Mathematical models for motion of the rear ends of vehicles

A new treatment of the path of the rear wheels of single and multiple axle vehicles produces simple first order differential equations for the motion of the rear wheels relative to the front wheels. We show for the first time, under the assumption of no slipping, that the path of the rear wheels depends only on the path of the front wheels and not on the vehicle speed. We examine motion along straight, circular and winding roads, giving closed form solutions in the first two cases. We also provide a straightforward algorithm for computing vehicle offtracking for any road geometry. We believe these results will be of significant benefit to road designers.     

Flag-Transitive affine planes of order at most 125

We complete the determination of all the flag-transitive affine planes of order at most 125. In particular, all such planes of order 81 are determined. We show that those with a solvable collineation group are obtained by constructions due to Kantor and Suetake.     

Gallium and oxygen accumulations on gallium nitride surfaces following argon ion milling in ultra-high vacuum conditions

Metallic gallium was observed on the surfaces of GaN commercial samples following argon ion milling. SIMS measurements confirmed that the commercial GaN had approximately 0.02% bulk oxygen present. The SIMS signal was standardized using a specimen of known oxygen content, as determined by elastic recoil detection analysis using 200 MeV heavy ions of ¹⁹⁷Au. Despite this 2–5% oxygen was observed by XPS in the bulk of the GaN after the argon ion milling. This oxygen is believed to be from the original surface oxide that re-cycles on the GaN surface during the ion milling.     

High-pressure reactions. III. Hydrolysis of polyacrylonitrile

Polyacrylonitrile prepared from γ-irradiated monomer was found to react readily with water over a pressure range of 5,130–34,200 atm. to yield polyacrylamide, while polymer prepared by conventional free-radical catalysts will not hydrolyze under the same conditions. Reaction rates at 85°C. were measured; hydrolysis was extremely rapid at higher temperatures. Results are presented to indicate the radical nature of the reaction. Addition of a free-radical source increases the amount of hydrolysis. Pressure has an effect on the properties of the resulting polyacrylamide.