Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDE) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, this paper applies the deep learning algorithm to solve a class of high-dimensional nonlinear partial differential equations with jump terms and their corresponding backward stochastic differential equations (BSDE) with jump terms. Using the nonlinear Feynman-Kac formula, the problem of solving this kind of PDE is transformed into the problem of solving the corresponding backward stochastic differential equations with jump terms, and the numerical solution problem is turned into a stochastic control problem. At the same time, the gradient and jump process of the unknown solution are separately regarded as the strategy function and they are approximated respectively by using two multilayer neural networks as function approximators. Thus, deep learning-based method is used to overcome the “curse of dimensionality” caused by high-dimensional PDE with jump, and the numerical solution is obtained. In addition, this paper proposes a new optimization algorithm based on the existing neural network random optimization algorithm, and compares the results with the traditional optimization algorithm, and achieves good results. Finally, the proposed method is applied to three practical high-dimensional problems: Hamilton-Jacobi-Bellman equation, bond pricing under the jump Vasicek model and high-dimensional option pricing model with default risk. The proposed numerical method has obtained satisfactory accuracy and efficiency. The method has important application value and practical significance in investment decision-making, option pricing, insurance and other fields.

One-dimensional shape memory polymer fibers (SMPFs) have obvious advantages in mechanical properties, dispersion properties and weavability. In this work, a method for fabricating semi-crystallization ethylene-vinyl acetate copolymer (EVA) fiber with two-way shape memory effect by melt spinning and ultraviolet (UV) curing was developed. Here, the effect of crosslink density on its performance was systematically analyzed by gel fraction measurement, tensile tests, DSC and TMA analysis. The results showed that the crosslink density and shape memory properties of EVA fiber could be facilely adjusted by controlling UV curing time. The resulting EVA fiber with cylindrical structure had a diameter of 247.13 ± 10.07 μm, and its mechanical strength and elongation at break were 64.46 MPa and 114.33%, respectively. The critical impact of the crosslink density and applied constant stress on the two-way shape memory effect were analyzed. Moreover, the single EVA fiber could lift more than 143 times its own weight and achieve 9% reversible actuation strain. The reversible actuation capability was significantly enhanced by a simple winding design of the single EVA fiber, which provided great potential applications in smart textiles, flexible actuators and artificial muscles.

The oscillating heat pipe (OHP) is a new member in the family of heat pipes, and it has great potential applications in energy conservation. However, the fluid flow and heat transfer in the OHP as well as the fundamental effects of inner diameter on them have not been fully understood, which are essential to the design and optimization of the OHP in real applications. Therefore, by combining the high-speed visualization method and infrared thermal imaging technique, the fluid flow and thermal performance in the OHPs with inner diameters of 1, 2 and 3 mm are presented and analyzed. The results indicate that three fluid flow motions, including small oscillation, bulk oscillation and circulation, coexist or, respectively, exist alone with the increasing heating load under different inner diameters, with three flow patterns occurring in the OHPs, viz. bubbly flow, slug flow and annular flow. These fluid flow motions are closely correlated with the heat and mass transfer performance in the OHPs, which can be reflected by the characteristics of infrared thermal images of condensers. The decrease in the inner diameter increases the frictional flow resistance and capillary instability while restricting the nucleate boiling in OHPs, which leads to a smaller proportion of bubbly flow, a larger proportion of short slug flow, a poorer thermal performance, and easier dry-out of working fluid. In addition, when compared with the 2 mm OHP, the increasing role of gravity induces the thermosyphon effect and weakens the 'bubble pumping' action, which results in a little smaller and bigger thermal resistances of 3 mm OHP under small and bulk oscillation of working fluid, respectively.