This paper reports the construction of synchronization criteria for the delayed impulsive epidemic models with reaction–diffusion under the Neumann boundary value. Different from the previous literature, the reaction–diffusion epidemic model with a delayed impulse brings mathematical difficulties to this paper. In fact, due to the existence of second-order partial derivatives in the reaction–diffusion model with a delayed impulse, the methods of first-order ordinary differential equations from the previous literature cannot be effectively applied in this paper. However, with the help of the variational method and an appropriate boundedness assumption, a new synchronization criterion is derived, and its effectiveness is illustrated by numerical examples.

The effect of molecular weight on the structure and properties of PAN precursor was studied by the combination of scanning electron microscopy (SEM), X-ray diffraction (XRD) and differential scanning calorimetry (DSC), etc. With the molecular weight increasing, the grooves on the surface become deeper and rougher, the interlayer spacing and crystallite size increase, and the exothermic reaction occurred later. The strength and breaking extension of PAN precursors increase gradually with the molecular weight increasing. The effect of molecular weight is greater than the effect of surface defects on strength for PAN precursor of high molecular weight.

The phosphate rock has great potential value in the application of cut-off walls for heavy metal contaminated sites. The effects of initial concentration of Pb2+, contact time, temperature and pH on the adsorption performance of phosphate rock modified soil-bentonite (PSB) were analyzed by Batch tests, also the microstructure and physicochemical properties of the adsorbent were characterized and analyzed by scanning electron microscopy (SEM), X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FT-IR). The results showed that the incorporation of phosphate rock improves the adsorption performance of the mixed material for Pb2+ in acidic environment, and the maximum adsorption amount of PSB can be 154% greater than that of soil-bentonite (SB). The kinetic analysis showed that intraparticle diffusion and liquid film diffusion participate in control of the adsorption process at the same time, and the Langmuir model could fit the isothermal adsorption data better. The adsorption process of PSB to Pb2+ is an exothermic reaction process, and the low temperature environment is beneficial to the adsorption of Pb2+. Studies on the microscopic mechanism show that the PO43− react with Pb2+ in the solution to form phosphate precipitation, and –OH and PO43− on the surface or interlayer of the adsorbent participate in the adsorption process of Pb2+.

The local structure evolution of polyacrylonitrile (PAN) fibers during pre-oxidation and carbonization was studied using X-ray diffraction (XRD) and radial distribution function (RDF). The nearest inter-chains distance of PAN is 6.88 Å, which is close to the diameter of the “rigid rod” model proposed by Warner. The third neighbor distances of carbon fibers are greater than that of graphite, indicating the planar six-member rings are absent in the carbon fibers from 500 to 1250°C. The structure of fibers transforms from long-range order to long-range disorder during the pre-oxidation process, then transforms from short-range order to long-range order during the carbonization process.