Physics-informed Neural Network Combined with Characteristic-Based Split for Solving Navier-Stokes Equations

In this paper, physics-informed neural network (PINN) based on characteristic-based split (CBS) is proposed, which can be used to solve the time-dependent Navier-Stokes equations (N-S equations). In this method, The output parameters and corresponding losses are separated, so the weights between output parameters are not considered. Not all partial derivatives participate in gradient backpropagation, and the remaining terms will be reused.Therefore, compared with traditional PINN, this method is a rapid version. Here, labeled data, physical constraints and network outputs are regarded as priori information, and the residuals of the N-S equations are regarded as posteriori information. So this method can deal with both data-driven and data-free problems. As a result, it can solve the special form of compressible N-S equations -- -Shallow-Water equations, and incompressible N-S equations. As boundary conditions are known, this method only needs the flow field information at a certain time to restore the past and future flow field information. We solve the progress of a solitary wave onto a shelving beach and the dispersion of the hot water in the flow, which show this method's potential in the marine engineering. We also use incompressible equations with exact solutions to prove this method's correctness and universality. We find that PINN needs more strict boundary conditions to solve the N-S equation, because it has no computational boundary compared with the finite element method

Effect of Leaf Surface Regulation of Zinc Fertilizer on Absorption of Cadmium, Plumbum and Zinc in Rice (<i>Oryza sativa</i> L.)

The accumulation of heavy metals in rice is bound to affect human health and safety. In order to ensure food security, this study explores the effect of leaf surface regulation of zinc (Zn) fertilizer on the safety of rice in cadmium (Cd)-plumbum (Pb) polluted farmland. Through field experiments, the leaf surface control treatment of zinc fertilizer was set up, and the effects of leaf surface control of zinc fertilizer on rice yield, Cd and Pb concentration in different parts and zinc, nitrogen, phosphorus and potassium concentration in brown rice were studied in the growing period of rice. The results showed as follows: (1) Spraying twice or more in the growth stage of rice could increase the yield by 6.77–7.29% compared with the blank, which was significantly higher than that of single spraying in a certain growth stage. (2) After spraying zinc fertilizer on the leaf surface, Cd and Pb concentration in brown rice decreased by 29.52–56.01% and 11.10–28.34%, respectively, compared with CK. Two or more times of spraying can make Cd concentration in brown rice meet the Chinese standard GB 2762-2022, and one time of spraying can make Pb concentration in brown rice meet the standard. (3) Leaf surface control of zinc fertilizer could reduce the Cd enrichment ability of rice plant parts, and the Cd enrichment coefficient of brown rice was significantly reduced by 28.18–55.02%. Leaf surface control of zinc fertilizer can reduce Cd and Pb concentration in brown rice by reducing the transport ability of heavy metal Cd and Pb in rice roots to straw and then to brown rice. (4) The zinc concentration in brown rice was 18.16–20.68 mg·kg−1, which was 18.21–34.64% higher than that in CK, and the zinc enrichment effect was the most significant after spraying three times. Meanwhile, the nitrogen, phosphorus and potassium concentration in brown rice also increased with the increase of spraying times. By comprehensive analysis, the leaf surface control of zinc fertilizer can reduce the Cd and Pb concentration in rice, and the Cd and Pb concentration in brown rice can meet the Chinese standard GB 2762-2022 by spraying twice. At the same time, it can improve the concentration of zinc, nitrogen, phosphorus and potassium in brown rice, is feasible and has high economic benefits

Effect of Leaf Surface Regulation of Zinc Fertilizer on Absorption of Cadmium, Plumbum and Zinc in Rice (Oryza sativa L.)

The accumulation of heavy metals in rice is bound to affect human health and safety. In order to ensure food security, this study explores the effect of leaf surface regulation of zinc (Zn) fertilizer on the safety of rice in cadmium (Cd)-plumbum (Pb) polluted farmland. Through field experiments, the leaf surface control treatment of zinc fertilizer was set up, and the effects of leaf surface control of zinc fertilizer on rice yield, Cd and Pb concentration in different parts and zinc, nitrogen, phosphorus and potassium concentration in brown rice were studied in the growing period of rice. The results showed as follows: (1) Spraying twice or more in the growth stage of rice could increase the yield by 6.77&ndash;7.29% compared with the blank, which was significantly higher than that of single spraying in a certain growth stage. (2) After spraying zinc fertilizer on the leaf surface, Cd and Pb concentration in brown rice decreased by 29.52&ndash;56.01% and 11.10&ndash;28.34%, respectively, compared with CK. Two or more times of spraying can make Cd concentration in brown rice meet the Chinese standard GB 2762-2022, and one time of spraying can make Pb concentration in brown rice meet the standard. (3) Leaf surface control of zinc fertilizer could reduce the Cd enrichment ability of rice plant parts, and the Cd enrichment coefficient of brown rice was significantly reduced by 28.18&ndash;55.02%. Leaf surface control of zinc fertilizer can reduce Cd and Pb concentration in brown rice by reducing the transport ability of heavy metal Cd and Pb in rice roots to straw and then to brown rice. (4) The zinc concentration in brown rice was 18.16&ndash;20.68 mg&middot;kg&minus;1, which was 18.21&ndash;34.64% higher than that in CK, and the zinc enrichment effect was the most significant after spraying three times. Meanwhile, the nitrogen, phosphorus and potassium concentration in brown rice also increased with the increase of spraying times. By comprehensive analysis, the leaf surface control of zinc fertilizer can reduce the Cd and Pb concentration in rice, and the Cd and Pb concentration in brown rice can meet the Chinese standard GB 2762-2022 by spraying twice. At the same time, it can improve the concentration of zinc, nitrogen, phosphorus and potassium in brown rice, is feasible and has high economic benefits

Vibration Analysis of Bilayered Graphene Sheets for Building Materials in Thermal Environments Based on the Element-Free Method

Graphene sheets are widely applied due to their unique and highly valuable properties, such as energy conservation materials in buildings. In this paper, we investigate the vibration behavior of double layer graphene sheets (DLGSs) in thermal environments which helps probe into the mechanism of energy conservation of graphene sheets in building materials. The nonlocal elastic theory and classical plate theory (CLPT) are used to derive the governing equations. The element-free method is employed to analyze the vibration behaviors of DLGSs embedded in an elastic medium. The accuracy of the solutions in this study is demonstrated by comparison with published results in the literature. Furthermore, a number of numerical results are presented to investigate the effects of various parameters (boundary conditions, nonlocal parameter, aspect ratio, side length, elastic foundation parameter, and temperature) on the frequency of DLGSs

Brilliant GeV electron beam with narrow energy spread generated by a laser plasma accelerator

The production of GeV electron beam with narrow energy spread and high brightness is investigated using particle-in-cell simulations. A controlled electron injection scheme and a method for phase-space manipulation in a laser plasma accelerator are found to be essential. The injection is triggered by the evolution of two copropagating laser pulses near a sharp vacuum-plasma transition. The collection volume is well confined and the injected bunch is isolated in phase space. By tuning the parameters of the laser pulses, the parameters of the injected electron bunch, such as the bunch length, energy spread, emittance and charge, can be adjusted. Manipulating the phase-space rotation with the rephasing technique, the injected electron bunch can be accelerated to GeV level while keeping relative energy spread below 0.5% and transverse emittance below 1.0  μm. The results present a very promising way to drive coherent x-ray sources