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We consider the convergence properties of return algorithms for a large class of rate-independent plasticity models. Based on recent results for semismooth functions, we can analyze these algorithms in the context of semismooth Newton methods guaranteeing local superlinear convergence. This recovers results for classical models but also extends to general hardening laws, multi-yield plasticity, and to several non-associated models. The superlinear convergence is also numerically shown for a large-scale parallel simulation of Drucker-Prager elasto-plasticity.

Room-temperature and low-temperature (77 K) scanning tunneling spectroscopy (STS) and voltage-dependent scanning tunneling microscopy (STM) data are used to study the local electronic properties of the quasi-one-dimensional Si(557)-Au surface in real space. A gapped local electron density of states near theΓ point is observed at different positions of the surface, i.e., at protrusions arising from Si adatoms and step-edge atoms. Within the gap region, two distinct peaks are observed on the chain of localized protrusions attributed to Si adatoms. The energy gap widens on both types of protrusions after cooling from room temperature to T = 77 K. The temperature dependence of the local electronic properties can therefore not be attributed to a Peierls transition occurring for the step edge only. We suggest that more attention should be paid to finite-size effects on the one-dimensional segments.

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