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The establishment of a financial system should not only consider the current situation, but also need to refer to the past. Due to the memory of the fractional derivative, a fractional-order system can more effectively describe the historical significance of the financial system. Most scholars use the prediction–correction scheme to study fractional-order systems. This paper provides a higher-precision numerical method for the financial system, which more effectively simulate the system. Based on the definition of the Grünwald–Letnikov fractional derivative, the integer-order system with nonconstant demand elasticity is extended to the fractional-order setting, and its dynamic behavior is studied, with some novel chaotic attractors found. The research results are helpful for improving the understanding of the financial system and the financial market and for predicting financial risks. [ABSTRACT FROM AUTHOR]

In order to stop and reverse land degradation and curb the loss of biodiversity, the United Nations 2030 Agenda for Sustainable Development proposes to combat desertification. In this paper, a fractional vegetation–water model in an arid flat environment is studied. The pattern behavior of the fractional model is much more complex than that of the integer order. We study the stability and Turing instability of the system, as well as the Hopf bifurcation of fractional order α , and obtain the Turing region in the parameter space. According to the amplitude equation, different types of stationary mode discoveries can be obtained, including point patterns and strip patterns. Finally, the results of the numerical simulation and theoretical analysis are consistent. We find some novel fractal patterns of the fractional vegetation–water model in an arid flat environment. When the diffusion coefficient, d, changes and other parameters remain unchanged, the pattern structure changes from stripes to spots. When the fractional order parameter, β , changes, and other parameters remain unchanged, the pattern structure becomes more stable and is not easy to destroy. The research results can provide new ideas for the prevention and control of desertification vegetation patterns. [ABSTRACT FROM AUTHOR]

The aim of this investigation was to evaluate the effect of microstructure heterogeneity on the tensile and low cycle fatigue properties of electron beam welded (EBW) Ti6Al4V sheets. To achieve this goal, the tensile and low cycle fatigue property in the EBW joints and base metal (BM) specimens is compared. During the tensile testing, digital image correlation technology was used to measure the plastic strain field evolution within the specimens. The experimental results showed that the tensile ductility and low cycle fatigue strength of EBW joints are lower than that of BM specimens, mainly because of the effect of microstructure heterogeneity of the welded joint. Moreover, the EBW joints exhibit the cyclic hardening behavior during low fatigue process, while BM specimens exhibit the cyclic softening behavior. Compared with the BM specimens with uniform microstructure, the heterogeneity of microstructure in the EBW joint is found to decrease the mechanical properties of welded joint. [ABSTRACT FROM AUTHOR]

The effect of Ni interlayer thickness on chemical composition, microstructure and mechanical properties of laser welding of Mo and stainless steel was analyzed systematically. Experimental results indicated that with the increase in thickness of Ni interlayer, the number of Mo Fe IMCs, the hardness at the Mo-FZ interface, the width and grain size in the heat affected zone of Mo side and the thickness of Mo Fe IMCs layer decreased significantly. The maximum tensile strength attained 351 MPa for joints with 0.1 mm thick Ni interlayer. With excessive (>0.1 mm) Ni addition in the welded joint, the mechanical properties deteriorated due to the formation incomplete fusion, void and crack defects. The tensile investigation showed that the weakest area of the joint was Mo Fe IMCs layer. When an appropriate thickness of Ni interlayer is used, the Mo Fe IMCs layer can be strengthened by increasing diffusion ability of Mo to FZ and Ni concentration in the Mo Fe IMCs and restraining of Mo Fe IMCs, consequently producing high-quality welded joints. • The addition of Ni interlayer can improve the weldability between Mo and Fe. • The tensile investigation showed that the weak area of the joint was Mo-Fe IMCs layer. • The Mo-Fe IMCs layer can be strengthened by using an appropriate thickness of Ni interlayer. • The maximum tensile strength attained 351 MPa for Mo/Fe joint with Ni interlayer of 0.1 mm thickness. [ABSTRACT FROM AUTHOR]

Direct welding of Mo and stainless steel is exceptionally difficult due to intrinsic brittleness of Mo and the formation of brittle Fe-Mo phases. To explore the feasibility of welding of Mo and stainless steel, the laser offset method was used in this study. Experimental results show that the offset of the laser beam toward stainless steel has a positive effect for the quality of Mo/Fe dissimilar joint. As the laser beam shifts from the Mo side to the stainless steel side, the formation of welding defects and Fe-Mo intermetallic compounds (IMCs) are effectively restricted because of the decrease amount of molten Mo. The decrease of Fe-Mo IMCs contributes to the reduction of hardness in the joints. With an increase of laser offset, the thickness of Fe-Mo IMCs layer decreased, consequently the tensile strength of joints increased first and then decreased in the laser offset range of 0.2–0.5 mm. The highest tensile strength of the joints is 290 MPa at the laser offset of 0.3 mm. All joints failed in the Fe-Mo IMCs layer with brittle fracture mode during tensile tests, indicating the weakest zone of the joint was Fe-Mo IMCs layer. A sound weld of Mo and stainless steel can be obtained if an appropriate thickness of Fe-Mo IMCs layer is produced by adjusting the laser offset. Unlabelled Image • Dissimilar laser welding of pure molybdenum to stainless steel has been investigated. • Microstructural evolution during joining Mo/Fe was elucidated. • Laser offset-microstructure-mechanical properties relation is established. • The highest tensile strength of the joints is 290 MPa at the laser offset of 0.3 mm. [ABSTRACT FROM AUTHOR]