Invariant measures for the 3D globally modified Navier-Stokes equations with unbounded variable delays

This article investigates the three-dimensional globally modified Navier-Stokes equations with unbounded variable delays. Firstly, we prove the global well-posedness of the solutions, and give the existence of the pullback attractor for the associated process. Then, we construct a family of invariant Borel probability measures, which is supported by the pullback attractor

Invariant sample measures and random Liouville type theorem for the two-dimensional stochastic Navier-Stokes equations

In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample measures for random dynamical systems via the approach of global random attractors. Then we consider the two-dimensional incompressible Navier-Stokes equations with additive white noise as an example to show how to check the sufficient conditions for concrete stochastic partial differential equations. Our results generalize the Liouville type theorem to the random case and reveal that the invariance of the sample measures is a particular situation of the random Liouville type theore

Orbital-angular-momentum-resolved diagnostics for tracking internal phase evolution in multi-bound solitons

The generation of multi-bound solitons is a fascinating subject of investigation in many conservative and dissipative systems, such as photonics, fluid mechanics, Bose-Einstein condensates, and so on. In this study, we demonstrate the successful extraction of phase dynamics between solitons in bound multiple solitons with up to seven constituents in a mode-locked Er laser system. By mapping the internal phase motions of multi-bound solitons to the spatial phase movement of cylindrical vector beams using orbital angular momentum (OAM)-based diagnostics, different categories of internal pulsations are revealed. We show that bound state of four solitons exhibits linear drifting relative phase evolution dynamics; while for bound multiple solitons with constituents from five to seven pulses, stationary relative phase dynamics are observed. These findings highlight the possibility of the OAM-based method access to the internal motion of multi-soliton molecules with more freedom of degrees and fuel the analogy with research on chemistry molecule complex

Pseudohexagonal Nb2O5 Anodes for Fast-Charging Potassium-Ion Batteries

High-rate batteries will play a vital role in future energy storage systems, yet while good progress is being made in the development of high-rate lithium-ion batteries, there is less progress with post-lithium-ion chemistry. In this study, we demonstrate that pseudohexagonal Nb2O5(TT-Nb2O5) can offer a high specific capacity (179 mAh g-1 ∼ 0.3C), good lifetime, and an excellent rate performance (72 mAh g-1 at ∼15C) in potassium-ion batteries (KIBs), when it is composited with a highly conductive carbon framework; this is the first reported investigation of TT-Nb2O5 for KIBs. Specifically, multiwalled carbon nanotubes are strongly tethered to Nb2O5 via glucose-derived carbon (Nb2O5@CNT) by a one-step hydrothermal method, which results in highly conductive and porous needle-like structures. This work therefore offers a route for the scalable production of a viable KIB anode material and hence improves the feasibility of fast-charging KIBs for future applications

CRISPR-Cas13a system: A novel tool for molecular diagnostics

The clustered regularly interspaced short palindromic repeats (CRISPR) system is a natural adaptive immune system of prokaryotes. The CRISPR-Cas system is currently divided into two classes and six types: types I, III, and IV in class 1 systems and types II, V, and VI in class 2 systems. Among the CRISPR-Cas type VI systems, the CRISPR/Cas13a system has been the most widely characterized for its application in molecular diagnostics, gene therapy, gene editing, and RNA imaging. Moreover, because of the trans-cleavage activity of Cas13a and the high specificity of its CRISPR RNA, the CRISPR/Cas13a system has enormous potential in the field of molecular diagnostics. Herein, we summarize the applications of the CRISPR/Cas13a system in the detection of pathogens, including viruses, bacteria, parasites, chlamydia, and fungus; biomarkers, such as microRNAs, lncRNAs, and circRNAs; and some non-nucleic acid targets, including proteins, ions, and methyl groups. Meanwhile, we highlight the working principles of some novel Cas13a-based detection methods, including the Specific High-Sensitivity Enzymatic Reporter UnLOCKing (SHERLOCK) and its improved versions, Cas13a-based nucleic acid amplification-free biosensors, and Cas13a-based biosensors for non-nucleic acid target detection. Finally, we focus on some issues that need to be solved and the development prospects of the CRISPR/Cas13a system

Multifocal laser direct writing through spatial light modulation guided by scalable vector graphics

Multifocal laser direct writing (LDW) based on phase-only spatial light modulator (SLM) can realize flexible and parallel nanofabrication with high throughput potential. In this investigation, a novel approach of combining two-photon absorption, SLM and vector path guided by scalable vector graphics (SVG) has been developed and tested preliminarily, for fast, flexible and parallel nanofabrication. Three laser focuses are independently controlled with different paths, which are according to SVG, to optimize fabrication and promote time efficiency. The minimum structure width can be as low as 74 nm. Accompanied with a translation stage, a carp structure of 18.16 $\mu$m by 24.35 $\mu$m has been fabricated. This method shows the possibility of developing LDW techniques towards full-electrical system, and provides a potential way to efficiently engrave complex structures on nanoscales

Robust Biomass-Derived Carbon Frameworks as High-Performance Anodes in Potassium-Ion Batteries

Potassium-ion batteries (PIBs) have become one of the promising candidates for electrochemical energy storage that can provide low-cost and high-performance advantages. The poor cyclability and rate capability of PIBs are due to the intensive structural change of electrode materials during battery operation. Carbon-based materials as anodes have been successfully commercialized in lithium- and sodium-ion batteries but is still struggling in potassium-ion battery field. This work conducts structural engineering strategy to induce anionic defects within the carbon structures to boost the kinetics of PIBs anodes. The carbon framework provides a strong and stable structure to accommodate the volume variation of materials during cycling, and the further phosphorus doping modification is shown to enhance the rate capability. This is found due to the change of the pore size distribution, electronic structures, and hence charge storage mechanism. The optimized electrode in this work shows a high capacity of 175 mAh g^{-1} at a current density of 0.2 A g^{-1} and the enhancement of rate performance as the PIB anode (60% capacity retention with the current density increase of 50 times). This work, therefore provides a rational design for guiding future research on carbon-based anodes for PIBs