Random attractors for a stochastic hydrodynamical equation in Heisenberg paramagnet

This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in˙ H 1 .     

Global well-posedness of the stochastic 2D Boussinesq equations with partial viscosity

This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global well-posedness result of this system under partial viscosity is proved by using classical energy estimates method.     

Well-posedness and dynamics for the fractional Ginzburg-Landau equation

This article studies the global well-posedness and long-time dynamics for the nonlinear complex Ginzburg–Landau equation involving fractional Laplacian. The global existence and some uniqueness criterion of weak solutions are given with compactness method. To study the strong solutions with the semigroup method, we generalize some pointwise estimates for the fractional Laplacian to the complex background and study carefully the linear evolution of the equation. Finally, the existence of global attractors is studied.     

OPTIMAL DECAY RATE OF THE COMPRESSIBLE QUANTUM NAVIER-STOKES EQUATIONS

For quantum fluids governed by the compressible quantum Navier-Stokes equations in $\Bbb R^3$ with viscosity and heat conduction, we prove the optimal $L^p-L^q$ decay rates for the classical solutions near constant states. The proof is based on the detailed linearized decay estimates by Fourier analysis of the operators, which is drastically different from the case when quantum effects are absent.     

Ultrafast Removal of Cadmium(II) by Green Cyclodextrin Metal–Organic‐Framework‐Based Nanoporous Carbon: Adsorption Mechanism and Application

Water contaminated with heavy metals has been identified as a significant threat to human health. Therefore, the development of safe and rapid water‐treatment techniques is necessary. We have synthesized an eco‐friendly γ‐cyclodextrin metal–organic framework (MOF)‐based nanoporous carbon (γ‐CD MOF‐NPC) material, conducted a comprehensive characterization of it, and found its rapid and effective Cd^II‐removal capacity. The γ‐CD MOF‐NPC could effectively sequester a majority of cadmium ions within one minute, and it still demonstrated excellent adsorption ability under various conditions, including different pH, adsorbent dosage, and coexistent ions. The maximum adsorption capacity was calculated to be 140.85 mg g^?1 by means of the Langmuir model. The adsorption was primarily due to the effect of ion exchange of oxygen‐containing functional groups, as determined by studying the ζ potential and Fourier transform infrared spectroscopy. Flow‐through experiments further proved the rapid Cd^II‐removal capacity and potential of the practical application of γ‐CD MOF‐NPC in water treatment according to the cytotoxic data.     

Weak attractors for the dissipative fractional Heisenberg equation

In this short paper, we consider the long time behaviors of the fractional Heisenberg equation and the existence of a global weak attractor is proved for the shift dynamics in the path space. The key ingredient is some new type of commutator structure introduced in this paper, which seems indispensable in proving the compactness of the dynamics. The technique introduced in this paper may also be useful to other fractional order partial differential equations.     

Effect of Two-Step Formosolv Fractionation on the Structural Properties and Antioxidant Activity of Lignin

The formosolv fractionation process has been demonstrated to be an effective approach toward lignin recovery as an antioxidant from lignocellulosic biomass. In this study, four lignin fractions, FL-88%, FSL-70%, FIL-70% and FL-EtAc, were isolated from Phragmites australis biomass through two-step formosolv fractionation (88% formic acid delignification followed by 70% aqueous formic acid fractionation). To better understand the structural properties of the lignin obtained from this fractionation process, four isolated lignins were successfully characterized by gel permeation chromatography (GPC), Fourier transform infrared (FT-IR), two-dimensional heteronuclear single quantum coherence nuclear magnetic resonance (2D-HSQC NMR) spectroscopy, thermogravimetric analysis (TGA) and gas chromatograph-mass spectroscopy (GC/MS). It was found that lignin depolymerization via β-O-4 cleavage occurred via a formylation, elimination and hydrolysis mechanism, accompanied by a competitive condensation reaction. Noteworthily, two-step formosolv fractionation can produce specific lignin fractions with different ABTS and DPPH radical scavenging activities. The FL-EtAc fraction with low molecular weight (M_w = 2748 Da) and good homogeneity (PDI = 1.5) showed excellent antioxidant activity, compared with the other three isolated lignin fractions, even equal to that of commercial antioxidant BHT at the same concentration of 2.0 mg·mL⁻¹. These findings are of great help for specific lignin from biomass as a natural antioxidant in the future.