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A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers$$TGV^2$$$TG{V}^2$and$$NsTGV^2$$$NsTG{V}^2$. Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by$$\Gamma $$$\Gamma$-convergence under a conditional uniform bound on the trace constant of the operators and a finite-null-space condition. Some first examples and numerical results are given.

Non-conservative dislocation climb plays a unique role in the plastic deformation and creep of crystalline materials. Nevertheless, the underlying atomic-scale mechanisms of dislocation climb have not been explored by direct experimental observations. Here, we report atomic-scale observations of grain boundary (GB) dislocation climb in nanostructured Au during in situ straining at room temperature. The climb of a edge dislocation is found to occur by stress-induced reconstruction of two neighboring atomic columns at the edge of an extra half atomic plane in the dislocation core. This is different from the conventional belief of dislocation climb by destruction or construction of a single atomic column at the dislocation core. The atomic route of the dislocation climb we proposed is demonstrated to be energetically favorable by Monte Carlo simulations. Our in situ observations also reveal GB evolution through dislocation climb at room temperature, which suggests a means of controlling microstructures and properties of nanostructured metals.

Nanograined metals have the merit of high strength, but usually suffer from low work hardening capacity and poor thermal stability, causing premature failure and limiting their practical utilities. Here we report a “nanodispersion-in-nanograins” strategy to simultaneously strengthen and stabilize nanocrystalline metals such as copper and nickel. Our strategy relies on a uniform dispersion of extremely fine sized carbon nanoparticles (2.6 ± 1.2 nm) inside nanograins. The intragranular dispersion of nanoparticles not only elevates the strength of already-strong nanograins by 35%, but also activates multiple hardening mechanisms via dislocation-nanoparticle interactions, leading to improved work hardening and large tensile ductility. In addition, these finely dispersed nanoparticles result in substantially enhanced thermal stability and electrical conductivity in metal nanocomposites. Our results demonstrate the concurrent improvement of several mutually exclusive properties in metals including strength-ductility, strength-thermal stability, and strength-electrical conductivity, and thus represent a promising route to engineering high-performance nanostructured materials.