Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to be structurally stable with respect to small perturbations of the background charge, provided that the electric field is positive at the shock location. Second, any steady transonic shock solution with the supersonic background charge is proved to be dynamically and exponentially stable with respect to small perturbation of the initial data, provided the electric field is not too negative at the shock location. The proof of the first stability result relies on a monotonicity argument for the shock position and the downstream density, and a stability analysis for subsonic and supersonic solutions. The dynamical stability of the steady transonic shock for the Euler-Poisson equations can be transformed to the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions. The analysis for the associated linearized problem plays an essential role

The dislocation mechanism of stress corrosion embrittlement in Ti-6Al-2Sn-4Zr-6Mo

An observation of the dislocation mechanisms operating below a naturally initiated hot-salt stress corrosion crack is presented, suggesting how hydrogen may contribute to embrittlement. The observations are consistent with the hydrogen-enhanced localized plasticity mechanism. Dislocation activity has been investigated through post-mortem examination of thin foils prepared by focused ion beam milling, lifted directly from the fracture surface. The results are in agreement with the existing studies, suggesting that hydrogen enhances dislocation motion. It is found that the presence of hydrogen in (solid) solution results in dislocation motion on slip systems that would not normally be expected to be active. A rationale is presented regarding the interplay of dislocation density and the hydrogen diffusion length