Discontinuous boundary implementation for the shallow water equations

Quasi‐bubble finite element approximations to the shallow water equations are investigated focusing on implementations of the surface elevation boundary condition. We first demonstrate by numerical results that the conventional implementation of the boundary condition degrades the accuracy of the velocity solution. It is also shown that the degraded velocity leads to a critical instability if the advection term is present in the momentum equation. Then we propose an alternative implementation for the boundary condition. We refer to this alternative implementation as a discontinuous boundary (DB) implementation because it introduces at each boundary node two independent mass–flux values that result in a discontinuity at the boundary. Numerical results show that the proposed DB implementation is consistent, stabilizes the quasi‐bubble scheme, and leads to second‐order accuracy at the surface elevation specified boundary. Copyright © 2004 John Wiley & Sons, Ltd.     

The effect of HCP on the formation of twin boundaries and dislocations in Ni–Co alloys

In this study, molecular dynamics (MD) was used to simulate the rapid solidification process of Ni₄₇Co₅₃ and Ni₄₈Co₅₂ alloys at a cooling rate of 10¹² K/s. The effects of HCP on the formation of twin boundaries and dislocations in two Ni–Co alloys are studied. It is found that the difference of HCP clusters is the main effect that producing discrepancies on microstructure of two alloys. The number of HCP clusters accounted for 9.23% in Ni₄₇Co₅₃ alloy. They are regularly arranged to form the number of single-layer twin boundaries, and each twin boundary ends in a dislocation. The FCC and HCP structures coexist in the same atomic layers, which is easy to create dislocations. The relatively standard FCC crystal and only 0.32% HCP clusters are formed in Ni₄₈Co₅₂ alloy at 300 K. That small amount of HCP clusters are dispersed on the surface, and cause the formation of dislocation in the border with FCC clusters.     

Intelligent Fault Identification for Rolling Bearings Fusing Average Refined Composite Multiscale Dispersion Entropy-Assisted Feature Extraction and SVM with Multi-Strategy Enhanced Swarm Optimization

Rolling bearings act as key parts in many items of mechanical equipment and any abnormality will affect the normal operation of the entire apparatus. To diagnose the faults of rolling bearings effectively, a novel fault identification method is proposed by merging variational mode decomposition (VMD), average refined composite multiscale dispersion entropy (ARCMDE) and support vector machine (SVM) optimized by multistrategy enhanced swarm optimization in this paper. Firstly, the vibration signals are decomposed into different series of intrinsic mode functions (IMFs) based on VMD with the center frequency observation method. Subsequently, the proposed ARCMDE, fusing the superiorities of DE and average refined composite multiscale procedure, is employed to enhance the ability of the multiscale fault-feature extraction from the IMFs. Afterwards, grey wolf optimization (GWO), enhanced by multistrategy including levy flight, cosine factor and polynomial mutation strategies (LCPGWO), is proposed to optimize the penalty factor C and kernel parameter g of SVM. Then, the optimized SVM model is trained to identify the fault type of samples based on features extracted by ARCMDE. Finally, the application experiment and contrastive analysis verify the effectiveness of the proposed VMD-ARCMDE-LCPGWO-SVM method.     

Experimental study of bubble dynamics in the neighbourhood of a vertical incomplete boundary

The bubbles have been widely used in biomedical field, military and chemical industry. The liquid jet generated by the bubble collapse through an orifice is utilized in needle-free injections and inkjet printing. In this paper we devised synchronized triggering equipment, experimentally investigated the mechanism in the interaction of an electric-spark generated a single bubble and a vertical wall with an air-back opening. Detailed observations were recorded and described for bubble oscillation, migration, jetting, as well as the high-speed water spike penetrating through the opening. The results revealed that there was a critical value of the bubble-wall distance, below which the bubble was directed away from the incomplete boundary, while the bubble may tear from the middle for larger distance. As the distance varied, we studied the volume of the water that rushed through the opening, the velocity at the tip of the water spike, and the center of the bubble as well as the migration of the bubble boundary. This work reveals that the high-speed water spike caused by the bubble may be a potential threat to the structures, specifically for cases with a small opening size and short bubble-boundary distance.     

Vector NLS solitons interacting with a boundary

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.     

Director configurations in nematic droplets with tilted surface anchoring

The polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength W_s ~ 10^–6 (J m^?2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.     

A numerical study of the motion of a wave running up a beach

The main difficulty for the numerical calculation of the wave running up a beach is the treatment of its moving water boundary. In this paper a scheme of turning the free boundary problem into a fixed boundary problem is designed. The calculated run-up height is consistent with the experiments. Some interesting wave phenomena are also found.     

On the boundary value problem of elastostatics in terms of stresses

The boundary value problem of elastostatics in terms of six components of the stress consists of nine equations and three boundary conditions. In this paper, we distinguished between the possible cases and impossible cases, i.e., the problem is or is not equivalent to a boundary value problem of six equations and six boundary conditions.     

SOLVING THE FREE BOUNDARY PROBLEM IN CONTINUOUS CASTING BY USING BOUNDARY ELEMENT METHOD

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