Study on the Formation of Reactive Material Shaped Charge Jet by Trans-Scale Discretization Method

The formation process of reactive materials shaped charge is investigated by X-ray photographs and numerical simulation. In order to study the formation process, a trans-scale discretization method is proposed. A two-dimensional finite element model of shaped charge and reactive material liner is established and the jet formation process, granule size difference induced particle dispersion and granule distribution induced jet particle distribution are analyzed based on Autodyn-2D platform and Euler solver. The result shows that, under shock loading of shaped charge, the Al particle content decreases from the end to the tip of the jet, and increases as the particle size decreases. Besides, the quantity of Al particles at the bottom part of the liner has more prominent influence on the jet head density than that in the other parts, and the Al particle content in the high-speed section of jet shows inversely proportional relationship to the ratio of the particle quantity in the top area to that in the bottom area of liner.

Study on Cavitation and Tribological of TiO2 Nano-Film on Bearing Pads Surface

Bearings play a vital role in the operation of a two-axis system. Long-term bearing use inevitably produce bubbles and frictional damage. Therefore, the protection of bearings is critical for the stable operation of a two-axis system. In this study, a TiO2 nanofilm is used to physically protect a bearing. The discretization method is used to analyse the cavitation process. Cavitation primarily occurs on the front surface of the pad during bearing operation. A finite element analysis of a bearing pad coated and not coated with TiO2 nanofilms shows that TiO2 nanofilms can effectively absorb the cavitation force exerted on pads, thereby reducing inflicted damage. Moreover, the TiO2 nanofilm reduces the friction coefficient of the pad surface, promoting good bearing capacity of the bearing during rotation. The TiO2 nanofilm serves as a protective layer that improves the anti-wear and bearing performance of a two-axis system.

A Hybrid High-Order method for creeping flows of non-Newtonian fluids

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for Leray-Lions scalar problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau-Yasuda models. Numerical examples complete the exposition.

Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays

The Cucker and Smale model is a well-known flocking model that describes the emergence of flocks based on alignment. The first part focuses on investigating this model, including the effect of time delay and the presence of a leader. Furthermore, the control function is inserted into the dynamics of a leader to drive a group of agents to target. In the second part of this work, leadership-based optimal control is investigated. Moreover, the existence of the first-order optimality conditions for a delayed optimal control problem is discussed. Furthermore, the Runge–Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. Finally, the capacity of the proposed control approach to drive a group of agents to reach the desired places or track the trajectory is demonstrated by numerical experiment results.

Coupled topology and shape optimization using an embedding domain discretization method

Density-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.

Novel ANN Method for Solving Ordinary and Time-Fractional Black–Scholes Equation

The main aim of this study is to introduce a 2-layered artificial neural network (ANN) for solving the Black–Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed to change the model into a sequence of ordinary differential equations (ODE). Subsequently, each of these ODEs is solved with the aid of an ANN. Adam optimization is employed as the learning paradigm since it can add the foreknowledge of slowing down the process of optimization when getting close to the actual optimum solution. The model also takes advantage of fine-tuning for speeding up the process and domain mapping to confront the infinite domain issue. Finally, the accuracy, speed, and convergence of the method for solving several types of the Black–Scholes model are reported.