The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating 2‐dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier‐Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kinds of Bessel functions. In addition, these functions have properties such as piecewise continuity. For the enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. In addition, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, 4 benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.     

Assessment of a high‐order MUSCL method for rotor flows

This work presents the implementation of a high‐order, finite‐volume scheme suitable for rotor flows. The formulation is based on the variable extrapolation MUSCL‐scheme, where high‐order spatial accuracy (up to fourth‐order) is achieved using correction terms obtained through successive differentiation. A variety of results are presented, including 2‐ and 3‐dimensional test cases. Results with the proposed scheme, showed better wake and higher resolution of vortical structures compared with the standard MUSCL, even when coarse meshes were employed. The method was also demonstrated for 3‐dimensional unsteady flows using overset and moving grids for the UH‐60A rotor in forward flight and the Enhanced Rotorcraft Innovative Concept Achievement tiltrotor in aeroplane mode. For medium grids, the present method adds reasonable CPU and memory overheads and offers good accuracy on relatively coarse grids.     

Overview on the Prediction Models for Sheet Metal Forming Failure:Necking and Ductile Fracture

The formability of the material determines the amount of available deformation before failure and thus is important for the production of various structural components in industries. The workability of materials is commonly evaluated by different forms of failure models during sheet metal forming(SMF) processes. In order to provide a whole picture about the prediction models for SMF failure, necking-related formability and ductile fracture-related formability studies in SMF processes are systematically summarized, the applicability and limitation of each model are highlighted, and the link between forming limit diagram and ductile fracture criterion is pointed out. Conclusions about some critical issues on failure in SMF are made.     

Reconstruction of stability for Gaussian spatial solitons in quintic–septimal nonlinear materials under $${{varvec{mathcal {P}}}}{varvec{mathcal {T}}}$$ P T -symmetric potentials

Nonlinear Dynamics - Gaussian spatial soliton solutions of both the constant-coefficient and variable-coefficient (2 + 1)-dimensional nonlinear Schrödinger equations in...     

Approximate time-optimal control of quantum ensembles based on sampling and learning

For a general quantum ensemble with Hamiltonian fluctuations, this paper proposes a sampling-based two-stage approximate time-optimal control algorithm with momentum terms and achieves a high-fidelity state transition of all member systems to a common target state within an approximate minimum time. The fidelity and the control time are respectively optimized in the two stages. In particular, the introduction of momentum terms greatly improves the convergence rate of the algorithm. Simulation experiments on a two-level quantum ensemble verify the effectiveness of the proposed algorithm.     

Oxygen consumption and chemisorption in low-temperature oxidation of sub-bituminous pulverized coal

Studying the effect of oxygen in coal oxidation is very important for understanding and controlling coal spontaneous combustion. However, the oxygen effect is not very easy to determine clearly due to the large effect of heat source on coal oxidation in temperature rising experiments. Here, focused on sub-bituminous coal, the oxygen effect was separated from coal oxidation by continuously measuring FTIR spectra of coal with respect to varying temperatures and under oxygen and nitrogen. The active groups’ real-time changes of coal oxidation, thermal treatment and oxygen effect were measured. The carboxylic ester and carboxyl units are the main functional groups that increase with temperatures increasing under oxygen and nitrogen, while the other functional groups decrease in quantity. The oxygen effect promoted the consumption of aliphatic hydrocarbons and hydroxyl groups and also promoted the formation of oxygen-containing groups (except hydroxyl). Four characteristic temperature stages involved in the oxygen effect and their key functional groups were identified. Simultaneously, the relationship of oxygen consumption and chemisorption in oxygen effect was analyzed. The starting temperature of oxygen chemisorption is between 50 and 60°C. The maximum contribution of oxygen effect was observed in methyl and methylene groups. These results are important for chemical control of coal spontaneous combustion. The oxidation of aliphatic hydrocarbon should be controlled before oxygen chemisorption. The value of oxygen consumption between 70 and 80°C can be measured accurately due to the constant chemisorption rate, which help to identify the tendency for spontaneous combustion. These results will help in better understanding of the reaction mechanism of coal oxidation, especially the oxygen effect.     

Luminescence decay of distant donor-acceptor pairs in phosphorous-doped ZnTe

Luminescence decay of isolated donor-acceptor pairs has been measured over the range of pair distance R ～ 180 Å in phosphorous-doped ZnTe. Analysis of the recombination rate as a function of the pair distance suggests an asymptotic behaviour of the acceptor envelope function of the type exp(-r/a_A), with $\text{a}{}_{\mathrm{A}}\text{= 40 ± 10}\text{A}\text{?}$. This effective Bohr radius would correspond to an hydrogenic mass $\text{m}{}^1\text{= (0.13 ± 0.03)}\text{m}{}_{\mathrm{o}}$, which is close to the light hole mass as measured from cyclotron resonance experiments, $\text{m}{}^1\text{= (0.154 ± 0.005)}\text{m}{}_{\mathrm{o}}$. A discussion on the validity of the isolated donor-acceptor pair model is also given.