-art technologies. This timely demonstration paves the way for further exploration of ultralow-threshold quantum-emitting devices with unmatched design freedom and spectral tunability.     

Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model

Nonlinear Dynamics - In this article, the authors simulate and study dark and bright soliton solutions of 1D and 2D regularized long wave (RLW) models. The RLW model occurred in various fields such...     

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.     

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.