A chaotic map with a flat segment can produce a noise-induced order

Matsumoto and Tsuda studied the effects of noise on chaos in a one-dimensional Belousov-Zhabotinsky (BZ) map and found noise-induced order, that is, an external noise destroys a chaotic behavior and produces some kind of order (periodicities). This phenomenon is very interesting in understanding the relation between chaos and natural phenomena. The present paper proposes a unimodal piecewise linear map which has a flat segment. It is shown numerically that the noise-induced order can be observed in this simple map in the same way as the BZ map. These numerical results clarify the mechanism of noise-induced order.     

Photoviscoplastic investigations of slip-line fields and principal-stress trajectories in viscoelastoplastic strip for drawing with back tension

Photoviscoplasticity is applied to the drawing with back tension through rollers and wedge-shaped dies in model tests of plane-strain state. The effects of the back tension on the slip-line fields and on the principal-stress trajectories for the strips are discussed in the light of experimental results obtained from the model tests. Actual strips are considered as viscoelastoplastic media in the actual drawing processes. The model specimens used are softened celluloid as the viscoelastoplastic medium for the strip and Araldite as the glassy elastic medium for the dies. At a suitable experimental temperature, the viscoelastoplastic strip is drawn viscoplastically through the gap between the dies mentioned above. The slip-line fields, the principal-stress trajectories in the strip and the normal pressure on the contact surface are greatly influenced by the effect of the back tension.     

Computational aspects of general minimax optimization

With an optimization problem of minimax type, we associate another problem which is, in turn, of maxmin type. We show that both the problems are equivalent in a sense and they have the same optimal value. The results obtained here are intimately related to Chebyshev (or uniform) approximation theory.     

Scattering of potassium atomic beams from various cleaved surfaces

Scattering of potassium atomic beams from cleaved surfaces of LiF, KCl and mica were studied. The observed spatial distributions follow the cosine distribution in most cases. At large incident angles the distributions from LiF and KCl deviate from the cosine and show apparent backscatterings. A simple model is proposed to interpret the backscattering in terms of macroscopic roughness of cleaved surfaces. The sticking coefficient S (t) is defined and the mass balance between the incident and outgoing atoms is examined. Mass balance holds within the limits of errors on the surfaces of LiF and KCl at temperatures above 400 K. On a mica surface deposition of potassium atoms is observed even at temperatures higher than room temperature. It is shown from the change of the sticking coefficient that the deposition does not proceed linearly in the initial period.     

Improved procedure for the reductive phenylation and cyclization of nitroarenes

The reductive phenylation of nitroarenes was improved by using iron pentacarbonyl (IPC) as a reducing reagent. The method was applied to the synthesis of ellipticine and dibenzazocine derivatives.