Modeling dislocation sources and size effects at initial yield in continuum plasticity

Size effects at initial yield (prior to stage II) of idealized micron-sized specimens are modeled within a continuum model of plasticity. Two different aspects are considered: specification of a density of dislocation sources that represent the emission of dislocation dipoles, and the presence of an initial, spatially inhomogeneous excess dislocation content. Discreteness of the source distribution appears to lead to a stochastic response in stress-strain curves, with the stochasticity diminishing as the number of sources increases. Variability in stress-strain response due to variations of source distribution is also shown. These size effects at initial yield are inferred to be due to physical length scales in dislocation mobility and the discrete description of sources that induce internal-stress-related effects, and not due to length-scale effects in the mean-field strain-hardening response (as represented through a constitutive equation)

The Dynamics of Entry and Exit

The relation between profits and the number of firms in a market is one of the essential topics in the field of industrial organization. Usually, the relation is modeled in an error-correction framework where profits and/or the number of firms respond to out-of-equilibrium situations. In an out-of-equilibrium situation one or both of these variables deviate from some long-term sustainable level. These models predict that in situations of equilibrium, the number of firms does not change and hence, entry equals exit. Moreover, in equilibrium entry and exit are expected to be equal to zero. These predictions are at odds with real life observations showing that entry and exit levels are significantly positive in all markets of substantial size and that entry and exit levels often differ drastically. In this paper we develop a new model for the relation between profit levels and the number of firms by specifying not only an equation for the equilibrium level of profits in a market but also equations for the equilibrium levels of entry and exit. In our empirical application we show that our entry and exit equations satisfy the usual errorcorrection conditions. We also find that a one-time positive shock to entry or profits has a small but permanent positive effect on both the number of firms and total industry profits.

The super-oscillating superlens

We demonstrate a lens that creates a sub-wavelength focal spot beyond the near-field by exploiting the phenomenon of super-oscillation