SIMULATION OF EFFECTS OF REACTIVE IMPURITIES ON PROPYLENE POLYMERIZATION IN LOOP REACTORS THROUGH GENERATION FUNCTION TECHNIQUE

The estimation of the amount of reactive impurities in a loop reactor is of strategic importance to the propylene polymerization industry. It is essential to investigate the level of impurities in order to develop reliable monitoring and control strategies. This paper described one approach based on generation function technique with the following two steps. First, a new mechanism for propylene polymerization was proposed by considering the effects of the reactive impurities in the material on the propylene polymerization. Second, a series of equations of population balance for the propylene polymerization in loop reactors were established based on the proposed mechanism. Accordingly, the equations were transformed into the mathematic matrix through the generation function technique to investigate the effects of the reactive impurities on the propylene polymerization. Significant effects of the reactive impurities were analyzed through computational simulation. The results show that the concentration of active centre on catalysts and the polymerization conversion both decrease with the increase of the initial concentration of any reactive impurity; hydrogen concentration decreases with the increase of the initial concentration of ethylene or butylenes, whereas, it increases with the increase of the initial concentration of propadiene; the simulated weight average molecular weight and the molecular weight distribution index of polymer resins both increase with the increase of the initial concentration of ethylene or butylenes. They decrease with the increase of the initial concentration of propadiene.

Mechanical Properties of Soil-Rock Mixture Filling in Fault Zone Based on Mesostructure

Soil-rock mixture(SRM)filling in fault zone is an inhomogeneous geomaterial,which is composed of soil and rock block.It controls the deformation and stability of the abutment and dam foundation,and threatens the long-term safety of high arch dams.To study the macroscopic and mesoscopic mechanical properties of SRM,the development of a viable mesoscopic numerical simulation method with a mesoscopic model generation technology,and a reasonable parametric model is crucially desired to overcome the limitations of experimental conditions,specimen dimensions,and experiment fund.To this end,this study presents a mesoscopic numerical method for simulating the mechanical behavior of SRM by proposing mesoscopic model generation technology based on its mesostructure features,and a rock parameter model considering size effect.The validity and rationality of the presented mesoscopic numerical method is experimentally verified by the triaxial compression tests with different rock block contents(RBC).The results indicate that the rock block can increase the strength of SRM,and it is proved that the random generation technique and the rock parameter model considering size effect are validated.Furthermore,there are multiple failure surfaces for inhomogeneous geomaterial of SRM,and the angle of the failure zone is no longer 45◦.The yielding zones of the specimen are more likely to occur in thin sections of soil matrix isolated by blocks with the failure path avoiding the rock block.The proposed numerical method is effective to investigate the meso-damage mechanism of SRM.

Arbitrary and reconfigurable optical vortex generation:a high-efficiency technique using director-varying liquid crystal fork gratings

A high-efficiency technique for optical vortex(OV) generation is proposed and demonstrated. The technique is based on liquid crystal fork gratings with space-variant azimuthal orientations, which are locally controlled via polarization-sensitive alignment layers. Thanks to the optical rewritability of the alignment agent and the dynamic image generation of the digital micro-mirror device, fork gratings can be instantly and arbitrarily reconfigured.Corresponding optical vortices carrying arbitrary azimuthal and radial indices are demonstrated with a conversion efficiency of 98.5%, exhibiting features of polarization control and electrical switching. The technique may pave a bright road toward OV generation, manipulation, and detection.

Metric of the gravitational field outside the neutron star

We have obtained the solution of the Einstein equation and the electric-magnetic field outside the neutron star, and at the same time, we investigated their asymptotic properties.

Modeling of the nonlinear acoustic field generated from a phased array using Gaussian superposition technique

The nonlinearity has significant effect on the ultrasonic therapy using phased ar- rays. A numerical approach is developed to calculate the nonlinear sound field generated from a phased array based on the Gaussian superposition technique. The parameters of the phased array elements are first estimated from the focal parameters using the inverse matrix algorithm; Then the elements are expressed as a set of Gaussian functions; Finally, the nonlinear sound field can be calculated using the Gaussian superposition technique. In the numerical simulation, a 64~ 1 phased array is used as the transmitter. In the linear case, the difference between the results of the Gaussian superposition technique and the Fresnel integral is less than 0.5%, which verifies the feasibility of the approach. In the nonlinear case, the nonlinear fields of single-focus modes and double-focus modes are calculated. The results reveal that the nonlinear effects can improve the focusing performance, and the nonlinear effects are related with the source pressures and the excitation frequencies.