GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^s(·)p(·),h(·),q(R³)with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN^4-2α-3/p(·)p(·),h(·)q(R³).The result of this paper extends some recent work.     

Explicit solutions and Darboux transformations of a generalized D-Kaup–Newell hierarchy

Nonlinear Dynamics - Darboux and Bäcklund transformations on integrable couplings are formulated and generalized. The generalization of the theory pertains to spectral problems where the...     

Interaction phenomena among lump,periodic and kink wave solutions to a (3 + 1)-dimensional Sharma-Tasso-Olver-like equation

In this article, we consider a (3 + 1)-dimensional Sharma–Tasso–Olver-like (STOL) model describing dynamical propagation of nonlinear dispersive waves in inhomogeneous media. Applying Hirota's bilinear technique and a trial function, we explore nonlinear dynamical properties of basic solutions to the STOL model. We find that the fission fusion pattern occurs in the collision between the lump and kink waves, the collision between the lump and periodic waves, and the collision among the lump, kink and periodic waves, which is a novel fascinating collision pattern. We also observe that a large value of the coefficient in the periodic function produces a hybrid lump wave by fission in the collision solution. To better understand the dynamic properties of the obtained collision solutions, we plot a number of 3D and contour diagrams by choosing suitable parametric values with the aid of the computational software Maple 18.     

Global Regularity of the Logarithmically Supercritical MHD System in Two-dimensional Space

In this paper, we study the global regularity of logarithmically supercritical MHD equations in $2$ dimensional, in which the dissipation terms are $-\mu\Lambda^{2\alpha}u$ and $-\nu\mathcal{L}^{2\beta} b$. We show that global regular solutions in the cases $0<\alpha<\frac{1}{2},\beta>1,3\alpha+2\beta>3$.     

Preparation of two-dimensional molybdenum disulfide for NO2 detection at room temperature

In this work, the two-dimensional MoS₂ film was prepared by sulfuring the molybdenum atomic layer on SiO₂/Si substrate. The reaction temperature, heating rate, holding time and carrier gas flow rate were investigated comprehensively. The quality of MoS₂ film was characterized by optical microscopy, atomic force microscopy, Raman and photoluminescence spectroscopy. The characterization results showed that the optimum synthesis parameters were heating rate of 25 °C/min, reaction temperature of 750 °C, holding time of 30 min and carrier gas velocity of 100 sccm. The MoS₂ gas sensor was fabricated and its gas sensing performance was tested. The test results indicated that the sensor had a good response to both reducing gas (NH₃) and oxidizing gas (NO₂) at room temperature. The sensitivity to 100 ppm of NO₂ was 31.3%, and the response/recovery times were 4 s and 5 s, respectively. In addition, the limit of detection could be as low as 1 ppm. This work helps us to develop low power and integrable room temperature NO₂ sensors.     

Photo-Controlled Macroscopic Self-Assembly Based on Photo-Switchable Hetero-Complementary Quadruple Hydrogen Bonds

A photo-switchable hetero-complementary quadruple H-bonding array, which consists of an azobenzene-derived ureidopyrimidinone (UPy) module ( Azo-UPy ) and a nonphotoactive diamidonaphthyridine (DAN) derivative ( Napy-1 ), is constructed based on a reversible photo-locking approach. Upon UV (390 nm)/Vis (460 nm) light irradiations, photo-switchable quadruple H-bonded dimerization between Azo-UPy and Napy-1 can be achieved with exhibiting 4.8×10⁴-fold differences in binding strength (ON/OFF ratios). Furthermore, smart polymeric gels with unique photo-controlled macroscopic self-assembly behavior can be fabricated by introducing such quadruple H-bonding array as photo-regulable noncovalent interfacial connections.     

Linear superposition formula of solutions for the extended (3+1)-dimensional shallow water wave equation

Nonlinear Dynamics - Active researches on the water waves have been done, and water waves are essentially complex waves controlled by gravity field and surface tension. Using the Hirota bilinear...     

Light-fueled dissipative self-assembly at molecular and macro-scale enabled by a visible-light-responsive transient hetero-complementary quadruple hydrogen bond

The development of out-of-equilibrium self-assembly systems using light as input fuel is highly desirable and promising for the fabrication of smart supramolecular materials. Herein, we report the construction of new artificial light-fueled dissipative molecular and macroscopic self-assembly systems based on a visible-light-responsive transient quadruple H-bonding array, which consists of an azobenzene-modified ureidopyrimidinone (UPy) module (Azo-O-UPy) and a nonphotoactive diamidonaphthyridine (DAN) derived competitive binder (Napy-1). The visible light (410 nm) irradiation can induce the E to Z isomerization of the azobenzene unit of E-Azo-O-UPy to produce Z-Azo-O-UPy with an opened UPy binding site, which can complex with Napy-1 to form a quadruply H-bonded heterodimer. The heterodimer is metastable and can be quickly disassembled in dark, owing to the fast thermal relaxation of Z-Azo-O-UPy to E-Azo-O-UPy. While introducing such transient quadruple H-bonding interaction into a linear polymer system or a polymeric gel system, light-fueled out-of-equilibrium polymeric assembly both at molecular and macro-scale can be achieved.