Stability analysis on dark solitons in quasi-1D Bose-Einstein condensate with three-body interactions.

The stability properties of dark solitons in quasi-one-dimensional Bose-Einstein condensate (BEC) loaded in a Jacobian elliptic sine potential with three-body interactions are investigated theoretically. The solitons are obtained by the Newton-Conjugate Gradient method. A stationary cubic-quintic nonlinear Schrödinger equation is derived to describe the profiles of solitons via the multi-scale technique. It is found that the three-body interaction has distinct effect on the stability properties of solitons. Especially, such a nonlinear system supports the so-called dark solitons (kink or bubble), which can be excited not only in the gap, but also in the band. The bubbles are always linearly and dynamically unstable, and they cannot be excited if the three-body interaction is absent. Both stable and unstable kinks, depending on the physical parameters, can be excited in the BEC system.

Numerical Simulation and Experiment of Electrically-Assisted Incremental Forming of Thin TC4 Titanium Alloy Sheet.

In order to integrally manufacture the large TC4 titanium alloy part, an electrically-assisted incremental forming process is cleverly proposed to solve the traditional hot forming disadvantages of expensive heating furnaces and long cycle period. The two-step simulation method including thermal-electricity coupling simulation and thermo-mechanical coupling simulation was selected to predict the temperature variations and the sheet deformation behaviors. The electrically-assisted incremental forming experiment of thin TC4 titanium alloy sheet was performed. The highest prediction error is 6% for springback angles. The thrice forming at 10.9 A/mm2 satisfies the precision requirement of the designed part. Therefore, the two-step simulation method can effectively calculate the electrically-assisted incremental process. The electrically-assisted incremental forming technique is very promising for the integral producing large titanium alloy part.

Fault diagnosis method and application based on unsaturated piecewise linear stochastic resonance.

Signal detection and processing have become an important way to diagnose mechanical faults. The classical bistable stochastic resonance (CBSR) method for signal detection can become saturated, where the amplitude of the output signal gradually stabilizes at a relatively low level instead of increasing with further increases of the input signal amplitude. This leads to difficulty in extracting the weak signals from strong background noise. We studied a new mechanism based on unsaturated piecewise linear stochastic resonance (PLSR). The piecewise linear potential model has a unique structure, which can independently adjust the barrier height and potential wall inclination, so the piecewise linear potential model has a rich potential structure. The rich potential structure makes the potential model unsaturated, thus ensuring that the output signals increase as the input signals increase. In addition, according to the piecewise linear model, the output signal-to-noise ratio (SNR) of the system is deducted. Analysis of the influence of signal strength, potential parameters, and angular frequency on the SNR shows that the optimal SNR can be obtained by adjusting the potential parameters. We propose a weak signal detection method for bearing fault diagnosis. This method can effectively extract the weak fault signals from rolling bearings in a strong noise background. The simulated and experimental bearing fault signals verify that the proposed PLSR method is superior to the CBSR method.