Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges

We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the perturbation is away from the wedge edge in the previous results is removed. One of the key ingredients is to identify a "good" direction of the boundary operator of a boundary condition of the shock along the wedge edge, based on the non-obliqueness of the boundary condition for the weak shock on the edge. With the identification of this direction, an additional boundary condition on the wedge edge can be assigned to make sure that the shock is attached on the edge and linearly stable under small perturbation. Based on the linear stability, we introduce an iteration scheme and prove that there exists a unique fixed point of the iteration scheme, which leads to the global existence and nonlinear structural stability of the attached weak transonic shock. This approach is based on neither the hodograph transformation nor the spectrum analysis, and should be useful for other problems with similar difficulties.Comment: 28 Pages; 2 figure

A novel explanation of charmonium-like structure in e+e−→ψ(2S)π+π−e^+e^-\to \psi(2S)\pi^+\pi^-

We first present a non-resonant description to charmonium-like structure $Y(4360)$ in the $\psi(2S)\pi^+\pi^-$ invariant mass spectrum of the $e^+e^-\to \psi(2S)\pi^+\pi^-$ process. The $Y(4360)$ structure is depicted well by the interference effect of the production amplitudes of $e^{+} e^{-} \to \psi(2S) \pi^+ \pi^-$ via the intermediate charmonia $\psi(4160)/\psi(4415)$ and direct $e^+e^-$ annihilation into $\psi(2S)\pi^+ \pi^-$. This fact shows that $Y(4360)$ is not a genuine resonance, which naturally explains why $Y(4360)$ was only reported in its hidden-charm decay channel $\psi(2S)\pi^+\pi^-$ and was not observed in the exclusive open-charm decay channel or $R$-value scan.Comment: 4 pages, 1 table, 2 figures. Accepted for publication in Phys. Rev.

High cycle fatigue and ratcheting interaction of laser powder bed fusion stainless steel 316L:Fracture behaviour and stress-based modelling

Variations in the physical and mechanical properties of parts made by laser power bed fusion (L-PBF) could be affected by the choice of processing or post-processing strategies. This work examined the influence of build orientation and post-processing treatments (annealing or hot isostatic pressing) on the fatigue and fracture behaviours of L-PBF stainless steel 316L in the high cycle fatigue region, i.e. 104 – 106 cycles. Experimental results show that both factors introduce significant changes in the plastic deformation properties, which affect fatigue strength via the mechanism of fatigue-ratcheting interaction. Cyclic plasticity is characterised by hardening, which promotes mean stress insensitivity and improved fatigue resistance. Fatigue activities, involving the initiation of crack at defects and microstructural heterogeneities, are of greater relevance to the longer life region where the global deformation mode is elastic. As the simultaneous actions of ratcheting and fatigue generate complex nonlinear interactions between the alternating stress amplitude and mean stress, the fatigue properties could not be effectively predicted using traditional stress-based models. A modification to the Goodman relation was proposed to account for the added effects of cyclic plasticity and was demonstrated to produce good agreement with experimental results for both cyclic hardening and softening materials.EDB (Economic Devt. Board, S’pore)Accepted versio