Two new mathematical models to predict the flow stress at hot deformation

Based on both linear and non-linear estimations of work hardening rate versus strain curves, two mathematical models have been developed to predict the flow curves under hot working conditions up to the peak. The models were tested for a mechanically alloyed Al6063/0.75Al2O3/0.75Y2O3 nanocomposite under different hot forming conditions. The predicted results from both models are found to be in accord with the experimental flow stress curves. However, the linear model (with an average error of 0.81%) predicted the flow stress more accurate than the non-linear model (with an average error of 1.94%).Comment: Written in spring of 2012, as an independent work. 19 Pages, 13 Figures, 3 Appendice

Is the Rayleigh-Sommerfeld diffraction always an exact reference for high speed diffraction algorithms?

In several areas of optics and photonics like wave propagation, digital holography, holographic microscopy, diffraction imaging, biomedical imaging and diffractive optics, the behavior of the electromagnetic waves has to be calculated with the scalar theory of diffraction by computational methods. Many of these high speed diffraction algorithms based on a fast Fourier transformation are in principle approximations of the Rayleigh-Sommerfeld Diffraction (RSD) theory. However, to investigate their numerical accuracy, they should be compared with and verified by RSD. All numerical simulations are in principle based on a sampling of the analogue continuous field. In this article we demonstrate a novel validity condition for the well-sampling in RSD, which makes a systematic treatment of sampling in RSD possible. We show the fundamental restrictions due to this condition and the anomalies caused by its violation. We also demonstrate that the restrictions are completely removed by a sampling below the Abbe resolution limit. Furthermore, we present a very general unified approach for applying the RSD outside its validity domain by the combination of a forward and reverse calculation